JOINT OPTIMIZATION OF THE RETAILER'S PRICE, REPLENISHMENT CYCLE AND PRODUCTION RATE IN A VMI SYSTEM WITH DISCOUNTING USING GAME THEORY

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BAHRAMI Z.; PASANDIDEH S.H.R.

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Paper Information

Journal: INDUSTRIAL ENGINEERING & MANAGEMENT SHARIF (SHARIF: ENGINEERING) Year:2019 | Volume:34-1 | Issue:2/2 Page(s): 79-88

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Title

JOINT OPTIMIZATION OF THE RETAILER'S PRICE, REPLENISHMENT CYCLE AND PRODUCTION RATE IN A VMI SYSTEM WITH DISCOUNTING USING GAME THEORY

Author(s)

BAHRAMI Z. | PASANDIDEH S.H.R. | Issue Writer Certificate

Keywords

Vendor managed inventoryQ1

pricingQ1

discountingQ1

stackelberg gameQ1

Abstract

We considered a two echelon supply chain with a vendor who manufactures a product to meet the demand for multiple retailers. It is assumed that demands faced by all the retailers are linear decreasing functions of their prices. The production rate is greater than the total demand rate faced by the vendor, consequently, there is no backordering. Cause of the system is under VMI contract, the vendor is responsible for the replenishment decisions of the retailers. He also bears the ordering costs. Thus, the retailers bear only their respective transportation, holding and purchase costs. In this model, the vendor makes n delivers to retailers in a given production setup. However, the size of the delivery batch increases each time by a factor x (x > 1) and the purchase cost decreases each time by a factor (0 < < 1). The principle aim of the paper is to maximize the profits of the vendor and the retailers by optimizing retailer's price, replenishment cycle and production rate. The Stackelberg approach between the members of the chain is used to solve the problem. In a Stackelberg model one of the members acts as the follower and determines the optimal values of own decision variables. Then the other one acts as the leader and makes decision about his/her strategies according to the best actions of the follower. In this case, the retailers are the followers and the vendor is the leader. The retailers first establish the optimal values of their prices and replenishment cycle and then based on the reactions of the retailers, the vendor optimizes his production rate. The optimal values of decision variables were gained by proofing the concavity of the profit functions and using the first necessary condition. At the end, a numerical example is provided to illustrate the use of the production-inventory model and perform a sensitivity analysis on the holding costs of the retailer and vendor, the purchase cost of the retailer and the number of retailers.

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APA: Copy

BAHRAMI, Z., & PASANDIDEH, S.H.R.. (2019). JOINT OPTIMIZATION OF THE RETAILER'S PRICE, REPLENISHMENT CYCLE AND PRODUCTION RATE IN A VMI SYSTEM WITH DISCOUNTING USING GAME THEORY. INDUSTRIAL ENGINEERING & MANAGEMENT SHARIF (SHARIF: ENGINEERING), 34-1(2/2 ), 79-88. SID. https://sid.ir/paper/107642/en

Vancouver: Copy

BAHRAMI Z., PASANDIDEH S.H.R.. JOINT OPTIMIZATION OF THE RETAILER'S PRICE, REPLENISHMENT CYCLE AND PRODUCTION RATE IN A VMI SYSTEM WITH DISCOUNTING USING GAME THEORY. INDUSTRIAL ENGINEERING & MANAGEMENT SHARIF (SHARIF: ENGINEERING)[Internet]. 2019;34-1(2/2 ):79-88. Available from: https://sid.ir/paper/107642/en

IEEE: Copy

Z. BAHRAMI, and S.H.R. PASANDIDEH, “JOINT OPTIMIZATION OF THE RETAILER'S PRICE, REPLENISHMENT CYCLE AND PRODUCTION RATE IN A VMI SYSTEM WITH DISCOUNTING USING GAME THEORY,” INDUSTRIAL ENGINEERING & MANAGEMENT SHARIF (SHARIF: ENGINEERING), vol. 34-1, no. 2/2 , pp. 79–88, 2019, [Online]. Available: https://sid.ir/paper/107642/en

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