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Mona Ahmadi Rad, Mohammadjafar Tarokh, Farid Khoshalhan ,
Volume 22, Issue 1 (IJIEPR 2011)

  This article investigates integrated production-inventory models with backorder. A single supplier and a single buyer are considered and shortage as backorder is allowed for the buyer. The proposed models determine optimal order quantity, optimal backorder quantity and optimal number of deliveries on the joint total cost for both buyer and supplier. Two cases are discussed: single-setup-single-delivery (SSSD) case and single-setup-multiple-deliveries (SSMD) case. Two algorithms are applied for optimizing SSMD case: Gradient search and particle swarm optimization (PSO) algorithms. Finally, numerical example and sensitivity analysis are provided to compare the total cost of the SSSD and SSMD cases and effectiveness of the considered algorithms. Findings show that the policy of frequent shipments in small lot sizes results in less total cost than single shipment policy .

Mona Ahmadi Rad , Farid Khoshalhan,
Volume 22, Issue 2 (IJIEPR 2011)


  inventory model,


  buyer ,


  lot for lot policy

In this paper, an inventory model for two-stage supply chain is investigated. A supply chain with single vendor and single buyer is considered. We assume that shortage as a backorder is allowed for the buyer and the vendor makes the production set up every time the buyer places an order and supplies on a lot for lot basis. With these assumptions, the joint economic lot size model is introduced and the minimum joint total relevant cost and optimal order quantity and optimal shortage quantity are obtained for both the buyer and the vendor at the same time. Numerical example is given and then Sensitivity analysis is performed to study the effects of changes in the parameters on optimum joint total relevant cost and optimal order quantity and optimal shortage quantity .

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