Abstract
This paper considers an assembly scheduling problem which minimizes the total weighted tardiness. The system consists of multiple manufacturing machines in the first stage and an assembly machine in the second stage. A job is composed of multiple components, each component is manufactured on a dedicated machine in the first stage, and the assembly starts on the assembly machine after the completion of all the components’ manufacturing in the first stage. This paper is to try to find effective and efficient schedules to minimize the total weighted tardiness of jobs. This paper analyzes some solution properties to improve search effectiveness and efficiency. Moreover, some lower-bound procedures are derived, and then four constructive heuristics and a branch-and-bound algorithm are suggested. The performances of the derived algorithms are evaluated through numerical experiments. For the problems with no more than 15 jobs, the branch-and-bound algorithm finds the optimal solutions within 20 minutes, and the performance of the four heuristics seems to be similar. However, for problems with more than 30 jobs, HWT shows the best performance among the four heuristics except for two machines.
Highlights
Academic Editor: Gordon Huang is paper considers an assembly scheduling problem which minimizes the total weighted tardiness. e system consists of multiple manufacturing machines in the first stage and an assembly machine in the second stage
A job is composed of multiple components, each component is manufactured on a dedicated machine in the first stage, and the assembly starts on the assembly machine after the completion of all the components’ manufacturing in the first stage. is paper is to try to find effective and efficient schedules to minimize the total weighted tardiness of jobs. is paper analyzes some solution properties to improve search effectiveness and efficiency
Allahverdi and Aydilek [12], Ha et al [13], and Lee and Bang [14] considered the two-stage assembly scheduling problem to minimize the total tardiness with two dedicated machines in the first stage and one assembly machine in the second stage
Summary
We present some dominance properties for the situation where all the job weights would be nonidentical. Some solution properties are characterized for jobs p and q as follows. If the following conditions hold, job q should be processed immediately before p:. E proof is the same as in Property 3. If the following conditions hold, job q should be processed immediately before p: wqTq(R) + wpTp(R) ≤ wpTp(S) + wqTq(S),. E proof can be made in a similar manner in Property 6. Let π denote a partial sequence whose processing order is already assigned. E heuristic algorithms in this paper are based on a scheme which selects one job that has not been yet allocated and attaches it to the end position of the partial sequence π. A specific procedure is as follows, where Cπ(j) denotes the possible completion time of job j when attaching job j to the end position of π, and Cπ(j) max[max1≤k≤mCkπ + ajk, Cπ] + bj, where Ckπ denotes the completion time of the last-positioned job in machine k in π
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