Production Allocation with Set-Up Penalties and Concave Material Costs

The problem of allocating known production requirements of several products for several warehouse locations to several different manufacturing plant sites is considered with specific treatment to concave cost structures and to both out-of-pocket and lost-production-time set-up penalties. The objective is to meet these production requirements at minimum total cost, which is the sum of the material costs, the manufacturing costs, the out-of-pocket set-up costs, and the distribution costs. A model is developed that is shown to be a mixed integer linear-programming model. A branch-and-bound solution procedure is then presented, and some computational results are discussed.