An Optimal Ordering Cycle at Interactions of Fuzzy Parameters and High Disposal Fees of Food or Drug Supply Systems

Abstract

In many cities the food and drug waste is invading their districts, and disposal fees are high. In this paper we investigate how to determine an optimal ordering cycle when the demand for products and the price are fuzzy variables, and lead time is constant, in the case of perishable food or drugs of unknown deteriorating ratio, and at high disposal fees. The parameters required for the solution are trapezoidal membership functions for the fuzzy demand, the fuzzy purchase cost for each item, the fixed cost to place the order, and the cost of disposal (i.e. disposal fee), the fuzzy deterioration rate, and the fixed storage cost specified for each item per period. The three fuzzy parameters in the total cost function are described as trapezoidal fuzzy variables so that the influence of volatility of these variables on the criterion function could be calculated. In the paper, the safety stock decays at the same rate as the rest of the inventory. Credibility distributions are given for such cases. Here, we demonstrated that the expected value of total costs in the ordering cycle is equal to the signed distance to the origin. The kurtosis of variables when appearing simultaneously, and their influence on the disposal fee are under investigation, therefore the trapezoidal membership functions are investigated. Through an extensive analytical study and the numerical example, we concluded the following: (1) for the items having a trapezoidal demand membership function, increasing the volatility of demand generates a membership function with a flatter shape, thus shortening the optimal ordering cycle, and (2) an increment of fuzziness reduces the optimal cycle length more gradually than the crisp values, when the sum of the purchase price plus the disposal fee of the product, or the demand, or the deterioration rate are increasing. This means that a high fuzziness reduces the sensitivity of the optimal cycle duration.