Possibilistic planning model to reduce the impact of forecasting demands into the manufacturing sector

VECCHIETTI ALDO; CÚNICO MARÍA LAURA

San Andrés Island

Congreso; III International Conference on Applied Mathematics ans Informatics (ICAMI); 2017

Universidad del Valle

Nowadays, the manufacturing companies face a strong competitive market that drives them optimize their operations in order to improve the control and allocation of resources in their productive environments. In this context, this work propose the development of a mathematical model for planning the production of a manufacturing company, that includes the formulation of the uncertainty in sales forecasts (consumption demands). In particular, this work proposes multi period production planning model in an extended time horizon, having imprecision in demands, with the objective to optimize productive resources, in an effort to reduce costs and thereby expand the profit. The variability in demand data are estimated through error rates (by excess and by default) from a known average value. This situation is represented using fuzzy triangular numbers. This formulation of the uncertainty allows the introduction of approximation errors that characterize the input data and which usually condition the feasibility in the results. The formulation adopted for the problem is a robust possibilistic programming approach that adapts the basic notions of chance-constraint theory for fuzzy environments. Specifically, the solution mechanism corresponds to a sequence of reformulations of the original model that results an equivalent linear crispy model. This last one evaluates several alternatives within the admissible values of occurrence and penalizes possible violations of the constraints that involves the diffuse values.The performance of the proposed model is evaluated in a case study involving two facilities that produce different groups of items. One of this production plants transport intermediate products to the second facility and final products to customers, while the other just works to satisfy the market demand. The imprecise data are modeled from available values (often inadequate) and the knowledge/experience of a decision maker. In reply, the decision variables of the model are the production plan which must be feasible for all possible values of uncertain demand. The solution obtained is robust because the cost (Objective Function value) obtained stays close (minimum deviation) to the optimum, for all (or almost all) the possible values of demand.