طراحی شبکه زنجیره تامین چند پله ای در تولید چابک

In this paper, we consider a supply chain network design problem in an agile manufacturing scenario with multiple echelons and multiple periods under a situation where multiple customers have heavy demands. Decisions in our supply chain design problem include selection of one or more companies in each echelon, production, inventory, and transportation. We formulate the problem integrating all decisions to minimize the total operational costs including fixed alliance costs between two companies, production, raw material holding, finished products holding, and transportation costs under production and transportation capacity limits. A Lagrangian heuristic is proposed in this paper. Optimizing a Lagrangian relaxation problem provides a lower bound, while a feasible solution is generated by adjustment techniques based on the solution of subproblems at each iteration. Computational results indicate the high quality solutions with less than 5% optimality gap are provided quickly by the approach in this paper. Further, compared to initiative managerial alternatives, an improvement of 15% to 25% is not unusual in certain cases for the proposed approach.

Companies today are faced with a competitive environment which brings challenges, such as how fast products are designed, manufactured, and distributed, while simultaneously having to consider improving production efficiency and total operational cost. The concept of Agile Manufacturing was proposed as a novel manufacturing paradigm in response to these challenges. An agile company is capable of operating in a competitive environment with market opportunities that are continually emerging and changing with uncertainty. Virtual organization, according to Goldman et al. [13], is defined as “an organizational tool for agile competitors who are integrated by sharing core competencies and resources to accomplish a particular product which could not be done solely by each of the competitors.” A virtual organization is formed opportunistically, and disbanded when its objective is attained. Companies in a virtual organization share core competencies, resources, skills, and costs, which make them able to respond to global market opportunities which each individual member is not able to on its own. Therefore, the concept of the virtual organization has emerged as a new organization model within Agile Manufacturing. Virtual organizations reflect and facilitate three major aspects of agile competition [13]: 1. The virtual organization model expresses the need of agile competitors to create or assemble new productive resources very quickly. 2. The virtual organization model expresses the need of agile competitors to create or assemble new productive resources frequently and concurrently because of the decreasing profitable lifetimes of individual products and services. 3. The virtual organization reflects the complexity of today's most profitable products, which often require access to a wider range of world-class competencies – research, prototyping, manufacturing, design, marketing, distribution, service, and within each of these many, more specialized competencies – than any one organization can afford to maintain “in between” customer opportunities or can identify in advance of unanticipated opportunities. When a market opportunity emerges, a virtual organization needs to be formed by a clearly established mechanism. The significant contribution of this paper is to provide an integrated production-logistics approach to partners selection for the virtual organization formation. These partners form a supply chain network based on their production and transportation capacities of partners, and the integrated optimization of costs in the supply chain network. In terms of supply chain network design, there are three planning stages: strategic, tactical, and operational [3]. Strategic or long-range planning involves decisions about company selection and facility location; tactical or medium-range planning involves decisions about production, inventory, and logistics. Operational or short-range planning involve within day or shift decisions such as routing and scheduling. Strategic and tactical planning are highly related and should be considered together in the Agile Manufacturing paradigm because of the short-lived durations of virtual organization. For example, the selection of suppliers which in turn defines their capacity to fulfill demand has an important impact on production planning. Therefore, more and more companies are coming to the realization that to minimize total operational costs, the supply chain should be optimized as a whole. In this paper, strategic and tactical decisions are considered simultaneously. Chauhan et al. [6] considers a similar problem of designing a partner-chain by an integrated production-logistics approach. A limiting characteristic of their work is the assumption that any member in the formed supply chain has only one supplier partner and only one customer partner, and there is only one unique final customer in the supply chain. In reality however, demands routinely come from multiple customers, and the financial penalty of not meeting customer demand are huge, especially for a short life-cycle product corresponding to a time-based new market opportunity. Overcoming this limitation is the main motivation of our research. Our contribution is in generalizing the limiting assumption of Chauhan et al. [6] and allowing multiple partners to be selected at any stage of the supply chain. It is worthy to note that although only a single assumption is relaxed, the problem structure becomes totally different, and the solution approach developed in their work is no longer applicable. Therefore, a methodology to design a supply chain network should be established along with an effective solution approach. Addressing this need is the major contribution of this paper. Fig. 1 illustrates the motivation of our research. In this motivational example, we assume raw materials are sequentially processed twice in order to create a final product. At each operation process, two companies are qualified as candidates. Fig. 1 shows the data setting in this motivation example, where {•}{•} denotes customer demands in successive three periods, [•][•] denotes production capacities in successive three periods, and (•)(•) denotes unit production and inventory holding costs. To make the example simple, we assume the alliance cost and the unit transportation cost between any partners are identical, which are 200 and 5, respectively; and the transportation is uncapacitated. Based on the unit production cost, Companies 1 and 3 are the best choices to be included in the virtual organization. Obviously, both of them have adequate production capacity to meet demands. (Note that Company 3 has 50 units of inventory at the end of first period.) But if they work together to form a supply chain, the supply chain cannot meet customer demands because Company 1 cannot provide 100 units (50 at most) to Company 3 as raw materials; thus, Company 3 cannot produce 100 units in the first period due to raw material shortage. The supply chain cannot meet the customer demand in the second period. Therefore, if only these two companies cooperate together, they cannot fulfill customer demands for all periods, although each of them can provide adequate production capacities individually. Our research answers the following questions: Do we include Company 1 and/or 3, and add more companies to fulfill demands? Which company should we select to complement the production capacity to meet all demands? These questions strongly motivate our research.In this paper, we present a mixed integer linear formulation to form the virtual organization for a particular product when a new market opportunity emerges based on production and transportation capacities of qualified companies, and on the integrated optimization of costs in a finite planning horizon. The strategic decision, which is the selection of companies to form the virtual organization, and the tactical decisions, which are production, inventory, and transportation of each company, are considered as a whole under a deterministic environment. A Lagrangian solution method is employed in this research to decompose the original problems into subproblems. A practical example of such a virtual organization is that of semiconductor manufacturing which has three major steps, silicon crystal to polished wafer, wafer fabrication (photolithography, etch, implantation, deposition), and testing and packaging. Wafer fabrication is capital intensive where initial investment of building a semiconductor factory is about 2 billion dollars. Therefore, partnerships that leverage spare capacity can avoid the construction of new plants. On the other hand, wafer testing and packaging are labor intensive and these factories are located where the labor cost is low. For the reason of scale economics, the three major steps cannot be finished in a company and a supply chain needs to be designed. Some companies that supply crystal silicon wafers are Applied Materials, MEMC, Wacker Chemie, Wafer World and Semiconductor Wafer, Inc. A huge number of companies are wafer fabricators, such as Intel, AMD, Texas Instruments, SK Hynix, TSMC, etc. Some companies focus on only wafer testing and packaging, such as Amkor Technology, ASE, UINSEM, and SPILL. There are many issues to be considered when setting up vendor-manufacturer relationships, such as products price, products quality, company production capacity, company location, transportation costs, etc. In response to a new chip development, opportunistic formation of supply chain from qualified members can leverage the results of our work. The remainder of the paper is organized as follows. In Section 2, a literature review of the related topics is presented. Section 3 presents the problem description and formulation. A solution approach based on the Lagrangian relaxation is presented in Section 4. Computational results of small, medium, and large problems are presented in Section 5. In Section 6, some extensions by relaxing assumptions in this paper are discussed. Finally, conclusions and future work are presented in Section 7. Appendixes contain two formulations used in the proposed solution approach developed in Section 4, and data used in the example in Section 4.3.

In this paper, we consider a supply chain formation problem under a situation where there are multiple customers and heavy demands. Due to the heavy demands and capacity limits for both production and transportation at each partner company, in order to avoid unfulfillment, multiple companies in each echelon could be selected to form the supply chain network. We integrate the formation of supply chain network and production, inventory, and transportation planning for companies included in the network. Considering the complexity of the problem, an effective solution approach based on Lagrangian relaxation is developed in this paper. A lower bound to the original problem is obtained by optimizing the relaxed problem. In order to obtain a best lower bound, the well-known subgradient search is employed to solve the Lagrangian dual problem. The lower bound increases with iterations. On the other hand, a feasible solution (upper bound) to the original problem can be obtained at each iteration by some “repairing” techniques developed in this paper. The subgradient search procedure starts with an initial feasible solution following a heuristic developed based on the work of Chauhan et al. [6]. As iteration increases, the upper bound decreases. To test the quality of our solution approach, three groups of examples are randomly generated, which are problems with small, medium, and large dimensions. Numerical results establish that the solution approach works very well. We have also compared the Lagrangian heuristic to two alternate approaches that might be adopted by a manager of the supply chain design, one biased towards production costs and the other towards alliance costs. The Lagrangian heuristic provides 15%–25% better solutions in certain large scale examples. This demonstrates the value of adopting the more rigorous approach developed here. In terms of future work, there are some considerations of stochastic demand, bill-of-materials for the product, some risks to a supply chain, inclusion of independently operated warehousing operation, and global issues such as taxes, tariffs and exchange rates.