Tactical fixed job scheduling with spread-time constraints

Abstract

We address the tactical fixed job scheduling problem with spread-time constraints. In such a problem, there are a fixed number of classes of machines and a fixed number of groups of jobs. Jobs of the same group can only be processed by machines of a given set of classes. All jobs have their fixed start and end times. Each machine is associated with a cost according to its machine class. Machines have spread-time constraints, with which each machine is only available for L consecutive time units from the start time of the earliest job assigned to it. The objective is to minimize the total cost of the machines used to process all the jobs. For this strongly NP-hard problem, we develop a branch-and-price algorithm, which solves instances with up to 300 jobs, as compared with CPLEX, which cannot solve instances of 100 jobs. We further investigate the influence of machine flexibility by computational experiments. Our results show that limited machine flexibility is sufficient in most situations.

Preemptive scheduling with transportation delays between machines

“…In the same context, one may also cite the case of scheduling problems with a subset of fixed jobs. Two versions exist for this issue (depending on the objective studied): the tactical version (Zhou et al, 2014;Yuan and Lin, 2005;Yuan et al, 2007) and the operational version (Eliiyi and Azizo glu, 2011). Other works handling this problem can be found in Arkin and Silverberg (1987), Woeginger (1994), Diedrich and Jansen (2009), Diedrich et al (2010), Rossi et al (2010), Jansen et al (2011) and Gavryushkin et al (2016).…”