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 pro-duction 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, avail-able 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 algo-rithm 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 achiev-ing to near optimal solutions within a reasonably computational time.