Quota Allocation to Distributors of the Supply Chain under Distributors' Uncertainty and Demand Uncertainty by Using Fuzzy Goal Programming

The supply chain consists of multiple components including suppliers, manufacturing centers, and distributors. The decisionmaking on quota allocation to distributors under Distributors’ uncertainty and demand uncertainty are important parts of supply chain of many firms. In this paper, fuzzy goal programming approach is applied for quota allocation to distributors of the supply chain. Customers are assumed as a random variable, and distribution is continuous and normal. Due to surge effect, the demand through supply chain is varied, which is calculated for a particular inventory policy for reserve stock, and sudden rise and fall of demand to the Std limits of normal distribution. The maximum and minimum values of demand at the distributors' stage are considered for various Std limits. And they formulate a fuzzy goal programming by considering linear member ship function. Commercially available LINDO software is used to solve the fuzzy goal-programming problem for quota allocation to the distributors. From the results, it is found that maximized sales revenue, minimized transportation cost, minimized late deliveries, and minimized defective items are increased from maximum STD limit to the minimum STD limit. Change in minimized late deliveries and minimized defective items are negligible to consider. Moreover, difference of maximized sales revenue and minimized transportation cost is significant to consider, and it is increased from maximum STD limit to the minimum Std limit of demand. This means maximum difference can be obtained at low fluctuation of the demand than the high fluctuation of the demand. The formulated Fuzzy Goal Program can be used to solve actual problems.