Optimal and simple algorithms to solve integrated procurement-production-inventory problem without/with shortage

¹ Department of Industrial Engineering, Faculty of industrial & Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
² School of Engineering and Sciences Tecnológico de Monterrey E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, Nuevo León, México
³ Department of Engineering, Ruddehn Branch, Islamic Azad University, Tehran, Iran

^* Corresponding author: lecarden@itesm.mx

Received: 22 June 2017
Accepted: 5 October 2017

Abstract

This research work deals with an imperfect production system considering the purchasing of raw materials in order to study the economic production quantity (EPQ). This manufacturing system produces perfect and defective finished products; defectives are considered as scrap. A single product is manufactured from multiple raw materials which are purchased from outside suppliers. In the integrated procurement-production-inventory (IPPI) model, one of the principal decisions, in addition to determining the optimal lot size to produce, is to define the number of optimal orders of each raw material with respect to rate of consumption in the manufacturing of finished product. Two cases are considered: without shortage (first model) and with shortage (backordering, second model). In the first model, the purpose is to determine jointly the optimal lot size to manufacture and the optimal number orders of each raw material in order to minimize the total cost. The second model obtains the optimal number of orders of each raw material, the optimal lot size to manufacture and the optimal shortage level with aim to minimize the total cost. This research also shows that both of the proposed inventory models are a convex programming problem, so exact algorithms to solve these inventory problems are proposed.