A tabu-search algorithm for scheduling jobs with controllable processing times on a single machine to meet due-dates

In many real-world production systems, it is important to schedule jobs such that they could be processed and shipped with no delay. In this paper, we consider the problem of scheduling n jobs with arbitrary release dates and due dates on a single machine, where job-processing times can be controlled by the allocation of a common resource, and the operation is modeled by a non-linear convex resource consumption function. The objective is to obtain an optimal processing permutation as well as an optimal resource allocation, such that all the jobs can be finished no later than their due dates, and the total resource consumption can be minimized. The problem is strongly NP- hard. A two-layer-structured algorithm based on the tabu-search is presented. The computational result, compared with that from a branch and bound algorithm, shows the algorithm is capable of producing optimal or near optimal solution for large-sized problems in an acceptable computational time.

[1]  Dvir Shabtay,et al.  Convex resource allocation for minimizing the makespan in a single machine with job release dates , 2004, Comput. Oper. Res..

[2]  Adam Janiak,et al.  Single machine scheduling problem with a common deadline and resource dependent release dates , 1991 .

[3]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[4]  Graham McMahon,et al.  On Scheduling with Ready Times and Due Dates to Minimize Maximum Lateness , 1975, Oper. Res..

[5]  J. K. Lenstra,et al.  Computational complexity of discrete optimization problems , 1977 .

[6]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[7]  T.C.E. Cheng,et al.  SINGLE-MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND EARLINESS, TARDINESS AND COMPLETION TIME PENALTIES , 1999 .

[8]  Mauro Dell'Amico,et al.  Applying tabu search to the job-shop scheduling problem , 1993, Ann. Oper. Res..

[9]  Fred Glover,et al.  Tabu Search: A Tutorial , 1990 .

[10]  Dvir Shabtay,et al.  A bicriteria approach to minimize maximal lateness and resource consumption for scheduling a single machine , 2007, J. Sched..

[11]  Dvir Shabtay,et al.  A survey of scheduling with controllable processing times , 2007, Discret. Appl. Math..

[12]  Zuren Feng,et al.  A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates , 2010, Ann. Oper. Res..

[13]  Dvir Shabtay,et al.  Parallel machine scheduling with a convex resource consumption function , 2006, Eur. J. Oper. Res..

[14]  Clyde L. Monma,et al.  Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions , 1990, Math. Oper. Res..

[15]  Adam Janiak.  One-machine scheduling problems with resource constraints , 1986 .

[16]  Dvir Shabtay,et al.  Minimizing the total weighted flow time in a single machine with controllable processing times , 2004, Comput. Oper. Res..

[17]  Dvir Shabtay,et al.  Single and two-resource allocation algorithms for minimizing the maximal lateness in a single machine , 2004, Comput. Oper. Res..

[18]  Stanislaw Zdrzalka.  Scheduling jobs on a single machine with release dates, delivery times and controllable processing times: worst-case analysis , 1991, Oper. Res. Lett..

[19]  Furkan Kiraç,et al.  A tabu search algorithm for parallel machine total tardiness problem , 2004, Comput. Oper. Res..

[20]  Dvir Shabtay,et al.  Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function , 2006 .

[21]  C. N. Potts,et al.  Technical Note - Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times , 1980, Oper. Res..

[22]  Chung-Yee Lee,et al.  Multiple-Project Scheduling with Controllable Project Duration and Hard Resource Constraint: Some Solvable Cases , 2001, Ann. Oper. Res..