A new fuzzy linear programming model for aggregate production planning for a supplier in the automotive industry

Supplying real world car manufacturers is a complex task, because suplliers operate in the presence of various sources of uncertanty, such as uncertainty in customer demand and uncertainty in manufactured quantities which depend on work force availability and efficiency, machine breakdowns, quality of manufactured products, ect. A new fuzzy linear programming (FLP) model for solving an aggregate production planning (APP) problem at a first tier supplier in the automotive industry is proposed. We propose to use the time as a measure of performance of the APP and to minimise the total time of manufacturing the required products, storing them in the supplier warehouse and preparing them for delivery to the customer in the planning time horizon. These times are uncertain and modelled using fuzzy numbers. We adapted a method for inferring membership functions based on collected historical data on production times and subjective experience of the production manager. The FLP model includes fuzzy coefficients in both the objective function and linear constraints. It is defuzzyfied into a crisp LP model by adapting an interactive method which makes a trade off between the acceptable value of an objective function and the feasibility degree of constraints. Different experiments are carried out to analyse the performance of the supplier’s APP in the presence of uncertainty. The obtained results are compared with the real world supplier’s performance recorded in practice.