Abbas-Ali Jafari - Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, Iran
Hassan Khademi Zare - Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, Iran
M.M Lotfi - Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, Iran
Reza Tavakkoli-Moghaddam - School of Industrial Engineering, College of Engineering, University of Tehran, Tehran

In many real production situations, jobs take longer times if the start later. This phenomenon is known as deteriorating jobs. This paper investigates two machine flowshop deteriorating jobs scheduling problem where its objective is to minimize the number of tardy jobs. The actual processing time of a job is an increasing function of its execution start time. The problem is known to be NP-hard; therefore, a branch and bound algorithm incorporating with several dominance rules and lower bounds is proposed to derive the optimal for thr problem. The computational experiments indicate that the branch and bound algorithm can solve most of the medium jobsize problems within reasonable time.

: Number of tardy jobs, Flowshop, Dominance Rules, Branch and Bound, Linear deteriorating jobs