Production costs in general, and workforce and inventory costs in particular, constitute a large fraction of the operating costs of many manufacturing plants. We introduce cooperative Aggregate Production Planning as a way to decrease these costs. That is, when Production Planning of two or more facilities (plants) is integrated, they can interchange workforce and products inventory; thus, their product demands can be satisfied at lower cost. This paper quantifies the cost saving and synergy of different coalitions of Production plants by a new linear model for cooperative Aggregate Planning problem. The developed approach is explicated with a numerical example in which inventory and workforce levels of different coalitions of facilities are evaluated. Afterward, a key question would be how the cost saving of a coalition should be divided among members. We tackle the problem using different methods of cooperative game theory. These methods are implemented in the numerical example to gain an insight into properties of the corresponding game results.

Aggregate Production Planning (APP) determines the optimal Production plan for the medium term Planning horizon. The purpose of the APP is effective utilization of existing capacities through facing the fluctuations in demand. Recently, fuzzy approaches have been applied for APP focusing on vague nature of cost parameters. Considering the importance of coping with customer demand in different periods at different and variable rates, in this research, demand is considered fuzzy and the APP decisions modeled through a bi-objective LP model optimizing Production and workforce level costs. The APP decisions are taken in two rounds, First The fuzzy model is transformed to a crisp goal programming counterpart and in the second round as the principal contribution of this paper, the APP decisions for rest of the horizon are updated based on actual demand occurred during starting periods. By generating several sample problems and using the Lingo, the validity of the proposed model is shown.

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.

One kind of mid-term Production system, Aggregate Production Planning, identifies the optimum Production plan for each Production period. The goal of Aggregate Production Planning is to forecast future demand swings. On the other hand, maintenance system identifies the proper time for preventive maintenance and restrains from break downs and reduces maintenance costs. Due to the importance of these two systems, in recent years, there has generated different models independently. The current research has proposed an integrated Aggregate Production Planning model considering the time and costs of maintenance. This model indicates the optimum Production size among the optimum time of preventive maintenance. As a final point, in order to check the reliability of the proposed model, an example has been examined. Results show that a considerable amount of cost has been saved by applying the model.

This paper proposes a simplified solution procedure to the model presented by Akinc and Roodman. The Benders" decomposition procedure for analyzing this model has been developed, and its shortcomings have been highlighted. Here, the special nature of the problem is exploited which allowed us to develop a new algorithm through surrogating method. The two methods are compared by several numerical examples. Computational experience with these data shows the superiority of the new approach. In addition, the required computer programs have been prepared by the authors using TURBO PASCAL 7.0 to execute the algorithm.

It is usual for a Production environment to encounter uncertainty and variable data that causes generating random parameters. Failure to pay attention to these changes will make the scheduling not adequately match the reality and cause many losses in Production environments. Considering the importance of the issue, in this article we use the Robust Optimization Approach to deal with uncertainty in the Aggregate Production Planning parameters. In this paper, in a robust model, it is assumed that the uncertainty of non-deterministic parameters is continuous and a completely new and innovative approach is proposed for Robust Optimization for risk-averse managers and then, an optimization strategy is used to examine the uncertainty. In order to investigate the model results, examples have been made in small and large sizes and the problem has been solved and analyzed using the GAMS software and Lagrange relaxation method. The results of the implementation of the proposed robust models in this paper, compared to the basic model, show that the results have more stability against uncertainty and this causes a significant reduction in risk.

In this paper, an optimization model for Aggregate Planning of multi-product and multi-period Production system has been formulated. Due to the involvement of too many stakeholders as well as uncertainties, the Aggregate Production Planning sometimes becomes extremely complex in dealing with all relevant cost criteria. Most of the existing approaches have focused on minimizing only Production related costs, consequently ignored other cost factors, for instance, supply chain related costs. However, these types of other cost factors are greatly affected by Aggregate Production Planning and its mismanagement often results in increased overall costs of the business enterprises. Therefore, the proposed model has attempted to incorporate all the relevant cost factors into the optimization model which are directly or indirectly affected by the Aggregate Production Planning. In addition, the considered supply chain related costs have been segregated into two major categories. While the raw material purchasing, ordering, and inventory costs have been grouped into an upstream category, finished goods inventory, and delivery costs in the downstream category. The most notable differences with the other existing models of Aggregate Production Planning are in the consideration of the cost factors and formulation process in the mathematical model. A real-life industrial case problem is formulated and solved by using a genetic algorithm to demonstrate the applicability and feasibility of the proposed model. The results indicate that the proposed model is capable of solving any type of Aggregate Production Planning efficiently and effectively.

Aggregate Production Planning is a multi-objective problem which is influenced by managerial preferences which is rarely considered with these preferences in many researches. In this paper, a multi-objective model for multi-product AggregateProduction-Planning has been proposed and implemented in an industrial ball-valves manufacturing company. In the first phase, preferences of various product groups have been determined via a multiple-attribute-decision-making method which is used as an input for the second phase. To do this, one of the outranking methods has been used because of the variety in the dimension and the nature of different attributes. In the second phase, a deterministic multi-objective mixed-integer mathematical model has been designed considering the needs of the company. This model not only concentrates on the benefits, but also considers the preferences of the products. The third objective function is decreasing work in process. To solve this model, ϵ,-constraint method has been used leading to a set of Pareto-optimal solutions, enabling the decision-maker to choose the best solution by trading off between the three objective functions. So top managers are able to decide how to provide product preferences and how to decrease WIP products while the benefits remain reasonable. The results show that using the proposed approach in the case study has improved 35%, 28%, and 56% total benefit, total utility, and WIP products, respectively.

In this paper, a bi-objective model is developed to deal with an Aggregate Production Planning problem in a multi product, multi period supply chain including multiple suppliers, factories and demand points. This bi-objective model aims to minimize the total cost of supply chain including inventory costs, manufacturing costs, work force costs, hiring, and firing costs, and maximize the minimum of producers' reliability by considering probabilistic lead times, to improve performance of the system and achieve a more reliable Production plan. Since the proposed bi-objective model is NP-hard, a Pareto-based multi-objective imperialist competitive algorithm (MOICA) is used. To evaluate the performance of presented algorithm, non-dominated sorting genetic algorithm (NSGA-II) is applied, too. The results show the capability and efficiency of proposed algorithm in finding Pareto solutions.