A branch and bound algorithm for a single item nonconvex dynamic lot sizing problem with capacity constraints

Abstract

We develop a branch and bound algorithm for solving a deterministic single item nonconvex dynamic lot sizing problem with production and inventory capacity constraints. The production cost function is neither convex nor concave. It is a composite function with a fixed setup cost to start the production and a piecewise linear convex variable production cost. The algorithm finds a global optimum solution for the problem after solving a finite number of linear knapsack problems with bounded variables. Computational experience with randomly generated problems suggests that the algorithm solves the dynamic lot sizing problem in a computationally efficient manner both in terms of CPU time and storage requirements.