ABSTRACT
In this paper, a generalized mathematical model formulation for Cellular Manufacturing System (CMS) using Hierarchical Production Planning (HPP) approach, which is a methodology to introduce the planning process by a series of mathematical models, is proposed. Particularly, the main objective of the CMS is to obtain the optimum method and this optimum method helps to solve the problem of minimizing the variable production costs (production cost, cells setup cost, inventory holding cost and regular capacity cost). Subsequently, the model is applied to two different real case studies and is solved by using operation research optimization software (Lingo-12.0 program). The model is divided into three main steps as follows: data collection, mathematical model formula, and results. The proposed mathematical model of the optimization can solve the problems of the system under utilizing the limited resources in a production plan. To prove the applicability of the proposed model, two real case studies are introduced. The results show generally that the proposed mathematical model can be used to minimize manufacturing total costs of products for similar cases. Specifically, for the first case (Electric Water Heater with capacity 50 liter (EWH1)); the results show that the total cost decreases by 8.46 % for the optimum conditions. In addition, for the second case, (Electric Water Heater with capacity 80 liter (EWH2)); the results indicate that the total cost decreases by 3.7% for the optimum conditions