We consider a multi-item production planning problem where items are grouped together into families. A family setup time is incurred when an item in a family is produced. Also, for each replenishment of a product an individual setup time may be incurred. The objective is to determine the time-phased production schedule that minimizes the total inventory holding cost under demand and capacity constraints. In this article we develop a finite branch-and-bound algorithm for solving the problem. In addition, we present a heuristic procedure to obtain an initial feasible solution. This feasible solution is the initial incumbent solution in the branch-and-bound algorithm and is also used for preprocessing the problem data. Computational results are reported.
In a recent paper, Pinto and Mabert [ 5 ] presented a lot-sizing rule and an improvement procedure for the joint lot-sizing problem with zero setup costs. We show that this procedure often yields infeasible schedules. We also present and discuss two interesting properties of the joint lot-sizing problem with zero setup costs. A numerical example to illustrate the second property is provided.Subject Areas: Inventory Management, Production/Operations Management, and Scheduling.
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