Solving a Multi-Objective Mathematical Model for Aggregate Production Planning in a Closed-loop Supply Chain Under Uncertain Conditions

One of the most important decisions taken in a supply chain is the issue of aggregate production planning where a program-within a medium time-range-- is determined for optimum manufacturing of all products using shared equipment and resources. This research presents a multi-objective model that helps the decision makers to make such decisions. The proposed model comprises four main objectives, the first one of which considers minimizing costs (including costs of manufacturing product, supplying, maintenance, inventory stock shortage, and expenditures related to man power). The second objective is defined as maximizing customers’ satisfaction. Minimizing suppliers’ satisfaction makes up the third objective and maximizing the quality of the manufactured products constitutes the fourth objective. In this model, the demand parameter is investigated under uncertain conditions; hence, other parameters influenced by this parameter are also presented under uncertain conditions occurring within three differing scenarios. This model is solved through LP- metric and the LINGO v14.0.1.55 software. At first the model is solved by means of numerical example; then it is solved by the actual data that are related to a military industry. Finally, process, variables like inventory level, overtime work hours etc, are valued with the help of closed-loop supply chain of the proposed model.