Heuristic approaches for determining minimum cost delivery quantities in supply chains

In this paper, we consider heuristic approaches for the determination of delivery quantities in a Supply Chain (SC). The problem under consideration is important for the design of delivery quantity negotiations between manufacturers and suppliers. We describe a Mixed Integer Programming (MIP) formulation for the optimisation problem to be solved. We explain how we can incorporate and use the suggested decision model into a decision-support system for Supply Chain Management (SCM). Because of the computational intractable large-sized mixed integer programs, we describe an efficient Genetic Algorithm (GA) in order to get near-to-optimal solutions of the mixed integer programs. We compare the GA with a Random Search Heuristic and a Branch and Bound (B&B) algorithm to solve the mixed integer programs. The different solution procedures are assessed with respect to solution quality and computational time based on stochastically generated test instances. The GA produces high-quality solutions with an acceptable computational effort. [Received 20 December 2006; Revised 01 June 2007; Second Revision Received 06 October 2007; Accepted 06 December 2007]