Title: A multi-constraint integrated vendor-buyer problem with beta distributed defective items under stochastic demand

Authors: Nughthoh Arfawi Kurdhi

Addresses: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Sebelas Maret University, Surakarta, 57126, Indonesia

Abstract: This study develops a multi-constraint stochastic integrated system involving a buyer and a vendor with a service level constraint, defective items, the limited buyer's storage space, and the maximum permissible set-up cost for the vendor. The reorder point, set-up cost, lead time, shipment quantity, and the number of deliveries are decision variables. The vendor sells the items to the buyer in a certain number of lots. There are some imperfect quality (defective) items in the arrival lot, and the defective rate is viewed as a beta random variable. The demand has a normal distribution. The shortage is permitted and it is partially backlogged. The Karush-Kuhn-Tucker approach is implemented to solve the discussed model that minimise the joint cost. Sensitivity analyses are performed to provide managerial implications. Using a profit-sharing structure, although both the vendor and the buyer have some business constraints, we observe that they can benefit from the coordinated supply chain.

Keywords: collaborative inventory model; defective items; investment; Karush-Kuhn-Tucker; service level constraint; set-up cost reduction; controllable lead time.

DOI: 10.1504/IJBPSCM.2021.117904

International Journal of Business Performance and Supply Chain Modelling, 2021 Vol.12 No.3, pp.233 - 258

Received: 07 Mar 2020
Accepted: 05 Apr 2021

Published online: 04 Oct 2021 *

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