Transshipment Network Research Articles

Applying Network Flow Optimization Techniques to Improve Relief Goods Transport Strategies under Emergency Situation

Given the seriously damaged emergency situation occurring after a large-scale natural disaster, a critical and important problem that needs to be solved urgently is how to distribute the necessary relief goods, such as drinking water, food, and medicine, to the damaged area and how to transport them corresponding to the actual supply and demand situation as quickly as possible. The existing infrastructure, such as traffic roads, bridges, buildings, and other facilities, may suffer from severe damage. Assuming uncertainty related with each road segment’s availability, we formulate a transshipment network flow optimization problem under various types of uncertain situations. In order to express the uncertainty regarding the availability of each road segment, we apply the Monte Carlo simulation technique to generate random networks following certain probability distribution conditions. Then, we solve the model to obtain an optimal transport strategy for the relief goods. Thus, we try to implement a necessary and desirable response strategy for managing emergency cases caused by, for example, various natural disasters. Our modeling approach was then applied to the actual road network in Sumatra Island in Indonesia in 2009, when a disastrous earthquake occurred to develop effective and efficient public policies for emergency situations.

Stability and Endogenous Formation of Inventory Transshipment Networks

This paper studies a cooperative game of inventory transshipment among multiple firms. In this game, firms first make their inventory decisions independently and then decide collectively how to transship excess inventories to satisfy unmet demands. In modeling transshipment, we use networks of firms as the primitive, which offer a richer representation of relationships among firms by taking the coalitions used in all previous studies as special cases. For any given cooperative network, we construct a dual price allocation under which the network is stable for any residual demands and supplies in the sense that no firms find it more profitable to form subnetworks. Under the allocation based on the marginal contribution of each firm to its network (called the MJW value), we show that various network structures such as complete, hub-spoke, and chain networks are stable only under certain conditions on residual amounts. Moreover, these conditions differ across network structures, implying that a network structure plays an important role in establishing the stability of a decentralized transshipment system. Finally, we consider the case when firms establish networks endogenously, and show that pairwise Nash stable networks underperform the corresponding networks in centralized systems.

A dynamic inventory model with supplier selection in a serial supply chain structure

Considering the inherent connection between supplier selection and inventory management in supply chain networks, this article presents a multi-period inventory lot-sizing model for a single product in a serial supply chain, where raw materials are purchased from multiple suppliers at the first stage and external demand occurs at the last stage. The demand is known and may change from period to period. The stages of this production–distribution serial structure correspond to inventory locations. The first two stages stand for storage areas for raw materials and finished products in a manufacturing facility, and the remaining stages symbolize distribution centers or warehouses that take the product closer to customers. The problem is modeled as a time-expanded transshipment network, which is defined by the nodes and arcs that can be reached by feasible material flows. A mixed integer nonlinear programming model is developed to determine an optimal inventory policy that coordinates the transfer of materials between consecutive stages of the supply chain from period to period while properly placing purchasing orders to selected suppliers and satisfying customer demand on time. The proposed model minimizes the total variable cost, including purchasing, production, inventory, and transportation costs. The model can be linearized for certain types of cost structures. In addition, two continuous and concave approximations of the transportation cost function are provided to simplify the model and reduce its computational time.

Economically optimal crop sequences using risk-adjusted network flows: Modeling cotton crop rotations in the southeastern United States

Crop rotation is a long-standing agricultural practice whose agronomic and economic benefits are well documented. The crop rotation decision at the farm level is very complex with a myriad of factors which can ultimately impact observed net returns from the decision choice. Network models have been proposed as one method of modeling this decision problem in a logically consistent framework. The aspect of this problem considered in this article is how to incorporate not only expected net returns from alternative rotation sequence choices, but also the relative impacts of net income risk on the decision process. A transshipment network formulation of the crop rotation decision problem is presented with the incorporation of risk constraints, providing the ability to derive sets of optimal solutions, allowing the decision maker to select optimal crop rotation sequence sets based upon net income risk preferences.

A fuzzy AHP based integer linear programming model for the multi‐criteria transshipment problem

PurposeThe purpose of this research is to develop a holistic approach to maximize the customer service level while minimizing the logistics cost by using an integrated multiple criteria decision making (MCDM) method for the contemporary transshipment problem. Unlike the prevalent optimization techniques, this paper proposes an integrated approach which considers both quantitative and qualitative factors in order to maximize the benefits of service deliverers and customers under uncertain environments.Design/methodology/approachThis paper proposes a fuzzy‐based integer linear programming model, based on the existing literature and validated with an example case. The model integrates the developed fuzzy modification of the analytic hierarchy process (FAHP), and solves the multi‐criteria transshipment problem.FindingsThis paper provides several novel insights about how to transform a company from a cost‐based model to a service‐dominated model by using an integrated MCDM method. It suggests that the contemporary customer‐driven supply chain remains and increases its competitiveness from two aspects: optimizing the cost and providing the best service simultaneously.Research limitations/implicationsThis research used one illustrative industry case to exemplify the developed method. Considering the generalization of the research findings and the complexity of the transshipment service network, more cases across multiple industries are necessary to further enhance the validity of the research output.Practical implicationsThe paper includes implications for the evaluation and selection of transshipment service suppliers, the construction of optimal transshipment network as well as managing the network.Originality/valueThe major advantages of this generic approach are that both quantitative and qualitative factors under fuzzy environment are considered simultaneously and also the viewpoints of service deliverers and customers are focused. Therefore, it is believed that it is useful and applicable for the transshipment service network design.

Stability and Endogenous Formation of Inventory Transshipment Networks

This paper studies a cooperative game of inventory transshipment among multiple rms. In this game, rms rst make their inventory decisions independently, and then decide collectively how to transship excess inventories to satisfy unmet demands. In modeling transshipment, we use networks of rms as the primitive, which o¤er a richer representation of relationships among rms by taking the coalitions used in all previous studies as special cases. For any given cooperative network, we construct a dual price allocation under which the network is stable for any residual demands and supplies in the sense that no rms nd it more pro table to form subnetworks. Under the allocation based on the marginal contribution of each rm to its network (called the MJW value), we show that various network structures such as complete, hub-spoke, and chain networks are stable only under certain conditions on residual amounts. Moreover, these conditions di¤er across network structures, implying that a network structure plays an important role in establishing the stability of a decentralized transshipment system. Finally, we consider the case when rms establish networks endogenously, and show that pairwise Nash stable networks underperform the corresponding networks in centralized systems. Subject classi cations: Games/group decisions: Cooperative. Networks. Inventory. Area of review: Manufacturing, Service, and Supply Chain Operations.

An Efficient and Robust Design for Transshipment Networks

Transshipment, the sharing of inventory among parties at the same echelon level of a supply chain, can be used to reduce costs. The effectiveness of transshipment is in part determined by the configuration of the transshipment network. We introduce chain configurations in transshipment settings, where every party is linked in one connected loop. Under simplifying assumptions we show analytically that the chain configuration is superior to configurations suggested in the literature. In addition, we demonstrate the efficiency and robustness of chain configurations for more general scenarios and provide managerial insights regarding preferred configurations for different problem parameters.

Enhanced Adjacent Extreme-point Search and Tabu Search for the Minimum Concave-cost Uncapacitated Transshipment Problem

Practicable methods for optimising concave-cost, uncapacitated transshipment networks are non exact. In this paper, one such effective method, that of adjacent extreme point search, is further developed to enhance its overall computational efficiency. The enhanced search algorithm is then imbedded in a tabu search scheme which proved capable of finding better solutions, by a wide margin in some instances. Another tabu search scheme, somewhat inferior in terms of solution quality but computationally more efficient, is also developed to provide an alternative solution vehicle for larger networks. Results of extensive computational testing are included.

Optimal expansion of capacitated transshipment networks

Optimal expansion of capacitated transshipment networks

Optimal expansion of capacitated transshipment networks

In this paper, we address the problem of allocating a given budget to increase the capacities of arcs in a transshipment network to minimize the cost of flow in the network. The capacity expansion costs of arcs are assumed to be piecewise linear convex functions. We use properties of the optimum solution to convert this problem into a parametric network flow problem. The concept of optimum basis structure is used which allows us to consider piecewise linear convex functions without introducing additional arcs. The resulting algorithm yields an optimum solution of the capacity expansion problem for all budget levels less than or equal to the given budget. For integer data, the algorithm performs almost all computations in integers. Detailed computational results are also presented.

A Review of Sensitivity Results for Linear Networks and a New Approximation to Reduce the Effects of Degeneracy

Estimating the reduced cost of an upper bound in a classical linear transshipment network is traditionally accomplished using the shadow price for this constraint, given by the standard calculation c̄ıj = cij + πj − πı. This reduced cost is only a subgradient due to network degeneracy and often exhibits errors of 50% or more compared to the actual change in the objective function if the upper bound were raised by one unit and the network reoptimized. A new approximation is developed, using a simple modification of the original reduced cost calculation, which is shown to be significantly more accurate. This paper summarizes the basic theory behind network sensitivity, much of which is known as folklore in the networks community, to establish the theoretical properties of the new approximation. The essential idea is to use least-cost flow augmenting paths in the basis to estimate certain directional derivatives which are used in the development of the approximation. The technique is motivated with an application to pricing in truckload trucking.

Regional Solid Waste Planning with WRAP

In spite of the abundance of mathematical models for solid waste management, planners and decision makers have been reluctant to use such models due to the difficulties in understanding and implementing them. An Environmental Protection Agency sponsored computer program, Waste Resource Allocation Program (WRAP), is aimed at this problem. WRAP greatly facilitates regional solid waste planning with its simple input requirements and clear output. By using Walker's fixed charge linear programming algorithm, WRAP occasionally finds global optima even to solid waste management schemes that are formulated as capacitated transshipment networks with concave costs and flows with losses. A case study using Region J in North Carolina is presented.

Graph Structures Underlying Submatrices of Network Flow Tableaux

This paper analyzes the substructure of linear programming tableaux for capacitated transshipment problems. Specifically, it demonstrates that submatrices of these tableaux correspond in a precise way to certain “contractions” of the transshipment network. The results are couched within the GNET/Depth network data structure of Bradley, Brown and Graves or the predecessor/thread/distance structure of Glover, Klingman, et al. An application to fixed-charge network problems is described.

Global Solutions for a Nonconvex Nonconcave Rail Network Model

This paper is concerned with developing long-range planning models of transportation systems to assist planners in assessing the impact of various levels of service in a transportation network. Railroad distribution networks are studied in particular, and emphasis is placed on the problem of determining optimal levels of service (improvements, degradations, abandonments) on each arc in the existing network. The problem is to optimally design a transportation system: the term “design” as used here, does not comprehend new networks, but more importantly, the optimization or “pruning” of existing transshipment networks. The model is formulated so that improvements to the shipping arcs are included as decision variables: The concave transshipment problem is extended to the case where coefficients of the shipping cost functions are treated as decision variables. Thus the model determines optimum movements of freight between nodes and optimum improvements/degradations to the network to minimize shipping costs plus maintenance costs on the shipping arcs. The result is a nonconvex, nonconcave transshipment problem which is then converted into a concave minimization problem for which global optimal solutions can be found. Several sample problems are solved.

An extension of the (szwarc) truck assignment problem

AbstractIn this journal in 1967. Szware presented an algorithm for the optimal routing of a common vehicle fleet between m sources and n sinks with p different types of commodities. The main premise of the formulation is that a truck may carry only one commodity at a time and must deliver the entire load to one demand area. This eliminates the problem of routing vehicles between sources or between sinks and limits the problem to the routing of loaded trucks between sources and sinks and empty trucks making the return trip. Szwarc considered only the transportation aspect of the problem (i. e., no intermediate points) and presented a very efficient algorithm for solution of the case he described. If the total supply is greater than the total demand, Szwarc shows that the problem is equivalent to a (mp + n) by (np + m) Hitchcock transportation problem. Digital computer codes for this algorithm require rapid access storage for a matrix of size (mp + n) by (np + m); therefore, computer storage required grows proportionally to p2. This paper offers an extension of his work to a more general form: a transshipment network with capacity constraints on all arcs and facilities. The problem is shown to be solvable directly by Fulkerson's out‐of‐kilter algorithm. Digital computer codes for this formulation require rapid access storage proportional to p instead of p2. Computational results indicate that, in addition to handling the extensions, the out‐of‐kilter algorithm is more efficient in the solution of the original problem when there is a mad, rate number of commodities and a computer of limited storage capacity.

Dynamic transshipment networks: An algorithm and its application to the distribution of empty containers

AbstractThe movement of vehicles and goods in a transportation system can be represented as flows through a time‐dependent transshipment network. An inductive out‐of‐kilter type of algorithm is presented which utilizes the basic underlying properties of the dynamic transshipment network to optimize the flow of a homogeneous commodity through the network, given a linear cost function. The algorithm is illustrated by its application to the problem of distributing empty containers from locations at which they are available to locations at which they are required.

Decentralized Transshipment Networks

In the usual formulation of the transshipment problem it is assumed that a single decision-maker is dealing with a unified network of nodes and arcs and that supply and demand levels at each source are determined a priori. This paper develops a transshipment model in which subnetworks are controlled by a decentralized management level and supply levels at each source node are to be determined by a central manager.