An efficient algorithm to solve a multi-objective robust aggregate production planning in an uncertain environment

Risk is inherent in most economic activities. This is especially true of production activities where results of decisions made today may have many possible different outcomes depending on future events. Since companies cannot usually protect themselves completely against risk, they have to manage it. In this paper, we present a multi-objective model to deal with a multi-period multi-product multi-site aggregate production planning problem for a medium-term planning horizon under uncertainty. The first objective function attempts to minimize sum of the expected value and the variability of total costs with reference to inventory levels, regular, overtime and subcontracting levels, backordering levels, and labor, machine and warehouse capacities. The second objective function highlighted the concept of customer service level through minimizing the expected value of maximum shortages among all customers' zones from which the variability of that is conducted. The last objective function aims to maximize workers productivity, a weighted average of productivity levels in all factories and in all periods which is weighted by the number of k-level labors. Then, we use an efficient algorithm that is a combination of an augmented e-constraint method and genetic algorithm to solve our proposed model. The results demonstrate the practicability of the proposed multi-objective stochastic model as well as the proposed algorithm.