تأثیر یک رویکرد برنامه نویسی ریاضی فازی برای طرح ریزی زنجیره تأمین تولید با تقاضای فازی

The main focus of this work is to prove the effectiveness of a fuzzy mathematical programming approach to model a supply chain production planning problem with uncertainty in demand. A fuzzy optimization model that takes into account the lack of knowledge in market demand is developed. This work uses an approach of possibilistic programming. Such an approach makes it possible to model the epistemic uncertainty in demand that could be present in the supply chain production planning problems as triangular fuzzy numbers. The emphasis is on obtaining more knowledge about the impact of fuzzy programming on supply chain planning problems with uncertain demand.

The concept of supply chain management (SCM), since their appearance in 1982 (see Oliver and Weber, 1982), is associated with a variety of meanings. In the eighties, SCM was originally used in the logistical literature to describe a new integrated approach of logistics management through different business functions (Houlihan, 1984). Then, this integrated approach was extended outside of the company limits to suppliers and customers (Christopher, 1992). In accordance with the Global Supply Chain Forum (Lambert and Cooper, 2000), the SCM is the integration of key business processes, from final users to original suppliers providing products, services and information which add value to clients, 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 (Gupta and Maranas, 2003). 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 modelling of supply chain planning processes through mathematical programming models (see, for instance, Alemany et al., 2009 and Mula et al., 2010). 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 (Bhatnagar and Sohal, 2005). Therefore, uncertainty is a main factor that can influence the effectiveness of the configuration and coordination of supply chains (Davis, 1993). 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 (Mula et al., 2005). Along the years many researches and applications aimed to model the uncertainty in production planning problems (Mula et al., 2006a). Different stochastic modelling techniques have been successfully applied in supply chain production planning problems with randomness (Escudero, 1994, Gupta and Maranas, 2003 and Sodhi and Tang, 2009). However, probability distributions derived from evidences recorded in the past are not always available or reliable. In these situations, the fuzzy set theory (Bellman and Zadeh, 1970) 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 (Dubois et al., 2002). 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 (Dubois and Prade, 1988). In this paper, for the purpose of demonstrating the usefulness and significance of the fuzzy mathematical programming for production planning, a fuzzy approach is applied to a supply chain production planning problem with lack of knowledge in demand data. The main contribution of this paper is an application of known possibilistic programming in a supply chain planning case study. Other applications of possibilistic programming in production planning problems can be found in Inuiguchi et al. (1994), Hsu and Wang (2001), Wang and Fang (2001), Lodwick and Bachman (2005), Wang and Liang (2005), Mula et al. (2008) and Vasant et al. (2008). However, previous researches mentioned above did not consider supply chain production planning problems. This paper is organized as follows. Firstly, in Section 2, the supply chain production planning model, which has been the basis of this work, is described. In Section 3, a fuzzy model is developed to incorporate the demand uncertainty in the supply chain production planning model. Then, Section 4 uses a supply chain case study to illustrate the potential savings and other benefits that can be attained by using fuzzy models in a fuzzy environment. In Section 5, conclusions are given.

Supply chain environments imply the production planning decisions have to be made under conditions of uncertainty in parameters as important as demand. In this paper, a supply chain planning problem has been presented as a fuzzy MILP model with fuzzy demand. The proposed fuzzy mathematical programming approach extends the formulation originally presented by McDonald and Karimi (1997) considering uncertain demand. This approach is based on the method for solving multi-objective linear programming problems with fuzzy parameters represented by triangular fuzzy numbers proposed by Gen et al. (1992). We have adapted this approach for solving fuzzy linear programming problems with a crisp objective function and fuzzy right-hand side numbers in less than or equal and greater than or equal type constraints. This fuzzy mathematical approach has provided freedom of action with regard to supply chain production planning problems where epistemic uncertainty appears in demand with no increment of the requirements of information storage and the same specified resource limit of 100 CPU seconds as used by the deterministic formulation. Also, compared with the stochastic programming approach, a solution can be obtained in an easier manner. Finally, as a result of the research carried out here, some circumstances have arisen that may open up possibilities for further research: (i) to adapt another fuzzy mathematical programming based approaches in order to prove their effectiveness to solve supply chain production planning problems; (ii) to use evolutionary computation with fuzzy optimization in order to solve more efficiently fuzzy supply chain production planning problems; and (iii) to integrate simulation models with fuzzy optimization and evolutionary computation models to better understand the behaviour and the results of the fuzzy supply chain production planning models.