(518e) Supply Chain Design Under Uncertainty With Time-Limited Transportation Contracts

A supply chain (SC) system is a network of facilities and operations involving raw material procurement, processing, and distribution to warehouses and customers. The main goal of the supply chain system is to satisfy the customer demand with a minimal cost. Increased market competition has tightened the profit margin in the chemical process industry, increasing the importance of cost-effective supply chain design and operation (You and Grossmann, 2008; Laínez et al., 2007).

This work considers design of supply chains under demand uncertainty. Most of the approaches presented in the literature optimize the SC network design by specifying a network superstructure and examining different combinations of node connections to maximize the net present value (NPV) of the system over a given time horizon. A predefined network superstructure restricts the opportunity of improving the net present value (NPV) of the supply chain by eliminating some of the node linkages. In order to improve the profitability of the supply chain, Lainez at al. (2009) presented a supply chain design approach, where they considered all possible node connections in the optimization formulation, with the selection of optimum node connections included as optimization decisions.  In many cases, the cost associated with the establishment of a transportation link is relatively small, in which case the transportation links could be changed if it is beneficial in terms of increasing the NPV of the supply chain. Ideally these links should be selected independently across time periods; however business practice may preclude this as transportation costs are generally determined based on the transportation quantities and duration of service. The minimum amount of time the transportation service has to be utilized is often determined by a transportation contract period and should be considered in the optimization formulation to calculate the cost. In this work, we proposed to incorporate such contractual linkage agreement information in the supply chain design phase.

We define the network design based on a model adapted from You and Grossmann (2008).  The transportation contracts are modeled using a formulation presented in Kelly and Zyngier (2007).  This formulation defines time markers for contract start and end times without introducing new binary variables, which is computationally advantageous.  A further aspect of this work is the handling of demand uncertainty though the use of a two-stage stochastic optimization formulation. Demand uncertainty information is captured by generating a number of discrete realizations of uncertain demand, giving rise to scenarios. The flexible design and operational planning problem is formulated as a dynamic discrete-time multi-period stochastic MILP model. The proposed approach uses net present value as an objective to be maximized.  The formulation is applied to the SC network introduced in Guillén-Gosálbez and Grossmann (2010) involving 15 chemicals and 6 production schemes.  The effects of contract periods on the SC design and operation is explored.  The framework is shown to improve the profitability of a SC over a design that does not consider contractual constraints, but where such constraints are imposed in subsequent operation.  Conclusions are drawn and avenues for further work identified. 

References

Guillén-Gosálbez, G. and Grossmann, I. (2010). A global optimization strategy for the environmentally conscious design of chemical supply chains under uncertainty in the damage assessment model. Computers & Chemical Engineering, 34(1):42-58.

Kelly, J. D. and Zyngier, D. (2007). An improved MILP modeling of sequence-dependent switchovers for discrete-time scheduling problems. Industrial & Engineering Chemistry Research, 46(14):4964-4973.

Laínez, J. M., Kopanos, G., Espu~na, A., and Puigjaner, L. (2009). Flexible design-planning of supply chain networks. AIChE, 55(7):1736-1753.

You, F. and Grossmann, I. E. (2008). Design of responsive supply chains under demand uncertainty. Computers & Chemical Engineering, 32(12):3090-3111.