Parallel machine match-up scheduling with manufacturing cost considerations

Abstract

Many scheduling problems in practice involve rescheduling of disrupted schedules. In this study, we show that in contrast to fixed processing times, if we have the flexibility to control the processing times of the jobs, we can generate alternative reactive schedules considering the manufacturing cost implications in response to disruptions. We consider a non-identical parallel machining environment where processing times of the jobs are compressible at a certain manufacturing cost, which is a convex function of the compression on the processing time. In rescheduling it is highly desirable to catch up the original schedule as soon as possible by reassigning the jobs to the machines and compressing their processing times. On the other hand, one must also keep the manufacturing cost due to compression of the jobs low. Thus, one is faced with a tradeoff between matchup time and manufacturing cost criteria.We introduce alternative match-up scheduling problems for finding schedules on the efficient frontier of this time/cost tradeoff. We employ the recent advances in conic mixed-integer programming to model these problems effectively. We further provide a fast heuristic algorithm driven by dual prices of convex subproblems for generating approximate efficient schedules.M.S. Aktürk ( ) · S. Gürel

Submodularity in Conic Quadratic Mixed 0–1 Optimization

“…Although the applicability of such cuts is restricted to certain classes of problems, they tend to be far more effective than the general cuts that ignore any problem structure. Aktürk et al (2009Aktürk et al ( , 2010 give second-order representable perspective cuts for a nonlinear scheduling problem with variable upper bounds, which are generalized further by Günlük and Linderoth (2010) and Atamtürk and Gómez (2018). Ahmed and Atamtürk (2011) give strong lifted inequalities for maximizing a submodular concave utility function.…”

The job shop scheduling problem with convex costs

“…While these times are considered to be constant in most scheduling problems, they are occasionally controllable -at least to some extent-by adjusting the allocation of resources to processing, such as energy, manpower, money, or subcontracting (Shabtay and Steiner, 2007). Various practical applications of this process feature are discussed in the literature: Janiak (1989), for example, considers a scheduling problem in steel mills, Trick (1994) refers to scheduling with tooling machines, and Aktürk et al (2010) address the scheduling of computer numeric control (CNC) turning operations. Scheduling with controllable processing times has received considerable attention from researchers.…”

Technical Note—A Conic Integer Optimization Approach to the Constrained Assortment Problem Under the Mixed Multinomial Logit Model

“…Although there is an extensive body of literature on convex conic quadratic optimization, development of conic optimization with integer variables is quite recent (Ç ezik and Iyengar, 2005;Narayanan, 2007, 2011;Atamtürk et al, 2013). With the growing availability of commercial solvers for these problems (for example, both CPLEX and Gurobi now include solvers for these models), conic quadratic integer models have recently been employed to address problems in portfolio optimization (Vielma et al, 2008), value-at-risk minimization (Atamtürk and Narayanan, 2008), machine scheduling (Aktürk et al, 2010), and supply chain network design (Atamtürk et al, 2012), airline rescheduling with speed control (Aktürk et al, 2014). However, to the best of our knowledge, this approach has not been previously used to solve assortment optimization problems.…”