Solving a generalized aggregate production planning problem by genetic algorithms.

This paper presents a genetic algorithm (GA) for solving a generalized model of single-item resource-constrained aggregate production planning (APP) with linear cost functions. APP belongs to a class of production planning problems in which there is a single production variable representing the total production of all products. We linearize a linear mixed-integer model of APP subject to hiring/firing of workforce, available regular/over time, and inventory/shortage/subcontracting allowable level where the total demand must fully be satisfied at end of the horizon planning. Due to NP-hard class of APP, the real-world sized problems cannot optimality be solved within a reasonable time. In this paper, we develop the proposed genetic algorithm with effective operators for solving the proposed model with an integer representation. This model is optimally solved and validated in small-sized problems by an optimization software package, in which the obtained results are compared with GA results. The results imply the efficiency of the proposed GA achieving to near optimal solutions within a reasonably computational time.