Mona Ahmadi Rad - PhD student at the Department of Industrial Engineering, K.N.Toosi University of Technology, Tehran, Iran
Mohammad Jafar Tarokh - Associate Professor at the same Department
Farid Khoshalhan - Associate Professor at the same Department

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, numericalexample 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.

Integrated inventory model Lot-splitting strategy Backorder particle swarm optimization