Application of fuzzy sets to manufacturing/distribution planning decisions in supply chains
Introduction
How to integrate manufacturing/distribution planning decisions (MDPDs) to ensure the overall effectiveness of supply chain management (SCM) has attracted substantial interest from both practitioners and academics [2], [6], [14], [15], [16], [34], [38], [45]. For practical MDPD integration problems in supply chains, a decision maker (DM) typically attempts to achieve the following goals: (1) set overall production levels for each product category for each source (manufacturer) to meet fluctuating or uncertain demands for various destinations (distributors) over the intermediate planning horizon and, (2) generate suitable strategies regarding regular and overtime production, subcontracting, inventory, backordering and distribution levels, thereby determining the appropriate resources to be utilized.
Several techniques and algorithms have been developed to solve MDPD integration problems [3], [6], [35], [37], [45], [49], [50]. However, these conventional methods generally analyze the overall production strategy, inventory strategy, and flow of products through a facility over a single period to either minimize total costs or maximize profits [18]. Particularly when manufacturers and distributors use any of these available solution techniques to solve MDPD problems, many assume the goals and model inputs are deterministic. It is critical that the satisfying goal values should be uncertain if the unit cost coefficients and the related parameters are imprecise. This vagueness always exists in realistic MDPD problems [38], [40], [44]. Clearly, the conventional deterministic solution techniques described above cannot solve all of the MDPD programming problems in uncertain environments.
The possibility theory, developed by Zadeh in 1978, provides an effective methodology that considers parameter vagueness in various fields. Zadeh [58] showed that the possibility theory is based on the fact that much of the information upon which human decisions are based is possibilistic, rather than probabilistic, in nature. The possibility theory has more computational efficiency and flexibility in fuzzy arithmetic operations than conventional deterministic and stochastic programming techniques [8], [22], [28], [46], [48], [57]. In real-world MDPD integration problems, the unit cost coefficients in the objective function are frequently fuzzy in nature as some information is incomplete and/or unobtainable over the intermediate planning horizon. Therefore, this paper proposes a fuzzy mathematical programming approach, which possibility theory is the basis for solving MDPD integration problems with imprecise goal and forecasts demand in supply chains. The proposed approach minimizes the total manufacturing and distribution costs associated with inventory, subcontracting and backordering levels, the available machine capacity and the labor levels at each source, along with the forecast demand and available warehouse space at each destination. It also considers constraint on the available budget.
The following details the organization of the remainder of this paper. Section 2 is dedicated to a review of the literature. Section 3 describes the problem, details the assumptions, and formulates the imprecise MDPD model. Section 4 develops the fuzzy programming approach for solving imprecise MDPD problems. Section 5 presents an industrial case for implementing the feasibility of applying the proposed approach to real MDPD problems. Finally, Section 6 presents the conclusions.
Section snippets
Literature review
How to integrate manufacturing and distribution planning systems simultaneously in a supply chain has attracted considerable interest from both practitioners and academics. Cohen and Lee [15] created an aggregate model that integrated material control, production, and distribution sub-models to establish a material requirement policy for all materials for each factory in a supply-chain production system. Barbarsoğlu and Özgür [3] developed a mixed-integer mathematical programming model with a
Problem description, assumptions, and notation
The following describes the multi-product and multi-time period MDPD problem examined in this paper. This study assumes that the logistics center of a supply chain attempts to determine the suitable MDPD integration plan for N types of homogeneous commodities from I sources (factories) to J destinations (distribution centers) to satisfy imprecise demand over a planning horizon H. Each source has a supply of the commodity available for distribution to various destinations. Each destination also
Model of the imprecise data
This paper assumes that a DM has already adopted the triangular fuzzy number to represent all of the imprecise data in the original MDPD model formulated above. In real-world situations, a DM is familiar with estimating the values of the upper bound (optimistic), lower bound (pessimistic), and modal value (most likely) parameters. The pattern of triangular fuzzy number is commonly adopted due to its ease in defining the maximum and minimum limits of deviation of an imprecise number from its
Case description
This study uses the Daya Technologies Corporation as a case study to demonstrate the practicality of the proposed fuzzy mathematical programming methodology [33], [52], [53]. The Daya Technologies Corporation is the leading producer of precision machinery and transmission components in Taiwan. Its products are distributed throughout Asia, North America and Europe. The conventional operational strategy used at the Daya’s ballscrew plant is to maintain a constant work force level over the
Conclusions
In real-world MDPD integration problems in supply chains, environmental coefficients, and related parameters are often imprecise due to incomplete and/or unavailable information over the intermediate planning horizon. This work presents a fuzzy programming approach for solving the multi-product and multi-time period MDPD problems with imprecise goal and forecast demand by considering the time value of money of related operating cost categories. The original multi-product and multi-time period
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