Abstract
The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much harder problem, a heuristic algorithm is proposed to find approximate solutions. Through computational experiments, the heuristic algorithms’ performance is evaluated with problems up to 500 jobs.
Highlights
Introduction and Literature ReviewMany objectives in scheduling are linked to due dates, which focus on meeting costumers’ delivery dates
Given that common due date (CDD) < F2 + Δ 2, jobs in M2 cannot be optimally scheduled by using the SCHED algorithm; instead this problem needs to be treated as a single machine problem with a restricted CDD, which can be optimally solved by using the dynamic programming (DP) procedures proposed by Hall et al [6]
Computational solution times increase approximately linearly with n for the unrestricted case and in proportion to n2 for the semirestricted case. These results confirm that JSSPET algorithm finds optimal solutions for both the unrestricted and the semirestricted cases for large random instances of the problem within no more than 20 minutes. Such result is made possible by the new optimality conditions extended from the single machine problem provided in this paper and which enable us to prove the optimality of the dynamic programming procedure
Summary
Introduction and Literature ReviewMany objectives in scheduling are linked to due dates, which focus on meeting costumers’ delivery dates. In Just in Time (JIT) manufacturing and production systems, it is intended to reduce both earliness and tardiness by constructing a job schedule in which the jobs are finished as close as possible to their due date. Much less has been published on scheduling problems for job shops (e.g., Lauff and Werner [30], Baptiste et al [31], Yang et al [32], and Wang and Li [33]). Lauff and Werner [30, 35] reviewed multistage systems involving earliness and tardiness problems with CDD as well
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