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


  • Indah Valentinova Sitanggang Universitas Sebelas Maret Surakarta
  • Cucuk Nur Rosyidi Universitas Sebelas Maret Surakarta
  • Azizah Aisyati Universitas Sebelas Maret Surakarta


Growing item, economic order quantity, imperfect quality, incremental discount, inventory system, supply chain


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.

Author Biographies

Indah Valentinova Sitanggang, Universitas Sebelas Maret Surakarta

Faculty of Engineering, Industrial Engineering Department, Universitas Sebelas Maret, Jl. Ir. Sutami 36A, Surakarta 57126, Indonesia.

Cucuk Nur Rosyidi, Universitas Sebelas Maret Surakarta

Faculty of Engineering, Industrial Engineering Department, Universitas Sebelas Maret, Jl. Ir. Sutami 36A, Surakarta 57126, Indonesia

Azizah Aisyati, Universitas Sebelas Maret Surakarta

Faculty of Engineering, Industrial Engineering Department, Universitas Sebelas Maret, Jl. Ir. Sutami 36A, Surakarta 57126, Indonesia.


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