Optimal manufacturing batch size with rework for a finite-horizon and time-varying demand rates inventory model^∗

¹ Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait.
lakdere.benkherouf@ku.edu.kw
² Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia.
mohd@um.edu.my

Received: 1 December 2015
Accepted: 1 February 2016

Abstract

This paper proposes a finite-horizon and time-varying demand rate function formulations for the optimal manufacturing batch size model with rework. The basic model is found in [Jamal et al. Comput. Ind. Eng. 47 (2004) 77–89.]. Two policies 1 and 2 are considered. In Policy 1 defective items produced in a given period are remanufactured within thesame period while Policy 2 accumulates the defective items until the last period. The search for the optimal manufacturing batch size for policies 1 and 2 is shown to reduce to the problem of determining the number of manufacturing-rework periods as well as their starting and finishing times. This leads to the examination of two mixed integer non-linear programming problem which are completely solved by appealing to some established techniques proposed in [Al-Khamis et al. Int. J. Syst. Sci. 45 (2014) 2196–2202]. Numerical results are also presented for illustration.