A branch and bound algorithm for a production scheduling problem in an assembly system under due date constraints

This paper focuses on a production scheduling problem in a tree-structured assembly system operating on a make-toorder basis. Due dates are considered as constraints in the problem, that is, tardiness is not allowed. The objective of the problem is to minimize holding costs of ®nal product inventory as well as work-in-process inventory. A mixed integer linear programming model is given and a branch and bound (B&B) algorithm based on a Lagrangian relaxation method is developed. In the algorithm, a subgradient method is used for obtaining good lower bounds of subproblems (or partial solutions) while a Lagrangian heuristic is used for upper bounds. Results of computational experiments on randomly generated test problems showed that the B&B algorithm found optimal solutions of problems of moderate sizes in a reasonable amount of computation time. Ó 2000 Elsevier Science B.V. All rights reserved.