Production, Manufacturing and LogisticsA possibilistic decision model for new product supply chain design
Introduction
Increasing competition in today’s global market and the heightened expectations of customers have forced enterprises to consider their supply chains more carefully. A supply chain (SC) can be considered as a network of stages that represent functionalities (including suppliers, manufacturers, distributors, and retailers) that must be provided to convert raw materials into the specified end-products and deliver these end-products to retailers or customers (Simchi-Levi et al., 2000). Each stage may have one or more options that can satisfy a required function. For example, a function might be the procurement of a raw material, the manufacture of an assembly, or the shipment of a product to a distribution center. Moreover, each stage is a potential location for holding a safety-stock inventory of the item processed at this stage to prevent inventory shortages. Adequate inventory policy has to be determined for each stage to improve customer service by increasing on-time deliveries and also to utilize fewer assets.
The SC configuration and inventory decisions have to be made after a new product design is complete but the vendors, manufacturing technologies or shipping options have not yet been determined. The decisions are important, because high profit margins and the importance of early sales in establishing market share for new products further increase the cost of shortage (Simchi-Levi et al., 2000).
Since multiple sources of uncertainty and complex interrelationships at various levels between diverse entities exist in the SC, it is very difficult to simultaneously determine the SC configuration and SC inventory policies to achieve target customer service levels. Progressively shorter product life cycles and growing innovation rates make product demand as well as other SC parameters (e.g., lead-time and cost) even more difficult to predict accurately, because the collection of statistical data becomes increasingly unreliable (Fisher, 1997).
Most research (Cohen and Lee, 1988, Lee and Billington, 1993, Newhart et al., 1993, Lee and Billington, 1995, Thomas and Griffin, 1996, Vidal and Goetschalckx, 1997, Beamon, 1998, Graves and Willems, 2000, Goetschalckx et al., 2002, Min and Zhou, 2002, Chen and Paulraj, 2004) has modeled the SC uncertainty (e.g., uncertain demand) by probability distribution that is usually predicted from historical data. However, whenever statistical data is unreliable or even unavailable, stochastic models may not be the best choice. Fuzzy set theory (Klir and Yuan, 1995) may provide an alternative approach for dealing with the SC uncertainty.
Little research has applied fuzzy set theory in the area of SC management and most research that has been done focused on SC inventory management and supplier selection. Petrovic et al., 1998, Petrovic et al., 1999 modeled the uncertain demand and supplier’s reliability (percentage of raw material order delivered) with fuzzy sets and developed a fuzzy isolated inventory model to determine the order-up-to level for each individual stage independently on the serial SC. According to the obtained order-up-to levels, a simulation approach was developed to evaluate the performance of the entire SC. Giannoccaro et al. (2003) developed a SC inventory policy using the periodical review policy based on the concept of fuzzy echelon stock. The market demand and inventory holding cost were represented by fuzzy sets and the order-up-to levels of inventory items were determined to minimize the SC holding cost on the serial SC. The major drawback of the above studies is that their fuzzy SC models could not evaluate the performances of entire SC directly. To overcome this problem, Wang and Shu (2005) developed a fuzzy SC model based on possibility theory to evaluate the entire SC directly and they applied a genetic algorithm approach to obtain optimal inventory policies.
In the literature of supplier selection using fuzzy set theory, Mikhailov (2002) developed a new fuzzy AHP approach to partnership selection in the formation of virtual enterprises. Nassimbeni and Battain (2003) developed fuzzy logic and neural-fuzzy approaches to rate the performance of suppliers in new product development. Kumar and Shankar (2004) developed a fuzzy goal programming approach to select vendors for minimizing multiple objectives including net cost, net rejections, and net late deliveries subject to constraints regarding budget, demand, etc.
The objective of the current paper is to model SC uncertainties with fuzzy sets and develop a possibilistic decision model to determine the SC configuration and inventory policies that minimize the total SC cost subject to also fulfilling the target service time of the end-product. We assume that sourcing options differ in terms of their direct costs and lead-times. Fuzzy sets are used to represent fluctuating customer demands, uncertain lead-times, and unreliable supply deliveries (in terms of delay time). It is also used to model preference information, such as customer preferences for the target service time. A fuzzy SC model extended from Wang and Shu (2005) is used to evaluate the performance of the entire SC directly. A genetic algorithm approach integrated with the proposed fuzzy SC model is developed to determine the optimal SC configuration and the order-up-to level for every stage at the same time.
The paper is organized as follows. Section 2 introduces fuzzy set theory to model the SC uncertainty and to evaluate the SC performance. The fuzzy SC model and the proposed genetic algorithm approach are described in Section 3. An example of a notebook computer SC is used to illustrate the concept developed in Section 4. Section 5 concludes this paper.
Section snippets
Modeling uncertain and preference information in SC by fuzzy sets
Fuzzy sets have been widely used to represent uncertain or preference information in many types of applications, such as: scheduling (Dubois et al., 2003, Wang, 2004), engineering design (Antonsson and Otto, 1995, Wang, 2001), production management (Guiffrida and Nagi, 1998), etc. They may provide an alternative and convenient framework for handling uncertain SC parameters, when there is lack of certainty in data or even lack of available historical data. This is because the possible range of a
Modeling the supply chain configuration
In this paper, a supply chain is modeled as a network of stages that represent functionality that must be provided to transform raw materials to final products (Graves and Willems, 2001, Lakhal et al., 2001). Each stage may have one or more options that can satisfy the required function. A function might be the procurement of a raw material, the manufacture of an assembly, or the shipment of a product to a distribution center. Each option at a stage can be characterized by two attributes:
Illustrative example of a notebook computer manufacturing and distribution supply chain
A notebook computer supply chain adapted from Graves and Willems (2001) is used to illustrate the proposed approach. Fig. 7, Table 1, Table 2 display the notebook computer SC, options, and the corresponding data. Assume that the holding cost rate h = 0.45 and α = 250.
A notebook computer is composed of three major subassemblies: the LCD display, the circuit boards, and the housing. The LCD display is a standard component that is purchased from an external vendor (S3). The circuit board assembly
Conclusions
This paper proposed a possibilistic decision model to determine the SC configuration and inventory policies for new products with unreliable or unavailable statistical data. Fuzzy sets were used to model uncertain and flexible SC parameters. The fuzzy SC model was developed to evaluate the SC performance and the GA approach was used to determine the SC configuration and inventory decisions to minimize the total SC cost and maximize the possibility of fulfilling the target service level.
While
Acknowledgments
This research is partially supported by grant No. NSC-93-2213-E-035-013, NSC-93-2213-E-005-034, and NSC-94-2213-E-005-003 from the National Science Council of the Republic of China (Taiwan). We also want to thank the anonymous referees for their constructive comments on this paper.
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