Production, Manufacturing and LogisticsOutbound supply chain network design with mode selection, lead times and capacitated vehicle distribution centers
Introduction
The outbound supply chain network of an automotive company, shown in Fig. 1, consists of the activities involved in transporting finished vehicles from the assembly plants to dealers. Vehicle distribution centers (VDCs) are used to consolidate and distribute vehicles from different plants to dealers. However, for long-term planning purposes, individual dealerships are aggregated into demand areas that are county-level geographic areas that cover essentially the entire North American auto market. Each assembly plant produces a different vehicle type with some plants producing more than one type within the same facility. All vehicle types from the same plant are delivered to a destination using the same transportation mode to take advantage of economies of scale and to simplify the delivery process (e.g., loading, unloading, tracking, etc.) of the vehicles. Therefore, different vehicle types produced in a plant are aggregated into one type. Vehicles produced in the plants are delivered to demand areas via one of two basic modes (see Fig. 1). Vehicles can be loaded on to trains at the plants and delivered to vehicle distribution centers (VDCs). They are then loaded on to trucks at the VDCs and sent to dealers. Vehicles can also be delivered directly from plants to dealers by truck, if the demand area is relatively close to the plant.
An important development in the automotive industry in recent years has been an increased interest in reducing the lead-time required to deliver vehicles from the assembly plants to the customer. The potential benefits of lead-time reduction in supply chain management have been widely documented, and include responsiveness to market changes, reduced pipeline inventory and improved customer satisfaction. The lead-time required to move vehicles through the outbound supply chain is the sum of the lead times at the nodes of the network (plants and vehicle distribution centers) and the transportation time. The lead-time at the nodes, in turn, is affected by the volume of flow through each node. Hence we study a network design model that includes lead-time related costs as well as the more traditional fixed costs of locating facilities and transportation costs.
In the network design model of an outbound supply chain with capacitated VDCs, the decisions to be taken can be outlined as follows:
- (1)
Where should the vehicle distribution centers (VDCs) be located?
- (2)
What should the size (capacity) of the VDCs be?
- (3)
How should the vehicles be delivered to demand areas, by trucks or through a VDC?
- (4)
What should the volume at each distribution location be?
The objective function is to minimize total cost, given by the sum of transportation cost, lead-time cost and fixed costs.
This research extends our previous work (Eskigun et al., 2001) by considering capacity restrictions on VDCs in the form of a limit on the number of vehicles delivered through a single VDC over a planning period. The imposition of a capacity limit at each VDC is important to prevent an excessive number of vehicles being delivered through a single VDC, causing congestion in the facility and increasing the total delivery lead-time for the network. The size of a VDC does not affect the fixed cost of establishing a new VDC, which is independent of the volume of vehicles delivered through the VDC.
In the remainder of this paper we first review previous related work and then present the network design model with capacitated VDCs. A solution algorithm based on Lagrangian relaxation is given in Section 4, and a number of scenario analyses are discussed in Section 5. We conclude with future research directions in Section 6.
Section snippets
Previous related work
In the United States, non-military logistics costs are estimated to be over 11% of the Gross National Product (GNP) and constitute about 30% of the cost of the products sold (Thomas and Griffin, 1996). Hence, an extensive literature addresses the coordination of logistics operations and the design of effective production and distribution systems. This body of work includes Bluemenfeld et al. (1987), Brown et al. (1987), Cohen and Lee (1988), Van Roy (1989), Benjamin (1990), Chandra and Fisher
Capacitated network design model (NDMC)
Our capacitated network design model (NDMC) is a static model in the sense that it considers a fixed set of demands that have to be met by the outbound supply chain throughout the planning period. While it is clearly desirable to incorporate time-varying stochastic demands, the sheer size of the problem faced in the industrial context renders it computationally difficult to address these issues directly. Hence we choose to begin by developing a static deterministic model, which will permit us
Solution approach
NDMC is a large-scale integer linear programming (ILP) model. The size of the problem instance increases as O(IJK) with an increase in the number of plants I, the number of possible VDC locations J, and the number of demand areas K. Hence, it is impractical to obtain exact solutions for NDMC in reasonable computational time. We have thus developed a Lagrangian heuristic to obtain near-optimal solutions in short computation times.
In our Lagrangian heuristic some of the complicating constraints
Scenario analyses
Scenario analyses are conducted to evaluate the performance of LH-NDMC and to observe how the supply chain behaves under different conditions. In all scenarios, industrial data representing a substantial portion of the company's actual network is used. The monetary value of the lead-time and the capacity limits on the number of vehicles delivered through a single VDC are varied so that their effects on some supply chain performance indicators are observed. In total, 56 scenarios are generated
Conclusions and future directions
We have developed a large-scale network design model for the outbound supply chain of an automotive company. Since delivering high volume of vehicles through a single VDC might result in inefficiencies and congestion in the system, fixed capacity limits are considered on the number of vehicles delivered through a VDC. It is, however, assumed that the dwell time at plants and VDCs consists of a constant component and a load make-up time component. A Lagrangian heuristic is developed to solve
Acknowledgements
This research was supported by General Motors Research and Development and the National Science Foundation under Grant No. DMI-9634914.
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