A Capacitated Production Planning with Outsourcing: A General Model and Its Algorithm

Abstract

This paper addresses a capacitated production planning (CPP) problem with outsourcing. Specially, the outsourcing problem considered in this paper has the following features: (1) all demands are met by production, inventory, outsourcing, and sale loss without postponement or backlog; (2) The goal of the solution to this problem is to minimize the total cost covering the production, setup, inventory holding, sale loss, and outsourcing activities; (3) different from previous studies which usually involved some special assumptions on the cost function for these activities, the cost function structure we consider in this paper are arbitrary and time-varying; and (4) we consider a general problem situation where the production, inventory, and outsourcing have a capacity limitation. It is likely that there is no solution in the model due to the consideration of such general cost functions and many constraints, hence we employ a Bellman/Ford algorithm for checking feasible solutions of the problem and resulting in a feasible solution region. After that, a proposed algorithm is applied for searching a global optimal solution with in the feasible solution region.