A multifamily dynamic lot-sizing model with coordinated replenishments

The paper considers 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. This article develops a finite branch-and-bound algorithm for solving the problem. In addition, it presents 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.