i
Delft University of Technology
FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING
Department Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl
This report consists of 126 pages including 8 appendices. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology and the author. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning the contents of the advice.
Specialization: Transport Engineering and Logistics Report number: 2016.TEL.7992
Title: Vessel routing for sweeping of marine litter in a port area Author: M.C.M. van Tol
Title (in Dutch) Routing van schepen voor het verwijderen van zee afval in een haven gebied
Assignment: Master thesis Confidential: no
Supervisor: ir. M.B. Duinkerken Date: January 22, 2016
N
OMENCL ATURE
L
IST OF ACRONYMS
Acronym
B&B Branch and Bound
DFJ Dantzig-Fulkerson-Johnson
FR Fixed Routes
IRP Inventory Routing Problem
LP Litter Periods
MI(L)P Mixed Integer (Linear) Program
MLP Marine Litter Prediction
MLS Marine Litter Sweeping
MTZ Miller-Tucker-Zemlin
OD On Demand
SP Stochastic Programming
TC/R Transport Cost / Removed
TSP Travelling Salesman Problem
VMI Vendor Managed Inventory
VRP Vehicle Routing Problem
C
ONVENTIONS
• A decimal separator is denoted with a point (.)
• A thousands separator is denoted with a comma (,)
L
IST OF SYMBOLS
Symbol
ati auxiliary variable for node i at period t [-]
bi entrance width of port compartment i [km]
ci j distance associated with traversing edge (i , j ) [km]
C distance matrix [-]
d number of scenarios [-]
Dt supply of marine litter via main waterway during period t [kg/day]
e average sweeping rate of vessel [kg/h]
Eit contribution of land based component for port compartment i during period t [kg/day]
E set of edges [-]
f fraction of marine litter present in main waterway that flows into all port compartments [-] fi fraction of marine litter present in main waterway that flows into port compartment i [-]
g number of vessels [-]
G graph [-]
h length planning horizon [days]
mit amount of marine litter of node i at end of period t [kg]
mi0 initial amount of marine litter of node i [kg]
mt hr es,imarine litter threshold of node i [kg]
n number of nodes [-]
N set of nodes [-]
pc penalty cost [(/kg]
ps probability of scenario s [-]
pt travel cost per distance unit [(/km]
q vessel capacity [kg]
r influence of order of entrances of port compartments along main waterway [-]
S set of scenarios [-]
tsi m current simulation time [days]
T set of periods [-]
uikt auxiliary variable for node i and vessel k at period t [-]
u vector containing variables uikt [-]
v average vessel speed [km/h]
V set of vessels [-]
w available time per period per vessel [h]
xikt (s) amount of marine litter removed at node i by vessel k in period t [kg] X theoretical upper bound amount of marine litter removed by one vessel in one period [kg] yi jkt edge (i , j ) is traversed or not by vessel k in period t [-]
y vector containing variables yi jkt [-]
Y sum of accumulation of marine litter during a period of two weeks [kg]
zkti node i is visited or not by vessel k in day t [-]
z vector containing variables zkti [-]
α scale parameter Weibull distribution [-]
β shape parameter Weibull distribution [-]
δ marine litter in system end of day 120 minus marine litter in system beginning day 21 [kg]
σ standard deviation [-]
ξt
i marine litter accumulation during period t of node i [kg]
C
ONTENTS
Nomenclature v Abstract ix 1 Introduction 1 1.1 Marine litter. . . 1 1.2 Problem statement . . . 2 1.3 Objective of research . . . 3 1.4 Research structure . . . 3 2 Problem analysis 5 2.1 Plastics in marine litter . . . 52.2 Quantitative studies. . . 6
2.2.1 Marine litter in rivers. . . 6
2.2.2 Marine litter in Port of Rotterdam . . . 7
2.3 Spatial distribution of marine litter . . . 8
2.3.1 Guanabara Bay. . . 8
2.3.2 Belgium ports . . . 9
2.4 Sweeping of marine litter . . . 10
2.4.1 Passive . . . 10 2.4.2 Active . . . 11 2.4.3 Comparison . . . 13 2.4.4 Proposed approach . . . 13 2.5 Summary . . . 14 3 Literature overview 15 3.1 Inventory Routing Problem . . . 15
3.1.1 Problem description . . . 15
3.1.2 Background . . . 17
3.1.3 Basic example . . . 17
3.1.4 Routing methods related to IRP . . . 19
3.1.5 Classification . . . 20
3.1.6 Static and dynamic IRP . . . 22
3.1.7 Solution approaches and policies . . . 23
3.2 Solution approaches stochastic IRP . . . 25
3.2.1 Two-stage stochastic programming problems . . . 26
3.2.2 Multi-stage stochastic programming problems . . . 28
3.3 Summary . . . 29
4 Modelling 31 4.1 Marine litter prediction model . . . 31
4.1.1 Location . . . 31
4.1.2 Accumulation rate . . . 32
4.2 Marine litter sweeping model . . . 33
4.2.1 Main assumptions . . . 34
4.2.2 Introduction to mathematical formulation. . . 35
4.2.3 Deterministic MLS model . . . 35
4.2.4 Stochastic MLS model . . . 40
4.3 Simulation models . . . 44
4.4 Summary . . . 46
5 Case study: Port of Rotterdam 47 5.1 Graph representation of a port . . . 47
5.1.1 Nodes . . . 47
5.1.2 Edges . . . 48
5.2 Vessel parameters . . . 49
5.2.1 Theoretical upper bound . . . 50
5.3 Fixed routes . . . 50
5.4 Sources of stochasticity . . . 51
5.4.1 Distribution of marine litter . . . 51
5.4.2 Supply of marine litter . . . 51
5.5 Scenario generation. . . 52 5.6 Summary . . . 53 6 Experiments 55 6.1 Experimental plan . . . 55 6.2 Verification . . . 56 6.2.1 MLP model . . . 56 6.2.2 MLS model. . . 56 6.2.3 OD policy . . . 63 6.2.4 FR policy . . . 64 6.3 Computational time . . . 65 6.4 Deterministic MLS model . . . 67
6.4.1 Experiment: length planning horizon . . . 67
6.4.2 Experiment: weight factors in objective function . . . 70
6.4.3 Experiment: comparing sweeping policies . . . 72
6.4.4 Experiment: marine litter thresholds. . . 76
6.5 Comparison deterministic and stochastic MLS model . . . 79
7 Conclusions and future research 81 7.1 Conclusions. . . 81
7.1.1 Conclusions for port authorities . . . 81
7.1.2 Conclusions for researchers . . . 82
7.2 Future research . . . 84 Bibliography 85 Appendix A 91 Appendix B 101 Appendix C 105 Appendix D 107 Appendix E 109 Appendix F 111 Appendix G 113 Appendix H 115
A
BSTRACT
Marine litter (also known as marine debris) is any persistent, manufactured or processed solid material that is discarded, disposed of or abandoned in the marine and coastal environment [UNEP, 2005] (page 3). It is estimated that between 6.4 million to 7 billion tonnes of litter enters the oceans each year [Cheshire and Adler, 2009] (page 6). In literature it is widely accepted that 80% of the marine debris originates from land based sources [GESAMP, 1991] (page 146), [Faris and Hart, 1994], [UNEP, 2006] (page iv), [Andrady, 2011].Since seaports usually are strategically situated with an inland waterway connection, it is not surprising that seaports have to deal with marine litter. Besides the negative environmental impact, marine litter also poses risks to vessels in port areas. The objectives of port authorities with respect to marine litter, the condi-tion of marine litter in a port area and the availability of cleaning vessels determine which sweeping policy is suitable to fulfil these objectives.
Concerning the condition of marine litter in a port area two extremes can be distinguished. For these ex-tremes simple sweeping policies are sufficient. One extreme is the condition wherein marine litter is present everywhere in very large amounts. The other extreme is the condition wherein marine litter is not a day-to-day problem and sweeping of marine litter one day-to-day in the year, for example, is fulfilling needs. This research considers the condition of marine litter in-between these two extremes, the number of cleaning vessels is a limitation and the objective of sweeping marine litter is to avert excessive amounts of marine litter and accompanying complaints. In this way the risk posed to vessels and the negative environmental impact is re-duced. Nowadays, these vessels are usually only deployed after complaints on excessive amounts of marine litter.
The less time is spent on travelling, the more time remains for sweeping of marine litter and thus the less sweeping capacity is required for removing a same amount of marine litter. Because the number of cleaning vessels is considered a limitation, minimization of the distance travelled is demanded. For minimization of the distance travelled, the distribution of the marine litter over the water surface is of importance. Many factors can influence the spatial distribution of marine litter, like wind and tides. Research considering the spatial distribution of marine litter has in common that accumulation sites (or hot spots) are present. At these sites, the marine litter tends to accumulate. If a prediction model for the location and accumulation of marine litter in a port area is developed, this could be used as input for averting excessive amounts of marine litter while minimizing the distance travelled. The problem that remains is how to use the output of a prediction model. Given that the locations of marine litter are dispersed, a cleaning vessel must address multiple locations over a certain time span. To avert excessive amounts of marine litter at these locations while minimizing the distance travelled, a routing method may be used. The objective of this research is to develop a routing method to avert excessive amounts of marine litter (and accompanying complaints) while minimizing the distance travelled, given a number of vessels. This routing method makes use of input from a prediction model considering the location and accumulation of marine litter.
Based on related literature, a model is proposed for a basic prediction of the location and accumulation of marine litter in a port area is developed. This model assumes that accumulation sites (or hot spots) are present in a port area and that these are situated in the port compartments. The accumulation of marine litter is modelled as a fraction of the marine litter present in the main waterway that flows into a port compartment. The fraction that flows into a port compartment is dependent on various factors, like entrance width of the port compartment, mutual location of the port compartment along the main waterway and wind direction.
The location and future litter accumulation of marine litter is taken into account in the routing method by considering an Inventory Routing Problem (IRP). The IRP is a combinatorial optimization problem, which considers the repeated distribution of goods between a central facility and a set of geographically dispersed customers over a certain planning horizon. The objective of the IRP is to derive a distribution policy with minimal total cost over the planning horizon without causing stock-outs or reaching maximum inventory level at the customers. In this research the IRP is considered as a collection problem. In a collection problem goods are produced at the customers. To prevent reaching maximum inventory level goods are collected at
the customers and brought to the central facility. In this research a cleaning vessel must address multiple locations over a certain time span. Above that, due to the continuous supply of marine litter by rivers, the amount of litter accumulates at the hot spots over time. The analogy between the problem considered in this research and the IRP holds that the hot spots of marine litter can be seen as geographically dispersed customers with an inventory of marine litter that increases over time. The consideration of the IRP as a collection problem corresponds to the situation wherein marine litter is collected by means of a cleaning vessel and brought to a central facility. The limited storage capacity at the customers is represented by setting a boundary value for the amount of marine litter per hot spot. In the end, the IRP is able to take into account a routing aspect and the accumulation of marine litter together for deploying cleaning vessels along the hot spots in the port area. The routing method (called MLS) is formulated in the form of a mixed integer linear program.
To avert excessive amounts of marine litter at nodes, marine litter should be removed timely at these locations. To determine which amounts of marine litter are excessive, a marine litter threshold is set per hot spot in the routing method. The situation wherein the amount of marine litter at a hot spot is below this threshold is considered acceptable, while it is considered undesirable if the amount of marine litter at a hot spot is above this threshold. It is assumed that if a threshold is exceeded, a complaint is received. If the marine litter threshold is exceeded, also the degree of this exceedance is of importance. The higher the exceedance, the higher the urgency to remove marine litter at this location.
In reality the input from the prediction model contains uncertainty. A way to take into account a stochas-tic input from a prediction model with respect to the accumulation of marine litter, is by means of stochasstochas-tic programming. The stochastic variant of the routing method is obtained by formulating a two-stage stochas-tic linear program. Contrary to the determinisstochas-tic variant, the stochasstochas-tic variant is able to take into account multiple scenarios with each a certain probability with respect to the accumulation of marine litter. In an experiment it is shown that the stochastic approach on average leads to better results compared to a deter-ministic approach. Above that, it is shown that the less uncertainty is present in the information considering the accumulation of marine litter, the better the retrieved results are.
To benchmark the performance of the MLS policy in the long-term, simulations are performed. Herein the performance of the MLS policy is compared with the performance of two other sweeping polices. The on demand (OD) policy is based on reacting to complaints on excessive amounts of marine litter. In a com-bination of a first-come-first-serve and nearest neighbour strategy, the complaints are remedied. The fixed routes (FR) policy makes use of predetermined fixed routes to remove marine litter. So like the developed routing method, the FR policy proactively sweeps marine litter. The predetermined fixed routes are based on clustering. To each cluster of hot spots one vessel is assigned. For each cluster a shortest Travelling Salesman Problem (TSP) route is determined and the corresponding vessel travels that route every day.
In a case study simulations based on the MLS, OD and FR policy are applied. Hereby it is assumed that the prediction of marine litter accumulation for the MLS model is equal to the realization. In the case study mul-tiple replication runs are performed to statistically underpin the benchmark. For each policy the minimum number of vessels for feasible (i.e. able to maintain the remaining amount of marine litter in the system stable) operation is determined. Subsequently the results for the minimum number of vessels for feasible operation are compared.
In the case study it appeared that both the MLS and FR policy succeed similarly in preventing complaints on excessive amounts of marine litter. On average the number of complaints reduced by around 40% with respect to the OD policy. However, if the urgency of the complaints is considered, it is shown that while ap-plying the MLS policy on average the urgency of the complaints is around 65% lower in comparison with the FR policy. Above that, on average the distance travelled is over 55% smaller for the MLS policy compared to the FR policy. This means that with less cost on cleaning vessels the same amount of marine litter is removed. In perspective of the objective of this research (developing a routing method to avert excessive amounts of marine litter while minimizing the distance travelled), this benchmark shows that qualitative good predic-tions for the location and accumulation of marine litter is of added value for sweeping of marine litter in a port area.
1
I
NTRODUCTION
1.1.
M
ARINE LITTER
Marine litter (also known as marine debris) is any persistent, manufactured or processed solid material that is discarded, disposed of or abandoned in the marine and coastal environment [UNEP, 2005] (page 3). This human-created waste is deliberately (e.g. illegal dumping) or accidentally (e.g. loss of cargo) released in the marine environment. It is estimated that between 6.4 million to 7 billion tonnes of litter enters the oceans each year [Cheshire and Adler, 2009] (page 6). Despite the fact that these numbers diverge widely, the sig-nificance of the problem of marine litter is clear. Currently marine litter is observed across all oceans in the world [Cheshire and Adler, 2009] (page iii).
Marine litter includes a wide range of materials, but plastics account by far for the most predominant share [Derraik, 2002], [Sheavly and Register, 2007], [Barnes et al., 2009]. Gregory and Ryan [1997] (page 63) states that plastics account for 60 to 80% of the total marine litter. Plastics are used world wide for many applications and in large amounts. The annual global demand for plastics has consistently increased over the recent years to around 245 million tonnes in 2011, of which nearly a third is converted into consumer packaging material [Andrady, 2011]. Derraik [2002] states that since plastics are lightweight, strong, durable and cheap, plastics are suitable for a very wide range of products. At the same time these are the reasons why plastics are a serious hazard to the environment. Plastic litter forms a serious environmental threat to marine animals. They are affected in various ways by plastic litter, such as entanglement, ingestion or the introduction of invasive species attached to the plastic litter [Derraik, 2002]. In the Netherlands, over 7.3 million euros is spent each year to clean up marine litter from waterways throughout the country [van Paassen, 2010]. Besides these community charges, marine litter also imposes cost to sectors like fishery, shipping and tourism [Mouat et al., 2010] (page iii).
According to Van der Wal et al. [2013] (page 5) a minor fraction of the plastic litter in rivers floats on the water surface, a major fraction is transported in suspension (often with a foil like appearance) and a small fraction is transported as part of the river bed. The latter is propagated at much lower speeds compared to the other two fractions. The fraction at the water surface is the most directly visible, but is certainly not rep-resentative for the amount of plastic litter present in rivers. Due to the fouling of algae, plastic litter increases in weight and may therefore descend to a lower fraction over time.
Marine litter can be classified into two sources: land based and marine based. Land based litter originates from terrestrial sources (e.g. street litter that is washed into a nearby waterway or sewer overflow) and marine based litter originates from marine activity (like container vessels, cruise ships and offshore platforms). Via waterways the land based marine litter is conveyed to one of the oceans. In literature it is widely accepted that 80% of the marine debris originates from land based sources [GESAMP, 1991] (page 146), [Faris and Hart, 1994], [UNEP, 2006] (page iv), [Andrady, 2011].
1.2.
P
ROBLEM STATEMENT
Since seaports usually are strategically situated with an inland waterway connection, it is not surprising that seaports have to deal with marine litter. Examples of marine litter in the port of Rotterdam are shown in Figure 1.1. The industry present upstream at the inland waterway may increase the amount of marine litter in port areas. Besides the negative environmental impact, marine litter also poses risks to vessels in port ar-eas. According to Mouat et al. [2010] (page 56) incidents with marine litter are reported wherein propellers, anchors and rudders were fouled or intake pipes and valves were blocked. In an interview with a company involved in cleaning operations in the Netherlands, it was indicated that besides marine litter also wood (ranging from large branches to trunks, see right of Figure 1.1) and seaweed are present in the port of Rot-terdam. Wood originates from natural areas situated upstream the inland waterway connection. Seaweed is for example flushed into the seaport by tidal currents. Despite these natural products do not directly pose an environmental risk, they do pose a risk to vessels in a port area. Wood could for example damage the hull of a vessel and seaweed could for example block intake pipes. Since the amount of seaweed is strongly dependent on water temperature, seaweed is only removed in port areas during the summer season. In the summer season, seaweed could form layers at the water surface of up to one meter thickness. In view of the port authorities, wood and seaweed are also regarded as marine litter (contrary to its formal definition).
Figure 1.1: Examples of litter in port of Rotterdam
The objectives of port authorities with respect to marine litter, the condition of marine litter in a port area and the availability of cleaning vessels determine which sweeping policy is suitable to fulfil these objectives. Concerning the condition of marine litter in a port area two extremes can be distinguished. For these ex-tremes simple sweeping policies are sufficient. One extreme is the condition wherein marine litter is present everywhere in very large amounts. If in this case the objective is to maximize the removal of marine litter, one could start with deploying as much cleaning vessels as possible and to sweep marine litter at the nearest location from a central point. The other extreme is the condition wherein marine litter is not a day-to-day problem and sweeping of marine litter one day in the year, for example, is fulfilling needs. In this case no large absolute differences in performance can be achieved by applying different sweeping policies. This research considers the condition of marine litter in-between these two extremes, whereby the number of cleaning ves-sels is limited and the objective of sweeping marine litter is to avert excessive amounts of marine litter and accompanying complaints. In this way the risk posed to vessels and the negative environmental impact is re-duced. Nowadays, these vessels are usually only deployed after complaints on excessive amounts of marine litter.
The less time is spent on travelling, the more time remains for sweeping of marine litter and thus the less sweeping capacity is required for removing a same amount of marine litter. Because the number of clean-ing vessels is considered limited, minimization of the distance travelled is demanded. For minimization of the distance travelled, the distribution of the marine litter over the water surface is of importance. Vari-ous research is performed with respect to the spatial distribution of marine litter, e.g. [Hinojosa et al., 2011], [Browne et al., 2010] and [Dameron et al., 2007]. According to Browne et al. [2010], many factors can influence the spatial distribution of marine litter. Factors are mentioned like wind, wave-action, tides and plastic size, shape and density. Research considering the spatial distribution of marine litter has in common that
accu-1.3.OBJECTIVE OF RESEARCH 3
mulation sites (or hot spots) are present. At these sites, the marine litter tends to accumulate. Most researches mentioned focuses on the distribution of marine litter on sea level. If a prediction model for the location and accumulation of marine litter in a port area is developed, this could be used as input for sweeping of marine litter. This prediction model could make use of, for example, meteorological data and tides forecasts. Addi-tionally, for instance drones could perform visual inspection, buoys with sensors sensors could measure the concentration of marine litter and historic records could provide information considering removal requests. Above that, during operation of a cleaning vessel data could be recorded with respect to the amount and loca-tion of litter removal. The problem that remains is how to use the output of a predicloca-tion model. Given that the locations of marine litter are dispersed, a cleaning vessel must address multiple locations over a certain time span. To avert excessive amounts of marine litter at these locations while minimizing the distance travelled, a routing method may be used. This routing method deploys the vessel along geographically dispersed hot spots in a port area while making use of information with respect to the spatial distribution of marine litter.
1.3.
O
BJECTIVE OF RESEARCH
As indicated in Section 1.1 many seaports have to deal with marine litter. Port authorities would like to avert excessive amounts of marine litter and accompanying complaints with a limited number of cleaning vessels. In this way the risk posed to vessels and the negative environmental impact is reduced. The objective of this research is to develop a routing method to avert excessive amounts of marine litter (and accompanying complaints) while minimizing the distance travelled, given a number of vessels. This routing method makes use of input from a prediction model. This prediction model provides, for example, information considering the location and accumulation of marine litter in a port area. The main research question is stated as follows:
What are the advantages and disadvantages of applying a cost-minimizing routing method to a port area in order to sweep marine litter by means of cleaning vessels?
The following sub research questions are formulated:
• What is marine litter?
• In which way can the location and accumulation of marine litter in a port area be modelled?
• In which way can the routing method to avert excessive amounts of marine litter while minimizing the distance travelled be modelled?
• In which manner can a prediction of the location and accumulation of marine litter be taken into ac-count for the routing method?
• In which manner can the performance of the routing method be benchmarked?
• What is the potential gain of the routing method?
• What is the added value of taking into account a prediction of the location and accumulation of marine litter into the routing method?
• Which recommendations can be formulated for port authorities with respect to sweeping marine litter?
1.4.
R
ESEARCH STRUCTURE
In Figure 1.2 an outline of the research is given. This scheme indicates the relations between the chapters and the order in which the chapters can be read. It is recommended to read the chapters in the order as proposed in this report. The research outline is used to elucidate the structure of this research.
After the introduction a problem analysis considering marine litter is performed in Chapter 2. In this chapter studies with respect to the composition, quantities or spatial distribution of marine litter and sweep-ing principles are discussed. In Chapter 3 a literature review is performed. This literature review concentrates on routing methods that could take into account a prediction considering the location and accumulation of marine litter and their solution approaches. In Chapter 4 a modelling phase is conducted. In this chapter various models are proposed. Firstly a prediction model for the location and accumulation of marine litter in a port area is developed. Secondly, an integer programming model is developed to represent the routing method. Based on the input from the prediction model, this integer programming model is used to determine when and how sweeping operations have to be performed. In Chapter 5 a case study is developed for the port
of Rotterdam. In other words, substance is given to the parameters required by the developed models. These parameters are applied in Chapter 6.
In Chapter 6 various experiments are performed. Firstly, the implementation of the routing method is verified. Subsequently, simulations are performed. The main objective of these simulations is to benchmark the performance of the routing method in the long-term. Hereby the performance is compared with the per-formance of two other sweeping polices. Finally, in Chapter 7 conclusions and recommendations for future research are formulated.
2
P
ROBLEM ANALYSIS
In this chapter a problem analysis is performed. Herein, various aspects of the research with respect to ma-rine litter, as introduced in Chapter 1, are treated. First of all, in Section 1.1 it is mentioned that mama-rine litter includes a wide range of materials, but plastics account by far for the most predominant share. In Section 2.1 plastics present in marine litter are discussed. In Section 1.1 it is also mentioned that the majority of marine litter is land based and conveyed via waterways to one of the oceans. In Section 2.2 various quantitative stud-ies from literature are discussed with respect to marine litter in rivers. In addition, findings on the presence of marine litter in the port of Rotterdam are presented. In the problem statement (Section 1.2) it is mentioned that if a prediction model for the location and accumulation of marine litter in a port area is developed, this could be used as input for averting excessive amounts of marine litter while minimizing the distance trav-elled. In Section 2.3 various studies related to the spatial distribution of marine litter are discussed. Lastly, different methods for sweeping of marine litter and their corresponding equipment are treated in Section 2.4.
2.1.
P
LASTICS IN MARINE LITTER
The term plastics refers to a group of synthetic polymers, like polyethylene (PE), polypropylene (PP) and polystyrene (PS). Plastics are considered persistent since they degrade very slowly. The entire degradation process of plastics, which is started with photodegradation and is concluded with the biodegradation by microorganisms, could take 50 years or more for completion [Webb et al., 2012]. Van der Wal et al. [2013] states that probably a major part of microplastics derive from the degradation of larger plastic items, like photodegradation and mechanical weathering.
Plastic litter is present in the marine environment in a range of shapes and sizes. From tiny fragments, micrometres in length, to larger items, including hulls of boats and fishing nets of a few meters long [Browne et al., 2010]. Plastic litter can be divided in two categories. Van der Wal et al. [2013] states that according to the international guidelines, plastic litter can be classified as macroplastis (particles larger than 5 milimetres) or microplastics (particles smaller than 5 mm). Subcategories of macroplastics are fine particles and coarse particles. If the size of a macroplastic particle is larger than 25 millimetre it is considered coarse, else it is considered fine. A key concern of microplastics is that they can be ingested by a much wider range of organ-isms (and thus enter the food chain) compared to larger items of debris [Barnes et al., 2009]. Microplastics are extremely difficult to remove from the marine environment [Mouat et al., 2010] (page 12). Therefore, it is not likely that sweeping of marine litter will directly contribute to reduce the amount of microplastics in the marine environment.
Figure 2.1: Various sizes of marine litter [Kroes et al., 2014]
2.2.
Q
UANTITATIVE STUDIES
2.2.1.
M
ARINE LITTER IN RIVERSAs indicated in Section 1.1, the majority of marine litter is land based and conveyed via waterways to one of the oceans. According to Rech et al. [2014] there are very few studies that provide quantitative data about the amounts and types of litter in rivers. A number of quantitative studies considering marine litter in rivers is listed in Table 2.1. Globally, a few sampling methods can be distinguished that are applied in these studies. The first method is sampling of river water. This method makes use of (fyke) nets or sieve grids to intercept marine litter from the river water. The second method is riverside sampling. This entails collecting litter items at the riverside. Besides own field measurements, the data of riverside sampling could originate from several other sources, like clean-up actions or removal by water management organisations. The third method is sampling of sediment. Herein bulk material is removed from the riverbed or riverbank. For classification of items found during sampling sometimes use is made of a classification method provided by the United Nations Environment Programme [Cheshire and Adler, 2009]. Two of the studies listed in Table 2.1 will be discussed in more detail in Section 2.2.1 (SK International [2013]) and 2.2.1 (Tweehuysen [2012]) because these are closely related to the case study (port of Rotterdam) considered in this research.
Table 2.1: Quantitative studies considering marine litter in rivers
Reference River(s) in Sampling method
Williams and Simmons [1997] United Kingdom Riverside van Paassen [2010] Netherlands Riverside Moore et al. [2011] United States River water
Claessens et al. [2011] Belgium Sediment
Tweehuysen [2012] Netherlands River water SK International [2013] Netherlands River water
Rech et al. [2014] Chile Riverside
Morritt et al. [2014] United Kingdom River water
Klein et al. [2015] Germany Sediment
SK INTERNATIONAL
In a partnership between SK International, Royal HaskoningDHV and ISI (Investments in Sustainable Inno-vations), field measurements are performed in the river Meuse. Hereto the vessel shown in Figure 2.2 is used. This vessel is equipped with a four meter long sieve ladder. By lowering the sieve, debris is intercepted from the river water. Various measurements are performed at multiple locations with each a duration of one hour. From the results of these measurements it appeared that 98% of all the debris was present in the most upper meter of the water column, whereby the majority of the debris appeared in the upper halve meter of the water column [SK International, 2013] (page 21).
2.2.QUANTITATIVE STUDIES 7
MOSAPURA
In the MosaPura project (Tweehuysen [2012]) field measurements are performed in the river Meuse. Hereto use is made of the so called WFW sampler and is shown in Figure 2.3. During operation the device is attached to the side of a vessel. The device consists of two floats and two sieves. One sieve is used to intercept debris that floats on the water surface and the other sieve filters the water up to a depth of 70 cm.
Figure 2.3: WFW sampler [Tweehuysen, 2012]
According to Van der Wal et al. [2013] no complete data sets are available on the presence of litter in port areas in the Netherlands and Belgium. To perform an estimation of the contribution of four main rivers in the Netherlands to the amount of litter in the North Sea, the results retrieved in the MosaPura project are extrapolated by Van der Wal. The results are listed in Table 2.2. This table indicates that the contribution of fine plastics to marine litter in the North Sea is larger than the contribution of coarse plastics. Moore et al. [2011] performed measurements on two rivers in California and also found that the quantity of fine macroplastics is far more abundant than coarse macroplastics.
Table 2.2: Estimations for macroplastic yearly discharge into the North Sea, adapted from Van der Wal et al. [2013] (page 12)
River Average water discharge [m3/y] Fine [m3/y] Coarse [m3/y]
Rhine 75 ·1012 500 - 5,000 50 - 500
Meuse 10 ·1012 100 - 1,000 10 - 100
Scheldt 5 ·1012 60 - 600 10 - 100
Ems 2.5 ·1012 50 - 500 5 - 50
Other rivers towards North Sea 235 ·1012 6,900 - 13,290 250 - 925
All rivers towards North Sea 350 ·1012 14,000 1,000
2.2.2.
M
ARINE LITTER INP
ORT OFR
OTTERDAMAs shown in Figure 1.1, the port of Rotterdam also faces marine litter. HEBO, a maritime service provider, is involved in cleaning operations in the port of Rotterdam. Hereto cleaning vessels are used. HEBO made quantitative information available considering cleaning operations of marine litter in the port of Rotterdam. For every cleaning operation the amount, location and date is registered. No information is registered con-sidering the exact composition of the marine litter, however it does correspond to marine litter in its informal definition (including wood and seaweed) as defined in Section 1.2. Since the location is not registered in enough detail, no further analysis is performed considering the location. The sample size comprises of 52 cleaning operations for a period of more than half a year. The main numbers are listed in Table 2.3. If the ma-rine litter removed is extrapolated to a period of 1 year, around 105 tons of mama-rine litter would be retrieved per annum.
Table 2.3: Statistics considering cleaning operations in port of Rotterdam
Period [days] 208
If the statistics considering cleaning operations in the port of Rotterdam are reviewed, it can be concluded that the port of Rotterdam has to deal with substantial amounts of marine litter. This makes the port of Rot-terdam a suitable candidate for a case study. The river Rhine and Meuse discharge via the port of RotRot-terdam into the North Sea. From the results presented by Van der Wal et al. [2013], it can be seen that the discharge of these rivers is associated with substantial amounts. It is therefore likely that marine litter in the port of Rot-terdam mainly originates from land based sources (upstream) the river Rhine and Meuse. In the presented research performed by SK International it appeared that 98% of all the debris was present in the most upper meter of the water column, whereby the majority of the debris appeared in the upper halve meter of the wa-ter column. Therefore, marine litwa-ter can effectively removed in the port of Rotwa-terdam by cleaning vessels that only filter the upper layer of the water column.
2.3.
S
PATIAL DISTRIBUTION OF MARINE LITTER
Research considering the spatial distribution of marine litter has in common that hot spots are present. At these sites, the marine litter tends to accumulate. In literature various research can be found on numerical modelling of the accumulation and movement patterns of marine litter on sea level, e.g. Potemra [2012], Lebreton and Borrero [2013] and Dameron et al. [2007]. To knowledge of the author, no model is available in literature for the spatial distribution of marine litter on port level. However, some of the research available available comes close to this application and is discussed in Section 2.3.1 and Section 2.3.2.
2.3.1.
G
UANABARAB
AYRio de Janeiro (Brazil) will be the host city of the 2016 Summer Olympics and Paralympics. On the eastern shore of Rio de Janeiro an oceanic bay is situated that covers an area of nearly 400 square kilometres (Gua-nabara Bay). In this bay the sailing and wind-surfing events will take place. A large problem is that the bay suffers from marine litter. The marine litter is mainly originating from the rivers that discharge into the bay. To improve water quality the local authorities are deploying cleaning vessels to remove marine litter from the water. However, the number of cleaning vessels is limited and the bay covers a very large area.
A Dutch technological knowledge institute developed a hydrodynamic prediction model for the Guan-abara Bay [Deltares, 2015a]. The objective of the prediction model is to support operations of cleaning ves-sels in the bay. By collecting and processing input data this model provides a 4-day forecast of the amounts, location, speed and direction of the floating debris in the bay (see for example Figure 2.4). The prediction model takes into account the discharge of 18 rivers into the bay. Part of the input for the model are meteoro-logical data and ocean current forecasts. It is stated that a horizontal resolution of 50 metres can be obtained with the model. Currently the cleaning vessels are operating without funded support, for example relying on practical experience. However, based on the output of the prediction model the cleaning vessels can focus operations to areas of the bay where the concentrations of marine litter are high. Recalling that the bay covers a very large area, the prediction model could provide useful input to improve operational efficiency.
2.3.SPATIAL DISTRIBUTION OF MARINE LITTER 9
2.3.2.
B
ELGIUM PORTSClaessens et al. [2011] performed a research to investigate the occurrence and distribution of microplastics. Measurements of the concentration of microplastics in the marine sediments of three coastal sea ports in Belgium are performed. An overview of the sample locations in the three ports is given in Figure 2.5. From these measurements it appeared that partially enclosed port areas (i.e. port compartments) exhibit the high-est abundance of microplastics. Claessens et al. [2011] states that could be partially related to the geometry of the port compartments. This will be explained in more detail.
Figure 2.5: Overview of sample locations in three port areas, adapted from Claessens et al. [2011]
The water quality of a port is dependent on the water movement. The water movement is dependent on various factors, such as geometric factors like port shape [Jiang and Falconer, 1983], entrance geometry [Yin et al., 2000] and internal structures [Jung et al., 2005], but also non-geometric factors like tides the density of water [Stoschek and Zimmermann, 2006]. Numerous experimental investigations have been performed on the exchange of water between a river and a port compartment. The first basic approach (funded by Rohr [1933]) only considered two-dimensional horizontal flow fields, neglecting vertical velocity profiles. Stoschek and Zimmermann [2006] states that one or more vertical vortices (i.e. circulations) occur in the harbor com-partments, as illustrated in Figure 2.6. This is caused by the river flowing by and therefore is called the flow effect. In Figure 2.6 the water flow is directed land inwards. Please note that if the water flow reverses due to tidal cycle, the direction of the vortices will change [Stoschek and Zimmermann, 2006]. Claessens et al. [2011] states that microplastics could get trapped into these vortices, instead of flushing out of the port. This an explanation for the measured high abundance of microplastics in the port compartments.
Figure 2.6: Water velocity profiles in river and port compartment, adapted from Stoschek and Zimmermann [2006]
As already stated, to knowledge of the author no model is available in literature for the spatial distribution of marine litter on port level. For developing a prediction model of the location and accumulation of marine litter in a port area, the research performed by Claessens et al. [2011] could form a useful starting point.
2.4.
S
WEEPING OF MARINE LITTER
In a study by Morritt et al. [2014] it is mentioned that the Port of London Authority (PLA) operates a cleaning service which collects around 250 tons of debris each year from the river Thames (2011: 248 tons, 2012: 239 tons). Hereto, the PLA operates two purpose-built vessels and about ten floating passive debris collectors (PDCs). These methods are based on two different methods for sweeping of marine litter. In this section these two different methods for sweeping of marine litter are discussed.
2.4.1.
P
ASSIVE PDCFunded by Beilu (a bottled water company), the PDC is developed by Keel Marine (see Figure 2.7). The water current moves the marine litter towards the structure. A metal cage hangs underneath the pontoon to inter-cept the marine litter from the riverine water. The PDCs are located at a number of key locations in the river Thames. The collector is able to swing round so the cage is always directed against the tide. The PDCs are emptied once in a while by a vessel of the PLA. The PDC is designed to intercept 40 tonnes of marine litter per year [Londonist, 2010].
Figure 2.7: Passive Debris Collector in river Thames [BBC, 2010]
PLASTIC VISSER
In a partnership between ISI (Investments in Sustainable Innovations), SK International and Royal Haskon-ingDHV the plastic fisher (“plastic visser”) is developed (see Figure 2.8). This pontoon is 6 meters wide and 12 meters long. Like for the PDC, the water current moves the marine litter towards the structure. The plastic fisher is equipped with two floating arms. Each arm has a length of 4 metres and is provided with a sieve grid of a few metres depth. By means of a spud pole the pontoon is moored. Contrary to the PDC, the plastic fisher is able to sort and shred the marine litter on board.
2.4.SWEEPING OF MARINE LITTER 11
2.4.2.
A
CTIVEAs stated in Section 2.2.2, HEBO is a maritime service provider and is involved in cleaning operations in the port of Rotterdam. Hereto marine litter is removed actively by means of cleaning vessels. Based on personal communication with HEBO insights were retrieved considering practical experiences from the field:
• Port compartments are locations where the marine litter tends to accumulate (this agrees with the find-ings as presented in Section 2.3.2).
• The occurrence of storms or large festivities upstream cause peaks in the amount of marine litter.
• Marine traffic hardly forms any hinder for cleaning operations. If a conflict situation occurs, the pre-vailing nautical rules are respected and usually only cause short waiting times.
• Cleaning operations during evening and night are allowed, but occur very rarely. Operations during these parts of the day are avoided due to limited sight in the absence of daylight.
In the remainder of this section three different types of cleaning vessels are discussed that could be used to actively sweep marine litter.
BUDDY8M
The first vessel considered is the vessel named “Buddy 8m”, see Figure 2.9. The vessel is designed by Water Witch Marine & Engineering. It is specifically designed for low cost of ownership and is thus not equipped with complex machinery. The vessel consists of two hulls in parallel. In between the hulls a debris basket is present that can be lowered to collect marine litter. The water width that is cleaned by sailing with the debris basket in lowered position covers around 2 meters. The debris basket can be raised to travel at higher speeds. The vessel is driven by an outboard engine. Various properties of this vessel are summarized in Table 2.4.
Table 2.4: Specifications Buddy 8m [Water Witch, 2015]
Length over all 8 m
Width over all 2.5 m
Max. speed 15 km/h
Max. carrying capacity 1,500 kg
Figure 2.9: Water Witch Buddy 8m [Water Witch, 2015]
THAMESCLEARWATER
As indicated in the introduction of this section, the PLA operates two purpose-built vessels. The vessel cor-responding vessel is the ”Thames Clearwater”, see Figure 2.10. It is designed by DAMEN Shipyards. At the front the vessel is equipped with a hydraulically operated debris basket. This debris basket can be lowered to various depths. The water width that is cleaned by sailing with the debris basket in lowered position cov-ers around 6 metcov-ers. Various properties of this vessel are summarized in Table 2.5. The safe working load indicates the weight that can be lifted without risk of damaging the hoisting equipment.
Table 2.5: Specifications Thames Clearwater I and II [DAMEN Shipyards, 2007]
Length over all 24.2 m
Width over all 8.2 m
Max. speed 16.5 km/h
Safe working load 1 ton Max. carrying capacity 15,000 kg
Figure 2.10: Thames Clearwater II with debris basket in raised position [De Decker, 2009]
AQS-700 AQUATICSKIMMER
The third vessel considered is the ”AQS-700 Aquatic Skimmer”, see Figure 2.11. The vessel is designed by Aquamarine. At the front the vessel is equipped with a so called “collecting head”. This collecting head con-sists of side wings and a conveyor belt. The side wings conduct the marine litter towards the conveyor belt, which subsequently transports the litter to the storage facility on the vessel. Like the other vessels, the col-lecting head can be raised to travel at higher speeds. The water width that is cleaned by sailing with the debris basket in lowered position covers around 4 meters. Various properties of this vessel are summarized in Table 2.6.
Table 2.6: Specifications AQS-700 Aquatic Skimmer [Aquamarine, 2015]
Length over all 15.5 m
Width over all 4.2 m
Max. speed 11 km/h
Max. carrying capacity 4,450 kg
2.4.SWEEPING OF MARINE LITTER 13
2.4.3.
C
OMPARISONIn this section a brief comparison of the two sweeping methods is given. This comparison considers four criteria. The differences and rating for each criterion are discussed below. The comparison is summarized in Table 2.7. A higher score means a better performance with respect to the other sweeping method.
• Operational cost: during operation of passive sweeping, the equipment can be left unmanned and no transport cost are involved. For the deployment of cleaning vessels one or multiple persons is required and due to travelling additional cost will be imposed. On the other hand, the storage facility of the passive sweeping equipment must be emptied timely. Hereto vessels are required with associated crew. However, it is estimated that the operational cost for the passive sweeping method are lower.
• Capital cost: the equipment required for passive sweeping does contain no or nearly no moving parts. This causes that the equipment required for passive sweeping itself is less complex compared to the equipment required for active sweeping. However, as already indicated the passive sweeping equip-ment must be emptied timely. Hereto vessels are required. Therefore, it is estimated that the capital cost for both sweeping methods is similar.
• Physical application area: the equipment for passive sweeping are preferably placed at locations where it forms the least or no hinder for marine traffic. This limits the application area of passive sweeping. Cleaning vessels may also form hinder for marine traffic, but are able to omit or respond to dangerous situations. Above that, the passive sweeping methods require water current to function. Therefore, the application area of the cleaning vessels is considered larger.
• Application area: both sweeping methods are able to intercept marine litter form the water. How-ever, a cleaning vessel is also able to react to situations wherein marine litter accumulated to excessive amounts and for example poses a risk to vessels. A cleaning vessel can set right this undesired situation. Passive sweeping equipment is not suitable for this purpose.
If all criteria have equal performance, the active sweeping method shows better overall performance. Above that, because the the hinder of marine traffic associated with the passive sweeping method is con-sidered insurmountable in a port area, this sweeping method is concon-sidered unsuitable for the application of sweeping marine litter in a port area. On the other hand, the active sweeping method is considered a proper alternative for sweeping of marine litter in a port area and is therefore considered in the remainder of this research. If necessary, the passive sweeping method could form a useful addition to the active sweeping method.
Table 2.7: Comparison passive and active sweeping method
criterion passive active
Operational cost 1 0
Capital cost 0 0
Physical application area 0 1
Application area 0 1
2.4.4.
P
ROPOSED APPROACHAs clarified in Section 1.2, port authorities usually clean the ports’ water by means of cleaning vessels. Within this active sweeping method globally two approaches can be distinguished: a reactive or a proactive ap-proach. With a reactive approach no action is undertaken as long as no complaints on excessive amounts of marine litter are registered. Only after a complaint is registered, a cleaning vessel is deployed to resolve the complaint. These complaints are for example submitted by employees or customers of a port area. As stated in Section 1.2, the reactive approach is usually applied in port areas.
In this research a proactive approach is proposed. With this approach marine litter is swept without complaints are the immediate cause. The underlying thought of this approach is that by proactively sweeping marine litter excessive amounts of marine litter can be averted and thus complaints could be prevented.
Above that, marine litter is also removed at locations where no complaint is submitted about. In this way the risk posed to vessels and the negative environmental impact of marine litter is reduced.
Besides the demand for a proactive approach, the number of cleaning vessels is also considered limited. The less time is spent on travelling, the more time remains for sweeping of marine litter and thus the less sweeping capacity is required for removing a same amount of marine litter. Because the number of clean-ing vessels is considered limited, minimization of the distance travelled is demanded. For minimization of the distance travelled, the distribution of the marine litter over the water surface is of importance. In the pro-posed approach the input from a prediction model for the location and accumulation of marine litter in a port area is used as input for averting excessive amounts of marine litter while minimizing the distance travelled. This prediction model could make use of, for example, meteorological data and tides forecasts. Additionally, for instance drones could perform visual inspection, buoys with sensors could measure the concentration of marine litter and historic records could provide information considering removal requests. Above that, dur-ing operation of a cleandur-ing vessel data could be recorded with respect to the amount and location of litter removal.
2.5.
S
UMMARY
In this chapter a problem analysis is performed. Herein, various aspects of the research introduced in Chapter 1 are treated. In Section 1.1 it is mentioned that marine litter includes a wide range of materials, but plastics account by far for the most predominant share. Various types and sizes of plastics in marine litter were dis-cussed in Section 2.1. In this section it is described that microplastics are extremely difficult to remove from the marine environment. Therefore, it is not likely that sweeping of marine litter will directly contribute to reduce the amount of microplastics in the marine environment. In Section 1.1 it is also mentioned that the majority of marine litter is land based and conveyed via waterways to one of the oceans. In Section 2.2 various quantitative studies from literature related to marine litter in rivers are discussed. In addition, findings on the presence of marine litter in the port of Rotterdam are presented. From the presented numbers, it can be con-cluded that the port of Rotterdam has to deal with substantial amounts of marine litter. This makes the port of Rotterdam a suitable candidate for a case study. During the presented field measurements performed in the river Meuse it appeared that 98% of all the debris was present in the most upper meter of the water column, whereby the majority of the debris appeared in the upper halve meter of the water column. Therefore, marine litter can effectively removed by a cleaning vessel that only filters the upper layer of the water column. If a prediction model for the location and accumulation of marine litter in a port area is developed, this could be used as input for averting excessive amounts of marine litter while minimizing the distance travelled, given a number of vessels. In Section 2.3 various studies related to the spatial distribution of marine litter are dis-cussed. To knowledge of the author no model is available in literature for the spatial distribution of marine litter on port level. However, the presented researches could be an useful starting point for the development of an prediction model for the spatial distribution of marine litter. Lastly, the active and passive method for sweeping of marine litter and corresponding equipment is discussed. Both methods are compared and it is concluded the active sweeping method is suitable for sweeping of marine litter in a port area. This sweeping method is considered in the remainder of this research. In Section 2.4.4 the reactive and proactive approach for actively sweeping marine litter are discussed. In this research a proactive approach is proposed. In the proposed approach the input from a prediction model for the location and accumulation of marine litter in a port area is used as input.
3
L
ITERATURE OVERVIEW
In this chapter a literature overview is given wherein two major subjects are treated. The first major subject considers the Inventory Routing Problem (IRP). In Section 3.1.1 a problem description of the IRP is given and the analogy between the problem considered in this research and the IRP is described. Subsequently in Sec-tion 3.1.2 and SecSec-tion 3.1.3 the background and a basic example of the IRP is provided. In SecSec-tion 3.1.4 the relation of the IRP with classical combinatorial optimization problems is described. Literature considering the IRP entails a wide variety of formulations. To get an overview of the differences and similarities in litera-ture considering the IRP, a classification of the IRP is given in Section 3.1.5. One of the solution approaches towards the IRP is by formulating an integer programming model and constructing a solution using CPLEX. A global overview is given on how CPLEX works in Section 3.1.7. The second major subject in this literature overview considers stochastic programming. This subject is treated because it forms a basis for approaching IRPs which include random parameters. Two classes of stochastic programs are discussed, namely two-stage stochastic programs (Section 3.2.1) and multi-stage stochastic programs (Section 3.2.2). Hereby mathemati-cal formulations and examples are given.
3.1.
I
NVENTORY
R
OUTING
P
ROBLEM
3.1.1.
P
ROBLEM DESCRIPTIONThere does not exist one standard version of the IRP [Coelho and Laporte, 2013b]. In this section it is at-tempted to describe the IRP in a general way. Subsequently the link with the problem introduced in Section 1.2 is clarified. The IRP considers the repeated distribution of goods between a central facility (often referred to as a depot) and a set of geographically dispersed customers over a certain planning horizon. The cus-tomers possess a limited storage capacity. The distribution of goods is performed by a fleet of vehicles, which may have a limited carrying capacity. At the depot the vehicles have the possibility to stand idle and to renew their carrying capacity. A cost is associated with travelling between a pair of customers and between the cen-tral facility and a customer. Above that, inventory holding cost may be present at the cencen-tral facility and the customers. The objective of the IRP is to derive a distribution policy with minimal total cost (consisting of transport cost and inventory holding cost) over the planning horizon without causing stock-outs or reaching maximum inventory level at the customers. The IRP comes down to performing three decisions [Coelho and Laporte, 2013b]:
• When to serve each customer?
• How much to transfer at each customer when it is served?
• How to combine customers into vehicle routes to minimize cost?
Optimization problems can be divided into two categories: those with continuous variables and those with discrete variables, which are called combinatorial [Papadimitriou and Steiglitz, 1998] (page 3). The ob-jective of optimization problems is to find an optimal object from a finite set of objects. Based on these descriptions the IRP is seen as a combinatorial optimization problem. As already stated, there does not exist one standard version of the IRP. For a mathematical formulation of the IRP the reader is referred to Section 4.2, however this formulation is problem specific.
In the description above the distribution of goods is mentioned. This could be either the delivery or col-lection (pick-up) of goods. In a delivery problem goods are consumed at the customers, to prevent stock-out goods are distributed from the central facility to the customers. In a collection problem goods are produced at the customers, to prevent reaching maximum inventory level goods are collected at the customers and
brought to the central facility. The IRP may consider both problems, however in literature the IRP is often considered as a delivery problem. Referring to the problem introduced in Section 1.2, a cleaning vessel must address multiple locations over a certain time span. Due to the continuous supply of marine litter by rivers, the amount of litter accumulates at the hot spots over time. So the analogy between the problem considered in this research and the IRP holds that the hot spots of marine litter can be seen as geographically dispersed customers with an inventory of marine litter that increases over time. In other words, a hot spot can be seen as a producing customer. The consideration of the IRP as a collection problem corresponds to the situation wherein marine litter is collected by means of a cleaning vessel and brought to a central facility. The limited storage capacity at the customers is represented by setting a boundary value for the amount of marine litter per hot spot. In the end, the IRP is able to take into account a routing aspect and the accumulation of marine litter together for deploying cleaning vessels along hot spots in the port area.
Up to now a general description of the IRP is given. In the remainder of this section it is attempted to set the IRP in a wider context and to clarify some basic properties of the IRP. First of all, the IRP integrates three components: inventory management, vehicle routing and distribution scheduling [Coelho and Laporte, 2013b]. The customers posses a limited storage capacity and consume or produce goods over time and the central facility has to prevent stock-out or reaching maximum inventory level at the customers. Therefore, the inventory component adds the time dimension to the spatial dimension of the routing component [Bertazzi et al., 2008] (page 50). An example considering the inventory level over time of a customer producing goods is shown in Figure 3.1. This example assumes a linear increase of inventory level over time and a periodic collection of goods.
Figure 3.1: Inventory level at a producing customer, adapted from Larson [1988]
The solution approaches for IRP problems may be classified into two categories: the frequency domain approach and the time domain approach. In the frequency domain approach decision like loads, routes and visit frequencies are only made once and for all. So based on a priori knowledge periodic operations are proposed. Contrary to the frequency domain approach, in the time domain approach operations are scheduled over a finite planning horizon. Decisions are made at the beginning of each period in the planning horizon, taking into account the current state of the system. Therefore, decisions made at the previous period influence the decisions at the current period. It could be that the time domain approach has the same efficacy as the frequency domain approach. This occurs if decisions made for the time domain approach equal the decisions of the frequency domain approach. However, this not necessarily true.
As stated at the beginning of this section, minimizing cost over the planning horizon is part of the objec-tive of the IRP. The planning horizon is a time span (e.g. one week). Andersson et al. [2010] states that the IRP has a long-term nature, but is used in a tactical planning environment in most applications. Therefore the reduction from a long-term planning horizon to a short-term is a crucial modification. This is clarified in 3.1.5, wherein the planning horizon is discussed in detail.
The only restrictions of the IRP mentioned at the beginning of section are that stock-outs (in case delivery to customer) and reaching maximum inventory levels (in case collection problem and delivery problem) must be prevented. However, customers often impose other restrictions by demanding various so called ‘quality of service features’. A few possibilities proposed by Coelho et al. [2012] are listed below. Various variants of the IRP can be formed by adding these additional features. Please note that if it is desired to incorporate multiple
3.1.INVENTORYROUTINGPROBLEM 17
quality of service features, not all features may be reconcilable with each other. Summarizing, the IRP offers many interesting possibilities.
• Quantity consistency: limits the quantity of products delivered/collected at a customer by customer specific range.
• Driver consistency: requires that each customer is only served by one driver
• Visit spacing: imposes minimum time span between two consecutive visits to one customer
3.1.2.
B
ACKGROUNDThe objective of this section is to provide information on the background of the IRP. Since the optimization of transport chains may result in significant savings, the industry is therefore continuously looking for im-provements. A relative recent development is the adaptation of new forms of relationships in supply chain management. One of these new forms is called Vendor Managed Inventory (VMI). Under a VMI policy a central facility monitors the inventory at the customers and determines the replenishment policy. In other words, the central facility acts as a central decision maker who solves an integrated inventory routing prob-lem [Archetti et al., 2007a]. This deviates from the traditional retailed managed inventory (RMI) policy, where the customer places orders at a central facility. In other words, under a VMI policy no customer orders are present. The central facility (and not the customer) determines how and when distribution takes place. This freedom offers the central facility more possibilities in deriving a distribution policy with minimal cost. The adaptation from VMI with respect to RMI is often described as a win–win situation. On one hand a central facility can decide when and how much to deliver to their customers and can smooth its distribution sched-ules and efficiently combining geographically close customers to reduce their distribution cost, on the other hand customers can benefit by savings on ordering cost [Coelho and Laporte, 2013b].
The underlying problem in optimizing a VMI policy is the IRP. The IRP represents a class of relatively new problems [Archetti et al., 2007b]. One of the first papers in the field of IRP was published by Bell et al. [1983]. The IRP can be seen either as an extension of an inventory management problem with the inclusion of a routing component, or as a routing problem extended with an inventory management component [Anders-son et al., 2010]. A large number of variants of the IRP have been introduced. The IRP has its application in many sectors, like in the oil and gas industry [Bell et al., 1983], retail [Gaur and Fisher, 2004] and the med-ical sector [Hemmelmayr et al., 2009]. There is a large variety of problems and solution approaches for the IRP, which makes structuring a literature review already a challenging task [Bertazzi et al., 2008]. While the term IRP is most commonly used, the IRP is denoted with many different names throughout literature. A (non-comprehensive) list of alternative names is given below:
• Vendor managed inventory routing [Rusdiansyah, 2005]
• Integrated inventory distribution problem [Abdelmaguid and Dessouky, 2006]
• Combined inventory management and routing problem [Andersson et al., 2010]
• Inventory control with vehicle routing [Michel and Vanderbeck, 2012]
3.1.3.
B
ASIC EXAMPLETo clarify the impact of joint decisions considering inventory and routing, a simple example introduced by Bell et al. [1983] is treated in this section. This example considers a depot and four geographically dispersed customers (see Figure 3.2). The product is supplied from the depot to the customers. Each customer pos-sesses an inventory with a storage capacity and consumes product every day, as listed in Table 3.1. One vehi-cle with a carrying capacity of 5,000 units is available. The initial inventory level at each customer is equal to the storage capacity. There are no limitations on the product availability at the depot and no inventory cost are taken into account. A time period of one day considered. The objective is to find a periodic distribution policy that minimizes the travel cost while no stock-out occurs at any of customers and the capacities of the inventories and vehicles are respected. Please note that this periodicity implies that the inventory levels at the end of a period should be equal to the initial inventory levels.
Table 3.1: Storage capacity and daily consumption [Bell et al., 1983]
Customer Storage capacity Daily consumption
1 5,000 1,000
2 3,000 3,000
3 2,000 2,000
4 4,000 1,500
Figure 3.2: Network indicating depot and customers [Bell et al., 1983]
An obvious distribution policy would be to let the vehicle perform two trips a day. In each trip the cus-tomers situated close to each other are combined. So one trip delivers 1,000 units to customer 1 and 3,000 units to customer 2. The other trip delivers 2,000 units to customer 3 and 1,500 units to customer 4. This solution is summarized in Table 3.2. The total travel distance is 420 miles. However, this distribution policy is not optimal. A better policy is to perform one trip on day one and two trips on day two. On day one 3,000 and 2,000 units are delivered to customers 2 and 3 respectively. On day two, the a trip delivers 2,000 units to customer 1 and 3,000 units to customer 2. The other trip delivers 2,000 units to customer 3 and 3,000 units to customer 4. So on day one customer 1 and 4 are not visited, while on day two all customers are visited. This schedules is repeated every two days. This solution is summarized in Table 3.3. The total travel distance is 760 miles for two days, or an average of 380 miles per day. This travel distance (with a planning horizon of two days) is nearly 10% less than the first proposed distribution policy (with a planning horizon of one day). Please note that the inventory levels at the customers are equal at the end of a period for both distribution policies. So the system is left in an equal state, therefore it is justified to draw a comparison between these two distribution policies. Adelman [2003] showed that the latter proposed distribution policy is optimal by means of dynamic programming.
Table 3.2: Solution A to example problem
Trip Day Customer 1 Customer 2 Customer 3 Customer 4 Distance [miles]
1 1 1,000 3,000 0 0 210
2 1 0 0 2,000 1,500 210
Table 3.3: Solution B to example problem
Trip Day Customer 1 Customer 2 Customer 3 Customer 4 Distance [miles]
1 1 0 3,000 2,000 0 340
2 2 2,000 3,000 0 0 210
