Reduction of Empty Container Repositioning Costs by Container Sharing

Transcription

1 Reduction of Empty Container Repositioning Costs by Container Sharing Herbert Kopfer and Sebastian Sterzik 1 Problem Description Empty container repositioning is a major cost driver for international container operators. While the share of empty containers of total sea-based container flows is around 20%, consultants estimate the rate of empty container transport for the hinterland even twice as high [1]. As [4] stated, most of the routes in the hinterland consist of pendulum tours comprising one full and one empty container move between the port, a trucking company s depot and the customers (receiver/shipper). Solutions to shrink the amount of empty container movements focus on moving empty containers which are available at some customer locations directly to places where they will be needed next. Based on this approach, this contribution investigates the rising possibilities to reposition empty containers in the seaport hinterland if trucking companies cooperate with each other. In the following we present two scenarios and solve several data sets to quantify the emerging cost savings for companies who exchange their empty containers. Both scenarios lead to an integrated model considering empty container repositioning and vehicle routing simultaneously. Imagine a hinterland transportation scenario (see Figure 1) in which full and empty containers have to be moved between different locations by at least two trucking companies. Each trucking company serves its own customer base with a homogeneous fleet of vehicles. We assume 40-feet-containers, i.e. a vehicle can only move one container at a time. The fleet is parked at a depot in which, moreover, empty containers can be stacked. Each vehicle starts and ends its tour at the depot of its trucking company. Additionally, it is assumed that there is a seaport terminal to which the trucks carry full and empty containers from customers places and vice versa. Time windows at the terminal as well as time windows at the customer nodes need to be taken into account. We distinguish two types of customers. On the one hand shippers offer freight which is to be transported to a foreign region via the seaport. The flow of a full container from the shipper to the terminal is defined as outbound full (OF) container. On the other hand receivers require the transport of Chair of Logistics, Department of Economics and Business Studies, University of Bremen, Wilhelm-Herbst-Str. 5, Bremen, Germany, {kopfer, sterzik}@uni-bremen.de 1

2 2 Herbert Kopfer and Sebastian Sterzik Fig. 1 Basic Scenario their goods from an outside region via the terminal. The flow of a full container from the terminal to the receiver is called inbound full (IF) container. It is obvious that a shipper requires an empty container before he can fill the freight in it. Additionally, an empty container remains at the receiver s location after the IF container is emptied. We define two time windows at each customer location: During the first time window the full/empty container has to be delivered to the customer location. After the container is emptied/filled, it can be picked up by a vehicle during the second time window. Moreover, trucking companies have to consider two additional transportation requests. Due to the imbalance between import- and export-dominated areas, they need to take care of outbound empty (OE) or inbound empty (IE) containers which either have to be moved to the terminal or derive from it. For these requests only the terminal as the destination or as the origin is given in advance. Hence, the locations that can provide empty containers for the OE requests and the destinations for the imported empty containers need to be determined during the solution process. This scenario was defined by Zhang et al. (2009) as the multi-depot container truck transportation problem (CTTP) [5]. The objective is to minimize the carriers total fulfillment costs consisting of fixed and variable costs. Hence, in a first step the number of used vehicles should be minimized while in the second step the optimization of the vehicles total operating time symbolizing the transportation costs should be pursued [3]. In this paper the first objective is formulated as a constraint and the minimization of the operating time is chosen as the objective function of our models. Thereby, the number of used vehicles within the employed models is raised iteratively until a feasible solution is found. The resulting solution approach leads to an integrated model which does not only consider vehicle routing but also empty container repositioning. Thus, solving the problem determines: a) where to deliver the empty containers released after inbound full/empty loads, b) where to pick up the empty containers for outbound full/empty loads, and c) in which order and by which truck the loads should be carried out. In this paper, two scenarios for the hinterland transportation are analyzed. In the first scenario empty containers are uniquely assigned to trucking companies, i.e. they can solely be used by the company they are assigned to. For instance, an empty container obtained at a receiver location served by a certain trucking company can exclusively be used for transportation requests of this company. This scenario is given by the above CTTP. In the second scenario companies can use empty containers of cooper-

3 Reduction of Empty Container Repositioning Costs by Container Sharing 3 Fig. 2 Possible Benefits through Container Sharing ating trucking companies. I.e. companies share their information at which locations empty containers are currently stacked and they agree with the mutual exchange of these containers. Thus, the cooperating companies can improve their routes and increase their profit by decreasing transportation costs in return. The permission of sharing empty containers among trucking companies leads to the multi-depot container truck transportation problem with container sharing (CTTP-CS). Figure 2 demonstrates the rising possibilities to reposition empty containers of two trucking companies cooperating with each other. Trucking company 1 has to serve a receiver and needs to move an IE container to the hinterland. Trucking company 2 has to serve a shipper and needs to move an OE container to the terminal (see Figure 2 (a)). In the non-cooperative case, as illustrated in Figure 2 (b), the only opportunity for both companies to reposition empty containers is moving them either to (trucking company 1) or from (trucking company 2) their own depot. If the exchange of containers is permitted, both companies could benefit through the emerging additional flexibility to allocate empty containers to a vehicle s tour (see Figure 2 (c)). The amount of the benefit of a cooperation highly depends on time and place conditions given by the time windows for pickup and delivery and by the locations of the terminal and customers. 2 Simultaneous Solution Approach Let V denote the nodes of a directed graph, consisting of customer node set V C, terminal node set V T and depot node set V D. There are two types of customers (V C = V S V R ), the node sets V S = V S i V S o and V R = V R i V R o describe the shipper and the receiver node sets. V S i and V R i refer to the first time window of the shipper/receiver, in which an empty/full container has to be made available. After the container has been completely filled or emptied, respectively, container c C can be picked up by a vehicle k K during the second time window (V S o and V R o). The terminal node set V T consists of V T i and V T o which correspond to the amount of ingoing and outgoing

4 4 Herbert Kopfer and Sebastian Sterzik containers. The number of all customer and terminal nodes is defined by n. In the trucking companies depots a large number a of empty containers can be stacked. Hereby, the depot set V D is subdivided into the start and end depot node sets V D s and V D e. Node i V C V T has to be reached during its time window, determined by the interval[b i /e i ]. We consider d trucking companies. The trucking company of vehicle k and customer i, respectively, is determined by d k and d i. For each two distinct stop locations, t i j represents the travel time from location i to location j. At node i V C V T a service time s i for the loading/unloading operation of a container is considered. While the binary decision variables y i jc and x i jk define whether container c/vehicle k traverses the arc from location i to j, L ic and T ik specify the arrival time of a container/vehicle at a location. minz= (T (n+d+dk )k T (n+dk )k) (1) k K c C i V c C R i V S i V D e c C i V c C y i jc = 1 i V C V T i (2) y i jc = 1 j V T o (3) i V D s c C y i jc = 1 i V T i (4) y i jc = a (5) y i jc = 1 j V T o V D e (6) y i jc y i jc = 0 i V C,c C (7) L jc L ic +t i j + s i M(1 y i jc ) i, j V,c C (8) k K x i jk = 1 i V C V T (9) x (n+dk ) jk = 1 k K (10) x i(n+d+dk )k = 1 k K (11) i V x jik x i jk = 0 i V C V T,k K (12) T jk T ik +t i j + s i M(1 x i jk ) i, j V,k K (13) b i T ik e i i V C V T,k K (14) x i jk d k = x i jk d i i V C V T, j V,k K (15) x i jk y i jc i V S o V R o V T, j V,c C (16) k K

5 Reduction of Empty Container Repositioning Costs by Container Sharing 5 x i jk y i jc i V C V T, j V S i V R i V T V D e,c C (17) k K T ik = L ic i V C V T,k K,c C (18) x i jk,y i jc 0,1 i, j V,k K,c C (19) T ik,l ic : real variables i V,k K,c C (20) By considering empty container repositioning on the one hand (2-8) and vehicle routing and scheduling (9-15) on the other hand, the presented model pursues the minimization of the vehicles total travel time. Since a container cannot drive on its own, it has to be assured that every container is transported by a vehicle. Equations (16)-(18) require that the vehicles are interlinked with the containers and that both pass every location at the same time. Thereby, the vehicles cover the containers routes but can skip the filling and emptying process of the container at a customer location. Restrictions (2)-(3) and (9) assure that every customer node is visited once and that a container enters/leaves the terminal nodes according to the number of outbound and inbound containers. While a vehicle starts and ends its route at the corresponding depot of the trucking company (10-11), the start and end node of a container can either be the terminal or the depot (4-6). Furthermore, the route continuity (7 and 12) and the time restrictions (8 and 13-14) have to be held. Restriction (15) defines the CTTP in which container sharing is not permitted. If the exchange of empty containers is allowed (CTTP-CS), the equation changes to: x i jk d k = x i jk d i i V S V R i V T o, j V,k K (21) 3 Computational Results We generated ten test instances based on Solomon s benchmark vehicle routing problem with time windows data sets [2]. Each data set consists of two trucking companies, five customer clusters (comprising one shipper and one receiver) and, additionally, one IE container and one OE container whereat each company has to serve six requests. To fit the factor that a cooperation is more profitable if the customer and terminal nodes are located close to each other, we randomly chose a coordinate for each customer type from one cluster of the c1-solomon data sets. According to Figure 2 the receiver and the shipper of a cluster belong to different trucking companies. Moreover, we adapted the time windows of these customers so that the receiver s second time window is consistent with the shipper s first time window. The obtained results in Table 1 indicate that the rising possibilities to reposition empty containers within a cooperation can lead to a huge reduction of fulfillment costs. Regarding the fixed costs, remarkable 37% less vehicles are used in the CTTP-CS compared to the CTTP on average. Besides, a reduction of 38% according to the number of used containers can be determined. The variable costs illustrated by the total travel time are decreased by 23%.

6 6 Herbert Kopfer and Sebastian Sterzik Table 1 Benefit of Container Sharing Data Set CTTP (Objective value/ CTTP - CS (Objective value/ Benefit of container Number of used vehicles/ Number of used vehicles/ sharing according to the Number of used containers) Number of used containers) objective values / 12/ / 8/ % / 12/ / 6/ % / 12/ / 8/ % / 12/ / 8/ % / 12/ / 8/ % / 12/ / 10/ % / 12/ / 8/ % / 12/ / 6/ % / 12/ / 8/ % / 12/ / 6/ % 4 Conclusions In this contribution, we illustrated the potential of container sharing in the hinterland of seaports. By implementing a holistic solution approach which considers empty container repositioning and vehicle routing and scheduling simultaneously, remarkable savings regarding fixed and variable costs could be obtained. However, the data sets were modified to highlight the advantages of the CTTP-CS compared to the CTTP. In a further step, we are going to develop heuristic approaches in order to analyze the benefit of a cooperation in bigger test instances and to investigate the precondidtions for successful container sharing scenarios. References 1. R. Konings. Foldable containers to reduce the costs of empty transport? a costbenefit analysis from a chain and multi-actor perspective. Maritime Economics & Logistics, 7:223249, M. M. Solomon. Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35(2): , R. Vahrenkamp. Logistik: Management und Strategien. Oldenbourg, Munich, 6th edition, A. W. Veenstra. Empty container repositioning: the port of Rotterdam case, chapter 6, pages Springer, Heidelberg, R. Zhang, W.Y. Yun, and I. Moon. A reactive tabu search algorithm for the multi-depot container truck transportation problem. Transportation Research Part E: Logistics and Transportation Review, 45(6): , Acknowledgements This research was supported by the German Research Foundation (DFG) as part of the Collaborative Research Centre 637 Autonomous Cooperating Logistic Processes - A Paradigm Shift and its Limitations (Subproject B7).