Designing the Intermodal Multiperiod Transportation Network of a Logistic Service Provider Company for Container Management
Tobias Sahlin
Master of Science in Industrial Engineering and Management Optimization and Supply Chain Management
Master’s Thesis, 30 credits 27th of May 2016
Abstract
Lured by the promise of bigger sales, companies are increasingly looking to raise the volume of international trade. Consequently, the amount of bulk products carried in containers and transported overseas exploded because of the flexibility and reliability of this type of transportation. However, minimizing the logistics costs arising from the container flow management across different terminals has emerged as a major problem that companies and affiliated third-party logistics firms face routinely.
The empty tank container allocation problem occurs in the context of intermodal distribution systems management and transportation operations carried out by logistic service provider companies. This master thesis considers the time-evolving supply chain system of an in- ternational logistic service provider company that transports bulk products loaded in tank containers via road, rail and sea. In such system, unbalanced movements of loaded tank con- tainers forces the company to reposition empty tank containers. The company’s motivation is to study whether or not there is any incentive to further investigate and develop a model supporting the planning decisions for transportation of empty tank containers. The problem involves dispatching empty tank containers of various types to the meet on-time delivery requirements and repositioning the other tank containers to storage facilities, depots and cleaning stations. To this aim, a mixed-integer linear programming (MILP) multiperiod op- timization model is developed aiming to make tactical decisions for the empty tank container allocation problem, or more specifically, for determining the best strategy for distributing the empty containers through the transportation network of the company.
The model is analyzed and developed step by step, and its functionality is demonstrated by conducting experiments on the network from our case study problem, within the boarders of Europe. The case study constitutes three different scenarios of empty tank container allo- cation. In addition, the case study network topology is utilized to create random instances with random parameters and the model is also evaluated on these instances. The computa- tional experiments show that the model finds good quality solutions, and demonstrate that cost and modality improvement can be achieved in the network, through repositioning of empty containers. Furthermore, an extensive sensitivity analysis is conducted to show the effect of the model’s parameters on its performance. The sensitivity analysis employs a set of data from our case study and randomly generated data to highlight certain features of the model and provide some insights regarding the model’s behavior.
Keywords: Supply chain, Distribution network, Repositioning, Intermodal transport, Sen- sitivity analysis.
Sammanfattning
Internationell handel ¨okar i takt med f¨oretags str¨avan om att uppn˚a h¨ogre f¨ors¨aljningsresultat genom ¨okade exportvolymer. Transporter mellan kontinenter av containrar lastade med bulkprodukter har ¨okat avsev¨art p˚a grund av den flexibilitet och tillf¨orlitlighet denna typ av transport erbjuder. Att minimera logistikkostnaderna f¨or transporter mellan olika ter- minaler har mynnat ut i ett betydande problem f¨or f¨oretag som erbjuder tredjepartlogistik.
”Tomcontainer allokerings problemet” involverar f¨oretag som erbjuder logistiska tj¨anster inom intermodala distributionssystem genom att l¨agga ut dessa tj¨anster p˚a externa lever- ant¨orer. Denna masteruppsats fokuserar p˚a ett internationellt f¨oretag som erbjuder trans- porter av bulkprodukter lastade i tankcontainrar via v¨ag, j¨arnv¨ag och sj¨o. I system av detta slag utf¨ors obalanserade transporter av lastade tankcontainrar, vilket tvingar f¨oretaget till att ompositionera tomma tankcontainrar. F¨oretaget motiveras av att unders¨oka om det finns incitament till att vidare analysera eller m¨ojligtvis implementera en matematisk mod- ell som st¨odjer ompositioneringsbeslut f¨or tomma tankcontainrar. Ompositionerings beslut baseras p˚a kundorder samt antaganden om huruvida framtida efterfr˚agan kommer uppst˚a eller ej. Problemet inkluderar att m¨ota efterfr˚agan och tillh¨orande krav fr˚an f¨oretagets kun- der. Kraven specificerar vilken tid leverans ska ske, vilket skick tankcontainern b¨or vara i samt vilken typ av tankcontainer som efterfr˚agas. En dynamisk blandad heltalsmodell som
¨
ar anpassad f¨or intermodal transporter samt den varierade efterfr˚agan av olika dimensioner av tankcontainrar utvecklas, med syftet att generera taktiska beslut f¨or det aktuella allok- eringsproblemet. Mer specificerat ¨ar m˚alet att best¨amma en optimal distributionsstrategi inom f¨oretagets transportn¨atverk.
Modellen utvecklas och valideras steg f¨or steg och dess funktionaliteter demonstreras genom en k¨anslighetsanalys baserat p˚a det Europeiska n¨atverket inkluderat i v˚ar fallstudie. Fallstu- dien inkluderar tre olika scenarion f¨or allokering av tomma tankcontainrar. Vidare nyttjas topologin av n¨atverket i fallstudien till att utf¨ora slumpm¨assigt utvalda instanser f¨or att utv¨ardera modellen. Dessa ber¨akningsresultat visar att modellen finner l¨osningar av god kvalitet och indikerar att det finns rum f¨or f¨orb¨attringar g¨allande f¨ordelningen av trans- portmedel. En utf¨orlig k¨anslighetsanalys presenterar vilken effekt modellens parametrar har p˚a modellens utf¨orande. Vi anv¨ander slumpm¨assigt utvald data f¨or k¨anslighetsanalysen och betonar vissa funktionaliteter av modellen samt delger insikter om modellens beteende.
Nyckelord: F¨ors¨orningskedja, Distributionsn¨atverk, Ompositionering, Intermodala trans- porter, K¨anslighetsanalys.
Acknowledgements
I wish to thank various people for their contribution to this project. Firstly, I would like to express my very great appreciation to my supervisor at Ume˚a university, Ahmad Hosseini, for his professional guidance, patience and willingness to share his knowledge and all the time he devoted to this work. I would also like to address my deepest gratitude to my supervisor at ORTEC, Ronald van Schieveen for an enthusiastic encouragement, patient guidance, and useful critiques during this project. Special thanks should be given to Robert Zwetsloot at Hoyer.
Sharing knowledge and giving time so generously have been very much appreciated. A great thanks also goes to Martijn Leenstra at ORTEC, who made this project possible in the first place. I would like to extend my thanks to all the employees’ at both Hoyer and ORTEC that have contributed to this master thesis.
Tobias Sahlin
Contents
1 Introduction 1
1.1 Project situation . . . 1
1.2 Hoyer . . . 1
1.3 ORTEC . . . 1
1.4 Background . . . 2
1.5 Tank container management at Hoyer . . . 4
1.6 Aim, scope & research question . . . 8
2 Literature Review & Motivation 10 2.1 Introduction to multi-modal transportation planning . . . 10
2.2 The empty repositioning problem . . . 10
3 Mathematical Theory 15 3.1 Network flow problems . . . 15
3.1.1 Minimum Cost Flow Problem . . . 15
3.1.2 Distribution Problem . . . 16
3.1.3 Transportation Problem . . . 17
4 Solution Methodology & Container Management Model 18
5 Computational Study & Sensitivity Analysis 32
6 Summary and Discussion 42
7 Final Recommendations & Future Research 44
References 47
List of Abbreviations
ORTEC Operation Research Technology ORD ORTEC Routing and Dispatch
LP Linear Program
NLP Non Linear Program
IP Integer Program
MILP Mixed-Integer Linear Programming MIP Mixed Integer Program
AIMMS Advanced Interactive Multidimensional Modeling System IDLE Integrated Development and Learning Environment 3PL Third-Party Logistics Provider
ISO International Standards Organization regulations
OECD Organization for Economic Co-operation and Development TMS Transportation Management System
cefic The European Chemical Industry Council
Dictionary
Empty repositioning:
transportation of empty tank containers can be referred to as repositioning of empty containers from surplus areas to demand areas.
Third party logistics service provider:
Company that provides their customers with outsourced logistical services. These logistical services are typically customized, based on requirements from their customers and market con- ditions.
Intermodal transportation:
transportation that includes a sequence of at least two different transportation modes where the transfer from one mode to another being performed at an intermodal terminal.
Intermodal terminal:
Interface between the different transportation modes included in a intermodal transport, such as a port or rail terminal. Intermodal terminals provides logistical services such as short-term storage, load and unload operations.
Tank container:
An intermodal container for transportation of bulk products such as liquids and gases.
Route: constitute a combination of sections or legs.
Pre-haulage:
section or leg representing the first miles of a route.
Long-haulage:
section or leg that constitutes the transportation after pre-haulage and before the end-haulage.
Often called terminal-to-terminal transit or door-to-door transit.
End-haulage:
section or leg representing last miles of a route.
List of Figures
1 Intermodal transportation as a concept . . . 4
2 The tank container . . . 5
3 An example of a typical tank container cycle . . . 6
4 The empty repositioning problem . . . 7
5 Planning levels for the empty repositioning problem . . . 11
6 Production-distribution model . . . 16
7 Generalized distribution network . . . 20
8 Topology of Hoyer’s distribution network . . . 33
9 Computational experiments under scenario 1 with different time discretizations . 36 10 Computational experiments under scenario 1 with different lengths of the plan- ning horizon, 1 . . . 37
11 Computational experiments under scenario 1 with different lengths of the plan- ning horizon, 2 . . . 38
12 Computational experiments under scenario 1 with transportation capacities, 1 . . 39
13 Computational experiments under scenario 1 with transportation capacities, 2 . . 39
14 Computational experiments under scenario 2 with limited storage time at inter- modal terminals, 1 . . . 40
15 Computational experiments under scenario 2 with limited storage time at inter- modal terminals, 2 . . . 40
List of Tables
1 Tank container classification . . . 21 2 Topology of Hoyer’s distribution network . . . 32 3 Computational experiments, scenario 1, Performance . . . 35 4 Computational experiments under scenario 1 with different time discretizations . 35 5 Computational experiments under scenario 1 with different lengths of the plan-
ning horizon . . . 37 6 Computational experiments under scenario 1 with capacity restrictions of trans-
portation modes . . . 38 7 Computational experiments under scenario 2 with limited storage time at inter-
modal terminals . . . 40 8 Computational experiments under Scenario 3 with the end-haulage . . . 41 9 Hoyer’s distribution network, countries and regions . . . 49
1 Introduction
This section describes the project’s situation and its stakeholders. Subsequently, it provides a background to the case study problem by describing Hoyer’s challenges and operations, and by introducing one of the main industries the company is active in; the chemical industry.
The aim, delimitation and research question of this project is presented at the end.
1.1 Project situation
This master thesis is proposed by Hoyer Gmbh in cooperation with ORTEC B.V. Hereafter will these companies be referred to as Hoyer and ORTEC, respectively. Hoyer is a current customer to ORTEC. The later company has implemented a transportation planning tool called OR- TEC Routing and Dispatching (ORD) into the transportation planning system of Hoyer. This product supports the process of distribution goods to customers with a fleet off vehicles. ORD support loading- and unloading actions or a combination of both. However, this solution is not implemented at Hoyer for any optimization procedures. Currently, Hoyer and ORTEC are in- vestigating whether or not an extended collaboration could include optimization. This research focuses on investigating if an optimization model supporting decisions regarding transportation of empty tank containers could be a part of this next step amongst the companies.
1.2 Hoyer
Hoyer has been a leading bulk logistic provider since 1946. The German family-owned company is an international third party logistics service provider, specializing in bulk, particularity in the chemical, oil, gas, petroleum and foodstuff industries. Hoyer executes transportation orders via road, train, short-sea and deep-sea, supported by strategically located terminals. Short sea shipping refers to coastal trade without crossing continents. Deep sea shipping or ocean shipping refers to maritime traffic that crosses continents. The company offers other services such as cleaning process of tank containers, heating and cooling, filling and blending procedures of bulk products. Hoyer owns approximately 34,000 tank containers, often mentioned as the company’s key resource.
1.3 ORTEC
ORTEC is one of the market leaders of providing advanced planning and optimization solutions and services. The result of these solutions and services are optimized vehicle and pallet loading, workforce scheduling, warehouse control, routing and dispatch and logistics network planning.
Some solutions are standardized products whereas others are tailor made after customers re- quests. ORTEC is active in a variety of industries which includes the retail, transportation, consumer goods, food and beverage, healthcare and the oil, gas and chemical industry.
1.4 Background
Third party logistical service providers are independent companies providing logistics services to their customers. Although they do not hold ownership of the product to be shipped, they are legally bound and responsible to perform the requested logistic activities from their customers.
It was revealed during one of the interviews with Hoyer that the European market of third party logistical service providers, offering logistical services for shipments of bulk products is characterized by an oligopoly market condition. The number of actors offering transportation of bulk products, such as chemical products, is highly restricted due to the high entering costs in this type of business. The main cause of this is the high valued tank container that can be seen as the key asset in this industry, providing safety of the shipment, maintains the quality of the product and facilitates shipments to be carried out via intermodal transports.
A high utilization grade of the tank containers is of great importance for any logistical ser- vice providers success. The high customer service level required from the clients reflects the competitive environment these companies are operating under. Furthermore, 3PL companies such as Hoyer are subject to a great deal of complexity not present in other industries. Firstly, the complexity stems from the uncertainty of trade patterns across the network and the un- balanced movements of loaded tank containers. This forces the actors to correct imbalances by transportation of empty tank containers, more commonly phrased as empty repositioning or empty moves. Secondly, the heterogeneous character of the chemical products requires suit- able means of transportation; certain products requires a certain type of tank container for its transportation in order to maintain the quality of the product and to ensure the safety of the shipment.
To match products and suitable tanks across geographically regions in a time wisely suitable matter is often a difficult task. In addition, the condition of the tank container is another important topic. If previous loaded product is not the same as the product for reloading, the tank container must be cleaned before reloading, necessitating availability of cleaning stations.
Furthermore, logistical service providers are operating under relatively narrow time frames while trying to fulfill the demand from their customers. The complexity in wise empty tank container assessment comprises two major causes of distress. The first regards the unavailability of empty tank container resulting in not being able to comply customer demand. This may lead to a customer loss and bad reputation. On the contrary, emergency shipment of empty tank containers attached with a high cost results in lower profit margins. The second governs a surplus of tank containers in some region or cluster which would imply lower tank container utilization.
An interview with Hoyer provided insight into their business model as an third party logistics service provider. In particular, the interview revealed that the success of the company’s business model depends to a large extent on the ability to establish customized services. On the other hand, the willingness from the customer to adapt to the logistical service providers could be another important factor to further improve the efficiency of the third party logistics relation- ship. Consequently, customer adaption is a crucial characteristic of a service logistic provider, necessitating a sufficient understanding of their clients business as well. Hoyer is active within a number of different industries and it is not possible to cover all these, neither is it part of the scope of this project. However, customers from the chemical industry represents a major part of Hoyer’s business. An introduction to the chemical industry is given below, providing further insight of the company’s operations and the challenges Hoyer are facing.
The European chemical industry accounts for 17% of the world’s chemical production, con- tributese551 billion annually and have 1.2 million employed workers (cefic, 2016) . Currently, there is an ongoing production shift within this field which will impact the global chemical logistic supply chain. Historically, the production of chemicals has been dominated by the OECD (Organization for Economic Co-operation and Development) countries. During the last decade the production has rapidly grown in non-OECD countries e.g. Asia and the Middle East due to lower energy price and increasing demand in these regions (Broeren, 2009). As a consequence, the European chemical industry’s competitive position is at risk. However, it was revealed during one of the interviews with Hoyer that the majority of the chemical products are not profitable enough for the non-OECD countries to ship to Europe due to its low margins.
Thus, the expected higher competition will rely more on the exports from Europe rather than imports.
Clusters plays an important role for the European chemical industry. The majority of the 300 European production sites included in an investigation conducted by the European Commisson were located in one of 30 strategically positioned clusters. Many upstream and downstream activities are integrated between the chemical plants in these clusters. Having a combination of key assets in place and the proxity to the customer market often determines the success of a cluster. However, complete supply chain integration is often non-existent. Despite numer- ous attempts of decreasing shipments of chemical goods by clustering, freight volume is still estimated to increase annually by 2.5 %. The industry is still widely spread out, often located closely to some major energy or other important raw material resource. In addition, chemical companies are often specialized and one company may supply the entire European market (The European Commisson, 2009). Thus, long distance transportation is a common practice in this field. This emphasizes the need of cost efficient and safe shipments.
While considering trade-offs regarding the cost, quality and safety of the shipment, Hoyer al- ways prioritize intermodal transportation, making the transportation safer, more competitive and environmental friendly. It was declared in a report conducted by the The European Chem- ical Industry Council (cefic) that the share of road transportation is in general very high, a declining usage of rail transportation has become evident due to the bottlenecks intermodal terminals may bring. At the same time, many actors argues that a large extent of the current intermodal transportation possibilities already have been captured; logistical service providers finds it difficult to increase intermodal movements and still secure high service levels. However, the majority of the chemical production companies and the logistical service providers still have positive view of reaching EU’s proposed goal of moving all transportation over 300 km to inter- modal transportation. In the endeavor of pursuing this goal, a number of obstacles that need to be tackled have been stated (cefic, 2014). The top four issues are as follows:
1. High costs. The cost structure of intermodal transportation compared to road trans- portation is the main issue that prevents further shifts from road to intermodal movements.
2. Intermodal connections missing. There is a lack of intermodal connections in Europe, especially while considering train connections between Benelux (Rotterdam) and France.
3. Insufficient frequency or capacity of intermodal connections. Already existent intermodal connections is insufficient in terms of frequency and capacity.
4. Last mile solution. The last leg of intermodal moves for the chemical industry is very complex with respect to quality, safety and costs. For example, cleaning stations or
1.5 Tank container management at Hoyer
Intermodal transportation
In the perspective of a transport planner at Hoyer, two different transportation options are always considered; transportation via road or by a sequence of at least two different modes i.e.
intermodal transportation. Intermodal transportation is prioritized whenever possible and can be defined as a shipment from its origin to its destination by a sequence of at least two different transportation modes where the transfer from one mode to another being performed at an intermodal terminal (loading/unloading terminal in Figure 1). In general, the transportation chain can be divided into three sections, (1) pre-haul; first miles after the loading process, (2) long-haul; terminal-to-terminal transit or as often mentioned, door-to-door transit and (3) end-haul; last miles for the unloading process. The pre-haul and long-haul transportation are carried out by road whereas for the long-haul transportation, all modes (road, rail, sea) can be considered (Steadieseifi, 2014). Pre, long or end haul may be referred to as a section or leg and a combination of sections or legs may be called a route.
Figure 1: Illustration of intermodal transportation as a concept.
For transportation via road Hoyer has entered into subcontracts with trucking companies. Av- erage drivers are not sufficient for transportation of chemical products. Drivers that transport chemical products must pass strict background checks and complete federally certified training and in-house-training for the company they are working for. However, these shipments may be seen as all three types of sections (pre-haul, long-haul and end-haul, (Figure 1). For transporta- tion via sea and railway, Hoyer has entered into subcontracts with external logistical service companies, providing not only transportation but also storage and handling services at inter- modal terminals. Each of these transportation service contracts represents long-haul sections (Figure 1).
Typically, the company charges their customers a fixed price for a logistical service. Each section and its associated transportation and operational costs are quoted and constitute the total price of the shipment. Thus, the profit (loss) obtained by Hoyer mainly depends on the costs from the external subcontracted logistical service providers and the costs from the subcontracted trucking companies. For this reason, there is strong incentives to minimize these costs, especially for empty movements as these shipments are not considered to generate profit.
For intermodal distribution of tank containers, the modern trend is towards flexibility and compability. Tank containers are designed as self-contained units; they can be transported via different modes without disturbing its content or violating security terms. Surely, this is very helpful for door-to-door delivery. Hoyer is required to allocate an suitable empty tank container for respective product that is demanded to be loaded and shipped. The tank may hold chemicals, gases, food-stuff or other products. A certain type of tank container for each kind of product is required to ensure the safety of the shipment and to maintain the quality of
the product as well as not to violate legal terms. For instance, it may be required to provide tank containers in the right condition. It can also be demanded to maintain a certain temperature of the product and a certain pressure and filling grade of the tank container. This emphasizes the need of different functionalities of the the tank container, illustrated by 2. Further, tanks for these purposes must comply with International Standards Organization regulations (ISO).
Figure 2: An illustration of a set of different functionalities of a tank container.
The tank container cycle
A transportation order of an empty tank container from a loading site may be seen as the first step of the transportation planning process. This is part of the planning of empty tank container logistics. The loading site may be a producer of chemical products that demands products to be transported to one of their customers. Subsequently, the transport planner allocates a suitable empty tank container for transportation via road to the customer for loading of products.
Whether or not it is possible to allocate the empty tank container in the neighborhood of this loading site depends on the planing of the empty tank logistics. Empty tank logistics will be explained in more detail later in this section.
Figure 3 illustrates a typical cycle for an intermodal transportation of a tank container. The pre-haul section in Figure 3 represents a loaded move from the loading site to an intermodal terminal, in this case a port terminal, but it could also be a train terminal. The long-haul section is the next step of the cycle. The transport planner sends a booking requests to a logistical service provider for transportation via a vessel. A database of departure and arrival times for train and vessels is used to find available trains and vessels. The rule of thumb is to only allocate tanks for shipments via road under 400 kilometers. For shipments over 400 kilometers the transport planner may choose between the modalities rail and sea. The criteria for this decision constitutes of the associated transit time, operational costs, safety and quality factors. The end-haulage take place after the door-to-door transit or the long-haul. The last miles for delivery is carried out via road (Figure 3).
Figure 3: An example of a typical tank container cycle. The tank container cycle is represented by the loaded moves; pre, long and end-haul and the empty tank container logistics.
As Figure 3 suggests, the empty container logistics takes place after the end-haul and the unloading of products at the unloading site until reloading at the loading site. The reader is encouraged to note that empty logistics itself may include all previous mentioned conceptual shifts; end, long and pre-haul. The planning of empty repositioning are trivial in some cases and more difficult in others. In the trivial scenario, there is a known demand of the tank container that just have been unloaded at an unloading site. The tank container is then reallocated to a cleaning station and subsequently transported to the demanding customer for reloading.
On the contrary, if there is no known demand for reloading after unloading, the situation becomes more complex. It is no longer obvious to what location the tank container should be repositioned to. In this situation, the transport planner has some different options to consider.
Firstly, the tank container can be moved to a region where demand of empty tank containers is expected to arise in the near future. Secondly, the tank can be shipped to one of the major internal depots located in, for instance, the Netherlands or Belgium for storage or it can simply be decided to store the tank in the current region. These decisions are based on communication among the transport planners and their business experience.
The empty repositioning problem
Empty repositioning is an important component of the container tank management. It is crucial to meet the demand of empty tank containers in order to reduce the risk of competitors providing the tank containers as requested and suffer loss of customers. In addition to this, tank container utilization can be improved and the storage, handling and transportation costs can be reduced if empty repositioning is planned wisely. Figure 4 illustrates the repositioning of empty tank containers (dotted lines) and transportation of loaded units (solid lines). Intuitively, the demand of empty tank containers varies across geographically regions or in other words, the loaded moves are unbalanced.
Recall that customers from the chemical industry tends to form strategically clusters. As a result of this may regions be distinguished by two different main characteristics. Some of the regions included in the distribution network of Hoyer can be called net exports regions. For net export regions, the total outgoing flow of loaded tank containers is relatively larger than the total incoming flow of loaded tank containers. In opposition, the total incoming flow is relatively larger than the total outgoing flow for import regions. The net export regions are characterized by major producers of chemical products. The net import regions are character-
ized by companies that demand the chemical product itself. In general, a net surplus of empty tank container can be associated with net import regions and a net demand with net export regions.
Given the unbalanced moves of loaded units, Hoyer is forced to reposition empty tank containers from net import regions to net export regions in order to supply the demand of empty tank containers. If the empty repositioning is not planned carefully the entire transportation network will operate inefficiently. For instance, the empty container management of Hoyer must account for the situation where loaded tank containers shipped away from some region do not match the incoming flow of tank containers to that region. However, if the flows would match, there is no guarantee that demand of these unloaded empty tanks container will arise in that particular region in the near future. Further, when an empty tank container is available after unloading, it may not be time wise possible to match this tank to a new demand for reloading. In addition, there are different types of tank containers with different functions that are matched to the products demanded to be shipped. This is illustrated by Figure 2. Neither is it preferably to keep the stock to high, this will reduce the tank container utilization significantly.
Figure 4: An illustration of the empty repositioning problem. Loaded moves are illustrated by solid lines and empty moves by dotted lines.
The tank containers managed by the company are either owned by Hoyer or leased. The opportunity of leasing may help to reduce regional imbalances. On the contrary are leasing contracts often long term based and expensive. It may therefore be difficult to save costs with this alternative. On the other hand may an increased owners ship be to risky or financially complex. In addition will leased tank require some extra attention, especially close the expire date of the leasing term. Leased tanks must then be allocated to a certain depot at a certain date for return to its owner.
In order to analyze and manage imbalances that occurs, Hoyer’s distribution network has been mapped after country and region. This can be obtained from Table 9 included in Appendix A.
Furthermore, imbalances are often analyzed after the dimensions (cbm) of the tank containers, indicated by Table 1 in chapter 4.
The following factors and business rules are taken into account while planning a shipment as a transport planner at Hoyer:
1. Matching the type of tank containers with the products to be shipped.
2. Previous product; Some products does not have any quality impacts on each other and therefore can cleaning process be avoided.
3. Frequency of intermodal connections; time schedule of the departures and arrivals for vessels and trains.
4. Capacity of intermodal connections; storage capacities at intermodal terminals and trans- portation limitations for the modes train and vessel.
5. Transportation, storage, and handling costs.
6. Condition of the tank container; cleaning processes and maintenance.
7. Management of leased tank containers; additional tanks may be brought into or out from the system.
8. Flow balance between empty and loaded tank containers across regions.
1.6 Aim, scope & research question
The aim of this thesis is to verify if there exists incentives to further investigate or possible implement a model supporting decisions for transportation of empty containers into the current transportation planning system of Hoyer. The reason why Hoyer shows interests in such model is to be able to reduce the costs for empty moves while still ensuring that customer orders can be met in time. Wise empty tank container management may improve the utilization grade of the tank containers and enhance the competitive edge of the company.
Outcome goals
Since both stakeholders of this project seeks an answer to the question whether or not there exists incentives to further analyze or possible implement an optimization model supporting the planning process of empty repositioning, is an answer to this question considered as a preferred outcome goal. Another goal is to mathematically formulate the problem as a mixed integer linear program. The program should meet the requirements stated by Hoyer and its validity should be confirmed.
Delimitations
Hoyer is an international logistic service provider and is operating world wide. However, deep sea shipments or ocean shipping, referring to shipments carried out by carriers that crosses oceans are excluded in this paper. The scope of this study regards hinterland- and intermodal transportation within the boarders of Europe.
There is two different types of transportation orders that Hoyer are receiving from their clients.
Namely, spot orders and dedicated orders. The spot orders are standardized orders that rarely are rejected. The dedicated orders refers to more advanced, customized shipments where the products may have an impact on the tank container. For instance latex is a chemical component
of glue which often is shipped in a tank container, this chemical product tends to fasten on the inside of the tank container, creating growing layers that eventually needs to be removed at a cleaning station. This work will be focused on spot orders only.
The planning level of the problem under consideration is referred to as a service planning level, which means that we are considering a medium term planning horizon. This project focuses on developing a service network model for Hoyer’s intermodal distribution system. In contrast to this includes operational models real-time decisions which are out of scope for this work.
Research question
The company, Hoyer, wishes to know whether or not there exists any incentive to further investigate and develop a mathematical model supporting the planning tactical decisions for flow management of empty tank containers.
2 Literature Review & Motivation
Prior to focusing on the empty repositioning problem, we first provide an introduction to multimodal transportation planning. The intent is to provide insights of why transporta- tion planning is of great importance and to describe the different planning levels trans- portation planning may constitute. Subsequently, we map the empty repositioning problem and present previous models carried out for this problem. We close this section with the motivation of this work.
2.1 Introduction to multi-modal transportation planning
Transportation planning has become a key component of the entire supply chain for many com- panies. The costs associated with transportation adds up to one third of the total logistics costs which emphasizes incentives for a cost efficient transportation coordination. The increasing pressure on companies to obtain higher profitability and operate more efficiently due to in- creasing competition makes the transportation planning even more important (Bhattacharyaa, 2014). Since the globalization has increased tremendously during recent decades and also new regulations making the international trade easier, new markets are rising where the produc- ers and customers are geographically apart from each other (Bhattacharyaa, 2014; Steadieseifi, 2014). In line with globalization, it is not possible to only transport by road, necessitating combinations of different modes i.e. multimodal transportation (Steadieseifi, 2014).
The existing literature in the research area for multimodal transportation problems is exten- sive. The multimodal transportation industry employs numerous application of optimization at the strategic, tactical, and operational level. The strategic level concerns problems related to investment decisions for the infrastructure of the transportation network. Tactical planning problems concerns the service network design of the infrastructure of the given network. These problems deal with issues related to the selection of routes on which services are offered and the allocation of resources to its demand. The planning problems associated with the operational level concerns the same issues described for tactical planning. But, for operational planning problems, real-time decisions are required. This makes the operational planning problems much more complex compared to strategic and tactical planning problems. An interested reader is recommended to read the paper conducted by Steadieseifi (2014) for an excellent review of multimodal transportation planning. This paper concerns the design of a planning system for an intermodal distribution network.
2.2 The empty repositioning problem
The literature domain of empty container repositioning may be classified into three different groups due to the research context. The first group focuses on seabourne networks ((Du and Hall, 1977), (Li et al., 2004) and (Song and Zhang, 2010)). The second group focuses on inland and intermodal transports and the third group includes empty repositioning as a subprob- lem ((Jula et al., 2006)). In general are intermodal networks more complicated compared to seaborne shipping networks. In addition is the time-scale between intermodal transportation
and seaborne shipping significantly different (Song and Dong, 2012). The subject of this work concerns inland and intermodal transportation. Subsequently, the literature from the second group will be emphasized in this section. In addressing the empty tank container repositioning problem, several decisons have to be taken under consideration. As previously mentioned, each decision belongs to a certain planning level. This is also shown in Figure 5. Braekers (2013) conducted an overview of the different planning levels for the problem under consideration. The main problem for each planning level is presented in the second column whereas the decisions related to these problems are presented in the third column. The arrows indicates the hier- archical relationship between these planning levels. At the strategic level, general policies are formed as guidelines for the next level; tactical planning. Similarly, will the tactical decisions set the framework for operational and real-time decisions (Braekers 2013; Crainic et al., 1993).
Figure 5: Overview of decisions for empty tank container repositioning (Braekers 2013; Crainic et al., 1993)
Strategic planning concerns long term decisions such as designing the physical network by deciding the locations for depots, cleaning stations and other facilities. At this level the size of the fleet is decided, customer zones are defined and general service policies are determined.
Tactical planing aims to secure an efficient allocation of the existing resources over a medium horizon. Typically, most of the decisions taken at this level concerns the problem of service network design. The following decisions should be included at the tactical level:
1. Service selection: the selection of routes/sections on which services are offered and the frequency of these services.
2. Distribution specification: specification for each origin-destination pair; service used, ter- minals passed through and operations/processes performed at terminals.
3. Empty balancing strategies: How empty container tanks have to be repositioned to meet future on-time delivery requirements.
4. Assignment of customer clusters to terminals: This assignment can be specified by the tank container type and the direction of the movement. The balancing flow should have
not be carried out in practical operations, it only indicates the magnitude of the balancing required over a given planning horizon.
5. Purchasing and leasing: Determination of number of tank containers to be brought in to the system form an external source or the amount to be returned and carried out from the system.
The operational level concerns problems in a highly dynamic environment. Two factor plays an important role at this level; time and the stochastic inherent of the system. The scheduling of services and the routing and dispatching of resources such as vehicles, tank containers and labour is considered at this level. Operational planning aims to make sure that all demands of empty tank containers are satisfied and to determine the transportation service in a cost efficient course of action as possible. In contrast to the tactical planing level, operational planning concerns the exact routing and allocation of resources in a real time fashion. Traditionally is the operational planning problem broken down into two separate optimization problems: (1) a container allocation problem and (2) a container routing model. The empty container allocation model aims to determine the best distribution among all locations in the system while making sure that the known and the predicted demand is satisfied. Given the distribution from the allocation model, the vehicle routing model aims to determine the most cost efficient routes (Braekers, 2013).
Empty repositioning problems were initially developed for empty freight cars in the railway industry. Misra (1972) (cited in Dejax and Crainic, 1987) addressed a deterministic model for freight cars distribution. The author provides an allocation model where the cost of correct- ing imbalances of empty freight cars are minimized. The problem was formulated as a linear program model and was solved with a solution approach based on the transport algorithm (Ford and Fulkerson, 1962) and the Simplex algorithm (Dantzig, 1963). White and Bomberault (1969)(cited in Crainic & Dejax, 1987) addressed a similarly problem as Misra (1972), modeling a linear program in a multi-period fashion. The introduction of dynamic time domains was a significant contribution to this research field (Dejax and Crainic, 1987).
Wang and Wang (2007) consider a multi-modal distribution network for ports and inland termi- nals including both demand and supply of empty containers to be meet. The authors presents a static integer program. Olivo et al. (2005) addressed an integer program for empty container repositioning between container depots and ports through an inland transportation network.
The integer program were solved by an linearisation technique.Shen and Khoong (1995) pro- posed a single-commodity simulation model applied under a rolling horizon fashion to minimize the total cost of empty containers. The problem were solved by a heuristic method.
An interesting work for empty repositioning was carried out by Choong (2002). The addressed model was developed in order to analyze the effect of the length of the planning horizon on empty container management for intermodal transportation. The research resulted in a single- commodity integer program allowing transportation via three different modes; barge, road and rail. Both long and short term container leasing are considered, however one drawback may be that the cost of short termed leased containers were considered to be independent of the lease term. The authors conclusions states that a longer planning horizon may allow higher utilization of slower cheaper modes, such as barge. The structure of this model is based on the deterministic single commodity model presented by Crainic et al. (1993) . The main difference between these two models is that Crainic et al. (1993) includes schedules for vessels and loaded moves in
the model and excludes the option of transportation via different modes and transportation capacities.
Newman and Yano (2000) addressed the problem of determining day-of-week scheduling con- tainers to be allocated for transportation via rail. The aim was to minimize total operating costs, including a fixed cost for each train, variable transportation and handling costs for each container and storage costs, while satisfying the demand from customers. To this aim empty moves were not included, however the model presented can easily consider demand as empty containers. The model presented is a deterministic linear integer program in a rolling horizon fashion. The solutions technique concerns a decomposition procedure that can be classified as classical heuristics.
Shintani et al. (2010) models the empty container flow as an integer program to optimize the empty repositioning in the hinterland. The authors shows the possibility to reduce operational costs through the use of foldable containers instead of standard containers.
An extension of the empty repositioning problem is to integrate assignments of loaded contain- ers. The demand of transporting loaded tank containers from a depot is rarely equal to the incoming flow of empty tank containers. Thus, the demand of empty movements arises from these unbalanced loaded movements. It is therefore natural to try to integrate these two types of movement into the same allocation model (Dejax and Crainic, 1987). Such models have been carried out by Errera (2009) and Karimi (2005). The former research resulted in a determinis- tic multi-commodity integer program. They solve the problem by a comercial solver and shows that integrating loaded assignments with empty moves in a single model can reduce both the fleet of containers and the operational cost. The later authors provided a deterministic linear program in a two-step event driven algorithm.
Crainic et al. (1993) presented a linear deterministic multi-period single-commodity model. In addition, the authors also address a deterministic mixed integer multi-period multi-period multi- commodity model. The models were developed in order to minimize total inland operational cost. Further, a mathematical formulation was introduced to deal with the stochastic nature of demand and supply of empty containers. Both loaded and empty moves are considered.
However, the authors did not present any results.
The problem considered by Deidda et al. (1987) includes the distribution of truck delivering loaded containers to import customers, the subsequent allocation of empty containers to export customers and the final dispatch of loaded containers to ports. The aim was to determine the allocation of empty tank containers and the routes for the trucks at a minimal operational cost.
A static integer program was presented.
To the best of our knowledge, no research have been reported to investigate the problem of empty repositioning in great details of a distribution network with the characteristics described in chapter 1. The current literature fails to capture many practical applications of distributing tank containers within this field. Such distribution system includes a number of different locations, each for different purposes. Train, port, and rail ship terminals enable terminal-to-terminal transits for intermodal transports, where rail ship terminals offers connections for both rail and sea. Cleaning stations and depots offers storage capabilities where the former also includes cleaning process. At an operational level the main concerns regards transportation via a certain modality, storage over space and time, matching the type of the tank container to product
requirements and ensuring suitable condition of the tank container. The relevant costs includes transportation, storage and customer demand backorder-costs. With this study we try to fill this gap and propose a mixed-integer linear programming (MILP) multiperiod optimization model is developed aiming to make tactical decisions for the empty tank container allocation problem. In this problem a set of empty tanks/supplies are unloaded at several unloading sites and transported via inland or intermodal moves to loading sites. The goal is to satisfy the demand of empty tank containers in a cost efficient course of action as possible.
3 Mathematical Theory
This section provides an introduction to network flow problems by describing and mathe- matically formulating some basic network flow problems.
3.1 Network flow problems
As previously mentioned, linear programs assumes that decision variables are continuous, x ∈ Rn. However, in the context of network flow problems such as the topic of this study, fractional values of the decision variables are not appropriate. In this situation should the decision vari- ables and their bounds be discrete, only holding integral values, x ∈ Zn. Below, we introduce some general network flow problems. Herein we do not emphasize whether or not the variables holds continuous or discrete integral values as this already has been discussed.
Networks appears in many different contexts. For instance, telephone networks allows us to communicate, electrical and power network brings light to our homes and manufacturing and distributions networks permits us easily access food and other products. Within these networks we wish to move some entity (e.g. product, message or electricity) from one point to another.
We seek to arrange these movements as efficiently as possible in order to provide good service to the end user at the lowest possible cost. Three commonly used network flow problems are stated below (Ahuja et al., 1993).
1. Minimum cost problem. Addresses the question of how a unit can be sent from one point to another to a minimal cost. Each route (arc) has a given cost and capacity.
2. Maximum flow problem. Given the capacities on each route (arc), how can we send as much as possible between two points without violating the capacities?
3. Shortest path problem. What is the shortest path from one point to another in a given network?
3.1.1 Minimum Cost Flow Problem
Let the graph G = (N, A) represent a directed network, where N is the set of nodes and A is the set of arcs. cij indicates the unit flow cost from node i to node j and uij represents the capacity, ij ∈ A. bi is a constant number, representing the demand (bi < 0) or supply (bi > 0) of node i. Let xij be the flow from node i to node j. The min cost flow problem can be formulated as below (Ahuja et al., 1993).
M in X
(i,j)∈A
cijxij, i, j ∈ A Subject to
X
j:(ij)∈A
xij − X
j:(ji)∈A
xji= bi, i ∈ N
0 ≤ xij ≤ uij, i, j ∈ A (1)
3.1.2 Distribution Problem
Supply chain management concerns management of material and information flow both in and between facilities such as manufacturing plants, vendors, distribution centers and retailers.
One of the main processes in a supply chain is the distribution and logistics planning (Lee et al. 2002). The distribution problem is a large class of network flow problems. A novel model may be described as the shipments from plants to retailers. This problem refers to a well-known special case of the min cost flow problem, named the transportation problem. Suppose that a car manufacturer has p number of plants where several car models m are manufactured. Let r represent the retailers demanding model m to be delivered. The objective is to obtain the flow that satisfies the demands in a cost efficient way as possible. The supplies and demands are assumed to be known. Figure 6 illustrates the problem.
Figure 6: Example of a production-distribution model (Ahuja et al., 1993).
Four different nodes is included in this network:
1. Plant nodes. Represents the various plants.
2. Plant/model nodes. Indicates model m to be manufactured at plant p.
3. Retailer/model nodes. Corresponds to the demand of retailer r of model m.
4. Retailer nodes. Represents retailer r.
The three types of arcs included in the network are as follows:
1. Production arcs. These arcs denotes the connection between plant nodes and a plant/model nodes. The associated cost of this arc represents the unit production cost of model m. It is possible to specify minimum and maximum production of each model from each plant by lower and upper bounds of these arcs.
2. Transportation arcs. These arcs connects plant/model nodes to retailer/model nodes.
The associated cost of this arc represents the unit transportation cost. These arcs may be included in a more complex distribution network. For instance, intermodal transportation requires at least three legs; (a) a delivery from a plant to a port via road; (b) a delivery from the port to another port by sea; (c) a delivery from the port to a retailer via road. The arcs may have upper and lower bounds imposed on their flow, representing the capacities specified by the contractual agreement with a logistical service provider.
3. Demand arcs. These arcs indicates the connection between retailer/model nodes and retailer nodes. The associated cost of this arc is zero and positive lower bounds equals the demand of model m from retailer r.
3.1.3 Transportation Problem
The transportation problem is a generalization of the min cost problem. For this problem the set of nodes N is divided into the two subsets N1 (supply nodes) and N2 (demand nodes). The number of nodes in these subsets is not necessarily equal. For each arc (i, j) in the set of arcs A ∈ N1 and and j ∈ N2. A classic example of the transportation is the distribution between warehouses and customers. In this example the set N1represents warehouses and N2 represents customers. An arc (i, j) in the set of arcs A represents a route from warehouse i to customer j (Ahuja et al., 1993).
4 Solution Methodology & Container Management Model
This section describes an empty tank container management model for an intermodal dis- tribution network, providing transportation planning proposals for repositioning of empty tank containers. A problem definition is provided, followed up by a mathematical formu- lation of the problem as a mixed-integer linear programming (MILP) model in a rolling horizon fashion. We provide three different scenarios for the model. Scenario 1 represents the generic empty container repositioning problem. Scenario 2 introduces some additional storage capacities to the terminals and so to the model. Scenario 3 considers both known and unidentified demand.
The first necessary step of this project conveyed a mapping of the current system. It was vital to map the companies logistic system and its operations in order to develop a service network model adequate for Hoyer’s transportation planning of empty moves. Thereby was the first step of the project to gain a fundamental understanding of Hoyers distribution network and its services; How is the distribution system structured, imbalances of loaded flow managed and what requirements are demanded by Hoyer’s customers? Answers to such questions were obtained during interviews with Hoyer. The project also included several progress meetings with Hoyer where the status of the project was updated, additional requirements added and the planning for the next steps scoped. These meetings were used as a foundation to develop the proposed model. Apart from the meetings with Hoyer, internal meetings at ORTEC have taken place.
These meetings included further decisions about in what course of action the project should proceed.
Other internal meetings included the topic of how to integrate the proposed model into ORD.
The contribution of these meetings lead to future ideas for the next steps that will take place after this project has been finalized. For instance, the idea of a ”sandbox environment” where ORD is connected to the proposed model in order to gain further knowledge about how the integration process should be performed in the future, was one result of these meetings. Further, it was decided to create a road map of the company’s planning procedures in a global perspective, not only focusing on empty moves. The road map would then be used to prioritize future implementation procedures and other improvements at Hoyer. The data gathering was an ongoing procedure until almost the end of the project. The complexity of gather adequate data stems from the fact that Hoyer is currently shifting from their older TMS system to ORD.
The obtained data was collected in the form of historically planning executions performed from 20150101 to 20160421.
Subsequently, this data was used to construct the distribution network and create samples of supply and demand of empty tank containers. As the data provides actual planning actions, further insights of the company’s operations were obtained by additional analysis. A profound discussion about the data collection will be presented in the case study of this work (Chapter 5). A literature review was conducted including different mathematical models and solutions techniques carried out in order to solve the empty container repositioning problem. The aim of this investigation was to find a basic model, adequate to the problem under consideration.
The basic model was subsequently adapted after the requirements provided by Hoyer in three different scenarios that will be presented later in this chapter. To solve the model in these scenarios we used the modeling software AIMMS combined with the CPLEX solver.
Problem description
This work centers on to designing a model for Hoyers’ intermodal distribution service network.
The model may facilitate decisions for the empty container management at a tactical level and help setting the framework for operational decisions. In order to provide a high service level and gain desired margins concurrently, the empty tank container management at Hoyer seeks to correct imbalances in a cost efficient course of action as possible while ensuring the on time delivery requirements are met. We consider transportation, storage and shortage costs.
We consider the company’s difficult problem of cost-efficiently repositioning empty tank con- tainers, given imbalanced trade flows. Typically, a logistics managers concerns regards the flow of loaded tank containers. Recall that a high loaded tank container utilization is crucial in this industry, given the high cost of the tank containers. As opposed to loaded transports, empty moves does not generate profit. Preferably, empty tank container management would not be considered at all. However, due to imbalances in loaded flows, the importance of empty container logistics becomes evident. The logistics in this aspect will have a direct impact on the profit margin. Minimizing these costly moves may reduce the operational cost considerably.
More specifically, the problem consists of deliver planning proposals regarding repositioning of empty tank containers, specifying the quantity, dimension (cbm), at what point in time, from what origin to what destination via a certain mode of transportation. These planning propos- als should in a cost efficient course of action as possible ensure the availability of empty tank container required to fulfill customers demand.
The physical network of Hoyers’ intermodal distribution system consists of depots, cleaning station, railway terminals, port terminals, rail ship terminals, supply customers (unloading sites) and demand customers (loading sites) and the transportation links between these locations.
This is illustrated by Figure 7. The figure also shows the possible alternatives of transportation modes between these locations, indicated by the arrows shape. The later part of the figure represents the possibilities to arrange shipments between the same type of location, for example may one depot be linked to another depot or several other depots. This model is developed in order to reallocate empty tank containers for a certain type of transportation order, namely spot orders. These orders regards standardized shipments. A request of a sport order is rarely rejected to be fulfilled. For precaution, we assume that any origin-destination pair associated with each of the three different modalities may have some transportation capacity limit.
It is important to distinguish between the locations presented in Figure 7. Each type of location can be distinguished to other types by its properties. Depots are mainly utilized for storage and cleaning stations for both storage and cleaning processes. A few depots and cleaning stations are controlled by Hoyer, mentioned as internal locations. The storage costs at these locations are relatively lower compared to external depots and cleaning stations. Railway, port and rail ship terminals provides the option for intermodal transportation, each with some corresponding mode or modes used for transportation.
Figure 7: Generalized distribution network for empty repositioning. Sections for every origin- destination pair are illustrated as directed links, the shape of the link indicates the modality.
Railway and port terminals are self descriptive whereas rail ship terminals requires some expla- nation. As indicated by Figure 7, rail ship terminals includes the option for both trains and ferries to arrive and depart from its terminal. The storage capacity of the empty tank containers is unlimited at cleaning stations and depots, in terms of the amount of empty tank containers to be stored. In contrast to this have intermodal terminals limited storage capacity. Further, we distinguish between demand and supply customers. Supply customers provides empty tank containers that becomes available after unloading of the products, while demand customers requires empty tank containers to be delivered to its site for loading of products. Note that the same customer can be both a demand and a supply customer.
The total supply of empty tank containers is made up of the stocks stored at each location, the amount in transit and the number of containers available for pick up at supply customer sites.
Tank containers cannot be stored at demand customer sites to fulfill future demand. Neither is storage at supply customers sites allowed. This implies that an available tank container at supply customer must be picked up in the same time period it is unloaded. It is possible to distribute empty tank containers from supply customer sites to all locations except demand customer sites. Customer s is linked to depots j, cleaning stations c, railway terminal r, port terminal p and rail ship terminal v in Figure 7.
Recall that distribution of chemical products requires matching of the tank containers function- alities and its dimensions to the products demanded to be shipped. Nevertheless are cleaning processes also necessary since demand customers often requires cleaned tank containers. For this reason, it is assumed that a dirty empty tank container is always sent to a cleaning station for a cleaning process before reloading at demand customer sites. In addition, a number of
legal requirements needs to be taken into account. This is of great importance to be able to ensure the safety of the shipment and quality of the product. For simplicity, only the condition (dirty, clean) and the volume (cbm) of the tank containers is taken into account in the model.
All other quality, safety and legal requirements are excluded. The span of different dimensions are assumed to be aggregated into different classes, indicated by Table 1. This is logical since Hoyer aggregates similarly while managing empty moves.
Classes A B C D E
Dimensions (cbm)
≤ 22.6 [22.7-24.5] [24.6 - 27.5] [27.6 - 32.5] ≥ 32.6
Table 1: Tank container classification, specified by its dimensions (cbm).
The demand of empty tank containers is assumed to be known and the length of the planning period horizon is determined to a certain length, assuring that the supply of empty tank con- tainers is known. Therefore can we also assume that the supply of empty tank containers is known. When the supply is insufficient and it is not time wise possible to reallocate empty tanks to demand customers, an emergency shipment from a resource outside the system is executed and will be indicated as a shortage in the model.
Mathematical formulation
The model we are proposing for this problem is in line with the modeling structure that Crainic et al. (1993) and Choong (2002) have used for their researches. That is a dynamic network model, applied in a rolling horizon framework. We propose a mixed integer program using the notations described later on in this section. Assumptions necessary to postulate are as follows:
1. The storage capacity at depots and cleaning stations are assumed to be unlimited.
2. Empty tank containers located at supply customer sites are always available for pick up and it is not possible to store at these sites.
3. If the demand of empty tank containers cannot be fulfilled, then an emergency transport is executed.
4. All shipment modes are assumed to have a certain capacity.
5. The supply and demand of empty tank containers are known for each type of container in any given time period.
6. Shipments to supply customers is not allowed in the model. The transportation cost for these shipments are infinite.
7. A container is assumed to always be dirty after unloading at a supply customer site.
8. A dirty tank container is never distributed to a demand customer.
9. It is assumed that the demand of empty tank containers are independent of the product type.
10. At all location where storage is allowed, the option for storage is independent of the condition of the tank container, it may be dirty or clean.
11. The option to store a tank container is independent of its condition.
12. Arrivals and departures to and from a location, respectively, take place in the beginning of the time period.
13. The unit transportation and the unit storage cost are assumed to be independent of the dimension and the condition of the tank container.
14. Transportation from a location to itself is not allowed. In the model, the cost for these shipments are infinite.
