Multiproduct production planning in the presence of work-force learning

Abstract

This paper explores the multiproduct production planning problem in the presence of work-force learning (MPPL). In this setting the work-force productivity reflects a learning-curve effect which can either increase or decrease (learn or forget) as a function of previous production volume. This research advances the understanding of MPPL along a number of dimensions. We formulate MPPL as a nonlinear mixed-integer programming problem and establish problem complexity, demonstrating that it is strongly NP-hard. We also discuss some important economic properties of production planning in the presence of learning. We then define a branch-and-bound algorithm for MPPL, as well as a tabu-search heuristic (TSH). In addition, we consider a previously defined heuristic for MPPL and demonstrate that its performance can be arbitrarily bad. Computational experiments on a large set of test problems were performed to assess the performance of the algorithm and the TSH procedure, and also to study the behavior of MPPL problems. The results of the experiments indicate that despite the underlying problem complexity, the algorithm is able to solve reasonably large problems, thus providing a basis for evaluating the heuristic solution quality. The TSH consistently obtains high-quality solutions to the test problems, suggesting that the tabu-search methodology offers an effective approach to complex production planning problems. MPPL problem difficulty is seen to vary with the number of periods in the planning horizon, the relative degree of labor intensity, and the relative demand behavior of products.