Int. J. Production Economics 111 (2008) 812–821 Optimal booking of machines in a virtual job-shop with stochastic processing times to minimize total machine rental and job tardiness costs Zohar Laslo a,Ã , Dimitri Golenko-Ginzburg b,c , Baruch Keren a a Department of Industrial Engineering and Management, Sami Shamoon College of Engineering, P.O.B 45, 84100 Beer Sheva, Israel b Department of Industrial Engineering and Management (Professor Emeritus), Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel c Department of Industrial Engineering and Management, Academic College of Judea and Samaria, Ariel 44837, Israel Received 8 June 2005; accepted 14 March 2007 Available online 8 May 2007 Abstract We treat a virtual job-shop problem of sequencing n jobs on m unique machines. Each machine is outsourced with known renting cost per time unit. The job-operation processing times have random durations, and each job has its tardiness penalty function. The objective is to determine in advance the machine booking schedule that maximizes an economic gain. We present a simulation based on a cyclic coordinate descent search- algorithm and greedy priority dispatching rule that delivers a rent timetable that minimizes the expected total cost. r 2007 Elsevier B.V. All rights reserved. Keywords: Job-shop; Predictive schedule; Simulation; Cyclic coordinate descent search-algorithm; Priority dispatching rule 1. Introduction Management often fails in adjusting the organi- zational facility availabilities with the delivery commitments to clients. On one hand, the occur- rence of ‘over-commitment’, i.e., accepting too many orders in relation to existing facilities is problematic (Engwall and Jerbrant, 2003), but on the other hand, facility redundancy is cost prohibi- tive. A predictive schedule serves very important functions in adjusting facilities to commitments or vice versa (Mehta and Uzsoy, 1998). An essential element in preparing the predictive schedule is to guarantee facility availabilities within the planning horizon (Bowers, 1995). A pre-schedule can outperform on-line dispatch- ing heuristic rules in shop environments where stochastic durations are assigned to the operation but uncertainty does not exceed a certain threshold (Aytug et al., 2005). Byeon et al. (1998) and Wu et al. (1999) proposed an elegant way to tradeoff between static and dynamic scheduling, showing how to make some important scheduling decisions before schedule execution and relegate the remain- der of the scheduling choices to future points in time. Small fluctuations on the shop-floor are dealt with dynamically but initial decisions impose structure in the shop. ARTICLE IN PRESS www.elsevier.com/locate/ijpe 0925-5273/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2007.03.018 Ã Corresponding author. Tel.: +972 864 756 40; fax: +972 864 756 43. E-mail addresses: zohar@sce.ac.il (Z. Laslo), dimitri@ bgumail.bgu.ac.il (D. Golenko-Ginzburg), baruchke@sce.ac.il (B. Keren).