Development of Order Quantity Optimization Model for Growing Item Considering the Imperfect Quality and Incremental Discount in Three Echelon Supply Chain

Abstract

This research develops an optimization model for determining the order quantity for growing items by considering the imperfect quality and incremental discount by involving three supply chain members: farmers, processors, and retailers. The farmers are responsible for caring for the newborn items until they reach their ready-to-eat weight. The processors perform two roles, namely processing and screening. In the processing role, the processors process the grown items by a slaughtering and packaging process. Afterward, they inspected the processed items and categorized the items into good and poor quality. Finally, they shipped the end products to retailers. The retailers are responsible for selling good-quality items to the final consumers. This research considers two kinds of poor quality. First is the poor quality of growing items in terms of mortality rate. The second is the poor quality of final products on the processor side. The processed items with poor quality are then sold to the secondary market at lower prices in one batch at the end of the period. This model also considers the incremental discounts offered by vendors to farmers and retailers to consumers for specific amounts of purchases. The model's objective function is to maximize the total supply chain profit, with the number of orders quantity, cycle time, and the number of batches delivery set as the decision variables. The sensitivity analysis results show that the most sensitive parameter in the model is the probability that the live items survive throughout the growth period.

Discontinuous Economic Growing Quantity Inventory Model

“…The models consider sending a certain number of equally sized batches to retailers. Hidayat et al [10] and Sitanggang et al [11] integrated incremental discount policies for the acquisition of growing items from a supplier. Sebatjane and Adetunji [12] developed a growing inventory model where some of the growing items have poor quality and a lower selling price after a 100% screening process.…”

“…(1) Determine the optimal value of m * using Equation (11) and then calculate the optimal value of ∆1(m) using Equation ( 8); (2) Calculate the values of ∆2(t) using Equation ( 9) with respect to the values of t within the interval of 30 to 100 days; (3) The point with the lowest value of ∆2(t) is the optimal slaughter age ( t * ); (4) Based on the optimal values of m * and t * , calculate the optimal value of the total cost (TC * (m,t) ) using Equation (7).…”

“…Given the stated data and Equation (11), the optimal number (m * ) is 48. Based on this optimal number, the optimal value of ∆1(m) would be $5531.6 using Equation (7), while the optimal slaughter age is computed as 51 by searching the whole feasible space in the range of 30 to 100 days.…”