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.


Dhaiban, A.K., Comparison between Linear Programming Model and Optimal Control Model of Production–Inventory System, Current Science, 112(9), 2017, pp. 1855-1863.

Dutta, D., and Kumar, P., Fuzzy Inventory Model without Shortage using Trapezoidal Fuzzy number with Sensitivity Analysis, IOSR Journal of Mathematics, 4(3), 2012, pp. 32-37.

Mishra, V. K. and Shanker, K., Optimal Ordering Quantities for Substitutable Items under Joint Replenishment with Cost of Substitution, Journal of Industrial Engineering International, 13(3), 2017, pp. 77-104.

Rezaei, J., Economic Order Quantity for Growing Items, International Journal of Production Economics, 155, 2014, pp. 109-113.

Nobil, A. H., Sedigh, A. H. A., and Cárdenas-Barrón, L. E., A Generalized Economic Order Quantity Inventory Model with Shortage: Case Study of a Poultry Farmer, Arabian Journal for Science and Engineering, 44(3), 2019, pp. 2653-2663.

Zhang, Y., Li, L. Y., Tian, X. Q., and Feng, C., Inventory Management Research for Growing Items with Carbon-Constrained, In: 2016 35th Chinese Control Conference (CCC). IEEE, 2016. p. 9588-9593.

Sebatjane, M. and Adetunji, O., Economic Order Quantity Model for Growing Items with Imper-fect Quality, Operations Research Perspectives, 6, 2019, pp. 100088.

Sebatjane, M. and Adetunji, O., Economic Order Quantity Model for Growing Items with Incremen¬tal Quantity Discounts, Journal of Indus¬trial Engineering International, 15(4), 2019, pp. 545-556.

Hidayat, Y. A., Riaventin, V. N., and Jayadi, O., Economic Order Quantity Model for Growing Items with Incremental Quantity Discounts, Capacitated Storage Facility, and Limited Budget, Jurnal Teknik Industri, 22(1), 2020, pp. 1-10.

Luluah, L., Rosyidi, C. N., and Aisyati, A., Optimization Model for Determining Order Quantity for Growing Item Considering Incre-men¬tal Discount and Imperfect Quality. In IOP Conference Series: Materials Science and Engi-neering, 1096(1), 2021, p. 012023. IOP Publis-hing.

Sebatjane, M., and Adetunji, O., Optimal Inven-tory Replenishment and Shipment Poli¬cies in a Four-Echelon Supply Chain for Grow¬ing Items with Imperfect Quality, Production & Manu-facturing Research, 8(1), 2020, pp. 130-157.

Konstantaras, I., Goyal, S. K., & Papachristos, S., Economic Ordering Policy for An Item with Imperfect Quality Subject to the In-house Inspec¬tion, International Journal of Systems Scien¬ce, 38(6), 2007, pp. 473-482.

Al Fauzi, A. L., Darti, I., and Suryanto, A. Kon-trol Optimal pada Model Economic Order Quan-tity (EOQ) dengan Inisiatif Tim Penjual-an, Jurnal Teknik Industri, 19(1), 2017, pp. 21-28.

Gharaei, A. and Almehdwe E., Economic Growing Quantity, International Journal of Production Economics, 223, 2020, p. 107517.

Gharaei, A., and Almehdawe, E., Optimal Sus-tain¬able Order Quantities for Growing Items, Journal of Cleaner Production, 307,2021,p. 127216.

Khalilpourazari, S. and Pasandideh, S.H.R., Modelling and Optimization of Multi-Item Multi-Constrainted EOQ Model for Growing Items, Knowledge-Based Systems, 164, 2019, pp. 150-162.

Sarjono, H., and Kuncoro, E. A., Analisis Perbandingan Perhitungan Re-Order Point, Binus Business Review, 5(1), 2014, pp. 288-300.

Sebatjane, M., and Adetunji, O., Three-Echelon Supply Chain Inventory Model for Growing Items, Journal of Modelling in Management, 15(2), 2019, pp. 567-587.

Sebatjane, M., and Adetunji, O., Optimal Lot-Sizing and Shipment Decisions in a Three-Echelon Supply Chain for Growing Items with Inventory Level-and Expiration Date-dependent Demand, Applied Mathematical Modelling, 90, 2021, pp. 1204-1225.

Jauhari, W. A., and Saga, R. S., A Stochastic Periodic Review Inventory Model for Vendor-Buyer System with Setup Cost Reduction and Service Level Constraint, Production & Manu-fac¬turing Research, 5(1), 2017, pp. 371–389.

Malekitabar, M., Yaghoubi, S., and Gholamian, M. R., A Novel Mathematical Inventory Model for Growing-mortal Items (Case Study: Rainbow Trout), Applied Mathematical Modelling, 71, 2019, pp. 96–117.

Khan, M., Jaber, M. Y., and Ahmad, A. R., An Integrated Supply Chain Model with Errors in Quality Inspection and Learning in Production, Omega, 42(1), 2014, pp. 16–24.

Hsu, J. T., and Hsu, L. F., An Integrated Vendor Buyer Cooperative Inventory Model in an Imperfect Production Process with Shortage Back¬ordering, International Journal of Ad¬van-ced Manufacturing Technology, 65(1–4), 2013, pp. 493–505.

Taleizadeh, A. A., Stojkovska, I., & Pentico, D. W., An Economic Order Quantity Model with Partial Backordering and Incremental Dis-count, Computers & Industrial Engineering, 82, 2015, pp. 21-32.

Wangsa, I.D., and Wee H.M., Integrated Inventory System with Freight Costs and Two Types of Quantity Discounts, International Journal of Logistics Systems and Management, 35(1), 2020, pp. 119-147.