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**1 - 2**of**2**### Fuzzy Genetic Approach to Economic Lot – Size Scheduling Problem

"... The aim of this paper is to consider formulation of Economic Lot size Scheduling Problem (ELSP) in fuzzy environment with fuzzy inventory costs and objective goal. A Genetic Algorithm (GA) is used to solve the problem in the sense that it is computationally simple, yet powerful in its search for imp ..."

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The aim of this paper is to consider formulation of Economic Lot size Scheduling Problem (ELSP) in fuzzy environment with fuzzy inventory costs and objective goal. A Genetic Algorithm (GA) is used to solve the problem in the sense that it is computationally simple, yet powerful in its search for improvement. This approach is defined as Fuzzy Genetic Approach (FGA). The ELSP is a problem of scheduling the production of several different items over the same facility on a repetitive manner. The facility is such that only one item can be produced at a time. The ELSP formulation in-turn is considered under the Basic Period (BP) approach with the cycle time, Ti, of each item modified and expressed as a real multiple ki of a fundamental cycle T. As the typical inventory analysis in the real world situations is sensitive to reasonable errors in the measurement of relevant inventory costs, the inventory costs are assumed to be vague and imprecise in this paper. The objective of minimizing the total inventory cost is also imprecise in nature. The impreciseness in these variables has been represented by fuzzy linear membership functions. The bench mark problem of Bomberger’s ELSP has been worked out to highlight the method, and the results are compared with those of corresponding crisp model results. The results indicate that the FGA gives good results and works better even for higher utilization levels of the ELSP.

### A Fuzzy Inventory System with Deteriorating Items under Supplier Credits Linked to Ordering Quantity

"... The inventory problem associated with trade credit is a popular topic in which in-terest income and interest payments are important issues. Most studies related to trade credit assume that the interest rate is both fixed and predetermined. However, in the real market, many factors such as financial ..."

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The inventory problem associated with trade credit is a popular topic in which in-terest income and interest payments are important issues. Most studies related to trade credit assume that the interest rate is both fixed and predetermined. However, in the real market, many factors such as financial policy, monetary policy and inflation, may affect the interest rate. Moreover, within the environment of merchandise storage, some distinc-tive factors arise which ultimately affect the quality of products such as temperature, hu-midity, and storage equipment. Thus, the rate of interest charges, the rate of interest earned, and the deterioration rate in a real inventory problem may be fuzzy. In this paper, we deal with these three imprecise parameters in inventory modeling by utilizing the fuzzy set theory. We develop the fuzzy inventory model based on Chang et al.’s [1] model by fuzzifying the rate of interest charges, the rate of interest earned, and the dete-rioration rate into the triangular fuzzy number. Subsequently, we discuss how to deter-mine the optimal ordering policy so that the total relevant inventory cost, in the fuzzy sense, is minimal. Furthermore, we show that Chang et al.’s [1] model (the crisp model) is a special case of our model (the fuzzy model). Finally, numerical examples are pro-vided to illustrate these results.