Tedarik zinciri planlamaya olabilirsel doğrusal programlama yaklaşımı

Son yıllarda, küreselleşmeyle artan rekabet ile birlikte, Tedarik Zinciri Planlamanın (TZP) önemi artmaktadır. Bu nedenle; TZP’de stratejik kararlarının verilmesi çok büyük önem taşımaktadır. Gerçek problemlerin hepsinde görüldüğü gibi, tedarik zincirinin ilgili süreçlerinde de belirsizlikler ile karşılaşılmaktadır. Bundan ötürü; TZP modellerinde belirsizliklerin göz ardı edilmemesi gerekmektedir. Literatürde TZP’deki belirsizlikleri modelleyen çalışmalarda uzun dönemli stratejik kararların kesin olarak verildiği ve bunların orta ve kısa vadede revize edilmeleri gerektiği tespit edilmiştir. Bu çalışmada, uzun dönemli kaynak atama, ürün tedariki ve üretim kararlarının verilebilmesi için bir Olabilirsel Doğrusal Programlama (ODP) modeli geliştirilmiştir. ODP modelini kullanmanın temel amacı, tedarikçi ilişkilerinde ve üretim planlamada esneklik sağlamak üzere bulanık kararların verilmesini olanaklı kılmaktır. Bu yüzden önerilen ODP’de, sadece talep ve verim oranları gibi kritik TZP girdileri değil aynı zamanda satış miktarı, üretim miktarı ve tedarik miktarı gibi karar değişkenleri de bulanık kabul edilmiştir. Önerilen ODP’nin amacı firmanın tedarik zinciri faaliyetleri sonucunda oluşan kârı en büyüklemektedir. Çalışmada ODP’yi çözmek için DP modeline çevrilmesi önerilmiştir. Bu amaçla girdi parametreleri ve karar değişkenleri üçgen bulanık sayılar ile ifade edilmiştir. ODP’de önerilen amaç fonksiyonu ve kısıtlar, üçgen bulanık sayılar için geliştirilen toplama ve çarpma işlemleri ile büyüktür/küçüktür ilişkileri ile DP’ye çevrilmiştir. Çalışmada ayrıca önerilen modelin etkinliği hipotetik bir örnek üzerinde gösterilmiştir.

Possibilistic linear programming approach for fuzzy supply chain planning

The interest in Supply Chain Planning (SCP) has recently raised due to the fact that the opportunity of an integrated planning of the supply chain (SC) can increase the profitability, reduce production and outsourcing costs and enhance customer service levels, so that the enterprises can cope with increasing competitiveness introduced by the market globalization. A SC is an integrated system which synchronizes a series of inter-related business processes in order to convert raw materials into the specified finished products and distribute and promote these products to retailers or customers. Supply chain planning problems are due to uncertainties like the other real life problems. Uncertainties that affect the SCs can be categorized in two groups: (i) environmental uncertainties, and (ii) system uncertainties. Environmental uncertainties include supply quantity, raw material costs, lead times, and demand product price while system uncertainties contain operation efficiency, resource usage efficiency, labor cost, production capacity, and stock level. Among these uncertainty types, demand has been the most important and extensively studied source of uncertainty. The emphasis on incorporating demand uncertainty into the planning decisions is appropriate given the fact that effectively meeting customer demand is what mainly drives most SCP initiatives. Furthermore, demand is the main source of uncertainties as the fluctuations of it affects the production system and suppliers gradually. The main idea of the proposed model is to make uncertain and therefore flexible decisions to cope with the uncertainties revealed in strategic SCP. Demand affects system uncertainty in which some other types of uncertainty also exist. System uncertainty and supply uncertainty mutually affects each other. In this circumstances to make crisp decisions may cause irrelevant or irreversible long term decisions that will need huge revisions in medium or short term. In this paper a Possibilistic Linear Programming (PLP) model is proposed to support strategic decisions of the enterprises concerning the production resources utilization and outsourcing. In order to deal with the external and internal uncertainties fuzzy inputs and fuzzy outputs are considered. The problem examined in the paper is described as; Given: (1) A supply chain that is the integration of the focal enterprise, its current suppliers and customers, as well as the potential suppliers and customers, and related products, semi-products and raw materials (in the rest of the paper “product” will be used for these three concepts),(2) Resources used to produce the products as well as their costs and capacity levels,(3) Outsourced products and other outsourcing opportunities, as well as their costs,(4)Production and outsourcing yield rates of product. Using the inputs defined above, the model proposed helps the enterprise make decisions about the following strategic questions: (1) Which product should be produced internally? (2) Which resources should be utilized to the production of which product? (3) Which products should be outsourced, and how much? (4) Demands of which market should be satisfied? The proposed PLP contains fuzziness in some of the constraint parameters and in all decision variables. The objective of the PLP model is to maximize the profit of enterprise’s SC facilities. To solve the proposed PLP model it is suggested to be transformed into a linear programming model, which can be solved easily with the least mathematical effort. Therefore the inputs and the decision variables of the model are represented by triangular fuzzy numbers. Then the summation, multiplication operations as well as the greater than and less than relations that are defined for triangular fuzzy numbers are employed to transform the PLP to a linear program. The proposed PLP model is then applied in a hypothetical example to evaluate the applicability and validity of the model and the solution methodology. As a result of the application it is realized that the uncertainty in the outputs depends on the uncertainty in the inputs. The uncertainty in the inputs affects both the uncertainty and the amount of profit. Under these circumstances the model aims to decrease the uncertainty on the decisions and increase the profit. Consequently model is proved to give satisfactory results.

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