A Fuzzy Optimization Model For Supply Chain Production Planning With Total Aspect Of Decision Making

Hamid Reza Feili, Mojdeh Hassanzadeh Khoshdooni
2011 Journal of Mathematics and Computer Science  
This paper models supply chain uncertainties by fuzzy sets and develops a fuzzy linear programming model for tactical supply chain planning in a multi-echelon, multiproduct, multi-stage with different methods of manufacturing in each stage, multidistribution centre and multi-period supply chain network. In this approach, the demand, process and supply uncertainties are jointly considered. The aim is to achieve the best use of the available resources and the best method of manufacturing at each
more » ... ufacturing at each stage for a product along the time horizon so that customer demands are met at a minimum cost. The fuzzy model provides the decision maker with alternative decision plans with different degrees of satisfaction. Keywords: Supply Chain Management, Supply Chain Planning, Fuzzy Sets, Uncertainty Modeling. shareholders, etc. This paper is related to one of these key business processes: the supply chain production planning. Supply chain production planning consists of the coordination and the integration of key business activities carried out from the procurement of raw materials to the distribution of finished products to the customer [5] . Here, tactical models concerning mainly about inventory management and resource limitations are the focus of our work. In this context, with the objective of obtaining optimal solutions related to the minimization of costs, several authors have studied the modeling of supply chain planning processes through mathematical programming models, for instance. However , the complex nature and dynamics of the relationships among the different actors of supply chains imply an important grade of uncertainty in the planning decisions [6] . Therefore, uncertainty is a main factor that can influence the effectiveness of the configuration and coordination of supply chains .One of the key sources of uncertainty in any production-distribution system is the product demand. Thus, demand uncertainty is propagated up and down along the supply chain affecting sensibly to its performance [7] . Along the years many researches and applications aimed to model the uncertainty in production planning problems [8] . Different stochastic modelling techniques have been successfully applied in supply chain production planning problems with randomness [9]. However, probability distributions derived from evidences recorded in the past are not always available or reliable. In these situations, the fuzzy set theory , represents an attractive tool to support the production planning research when the dynamics of the manufacturing environment limit the specification of the model objectives, constraints and parameters. Uncertainty can be present as randomness, fuzziness and/or lack of knowledge or epistemic uncertainty [10] . Randomness comes from the random nature of events and deals with uncertainty regarding membership or non-membership of an element in a set. Fuzziness is related to flexible or fuzzy constraints modelled by fuzzy sets. Epistemic uncertainty is concerned with ill-known parameters modelled by fuzzy numbers in the setting of possibility theory [11] . Few studies address the SC planning problem on a medium-term basis (tactical level) which integrates procurement, production and distribution planning activities into a fuzzy environment .The aim of this approach is to simultaneously optimize the decision variables of different functions that have been traditionally optimized sequentially [12] . Moreover, there is a lack of models contemplating the different sources of uncertainty in an integrated manner. Hence in this study, we develop a tactical supply chain model in a fuzzy environment in a multi-echelon, multi-product, multi-level, multi-period supply chain network. In this proposed model, the demand, process and supply uncertainties are considered simultaneously. In the context of fuzzy mathematical programming, two very different issues can be addressed: fuzzy or flexible constraints for fuzziness, and fuzzy coefficients for lack of knowledge or epistemic uncertainty [13] . The aim of this paper is to propose an SC planning model where the data, associated with all the sources of uncertainty in an SC, are illknown and modeled by trapezoidal fuzzy numbers. The main contributions of this paper can be summarized as follows:  Introducing a novel tactical SC planning model by integrating procurement, production and distribution planning activities into a multi-echelon, multiproduct, multi-level and multi-period SC network.  Achieving a model which contemplates the different sources of uncertainty affecting SCs in an integrated fashion by considering the possible lack of knowledge in
doi:10.22436/jmcs.002.01.08 fatcat:f7ydzdkapjbqlfjvtuchzvh4pe