Modeling of Purchase and Sales Contracts in Supply Chain Optimization

Abstract

This work presents a novel approach for modeling of different types of contracts that a company may sign with its suppliers and customers. The main objective is to expand the scope of current planning and supply chain optimization models by including the selection of the types of contracts as an additional decision. The solution approach relies on representing the decision of choosing different contracts using disjunctive programming for both short-term and long-term production planning models. The resulting formulation is converted into a mixed-integer linear programming (MILP) problem. The advantages of the proposed models are highlighted in two case studies of increasing complexity.

Optimal procurement contract selection with price optimization under uncertainty for process networks

“…The models for the three contract types (discount, bulk, and fixed duration) are proposed in Park et al (2006). In this section, we present the mixed-integer linear constraints obtained by reformulating the disjunctions using the convex hull approach.…”

“…It extends the short-term planning model described in Park et al (2006) by accounting for multiple sites. The procurement contract and pricing models are described in Sections 4.2 and 4.3.…”

“…We use the same three contract types described in Park et al (2006): discount after a certain purchased amount, bulk discount, and fixed duration contracts. These contract types are modeled with disjunctions and reformulated using the convex hull approach as mixed-integer linear programming (MILP) constraints.…”

“…where COST c j,s,t is the procurement cost of contract type c for raw material j in site s at time period t. Expressions for COST c j,s,t for each contract type c are given in Park et al (2006) and can be found in Appendix A.…”

“…We present some specific examples of this problem that are relevant to the Process Systems Engineering (PSE) community. Park et al (2006) used disjunctive programming to model three types of quantity-based contracts that a company may sign with suppliers and customers. The production planning and capacity expansion decisions are augmented by the selection of contracts.…”