Minimizing the Number of Tardy Jobs in the Single Machine Scheduling Problem under Bimodal Flexible and Periodic Availability Constraints
In single machine scheduling problems with availability constraints, machines are not available for one or more periods of time. In this paper, we consider a single machine scheduling problem with flexible and periodic availability constraints. In this problem, the maximum continuous working time for each machine increases in a stepwise manner with two different values allowed. Also, the duration of unavailability for each period depends on the maximum continuous working time of the machine in that same period, again with two different values allowed. The objective is to minimize the number of tardy jobs. In the first stage, the complexity of the problem is investigated and a binary integer programming model, a heuristic algorithm and a branch-and-bound algorithm are proposed in a second stage. Computational results of solving 1680 sample problems indicate that the branch-and-bound algorithm is capable of not only solving problems of up to 20 jobs but also of optimally solving 94.76% of the total number of problems. Based on numerical results obtained, a mean average error of 2% is obtained for the heuristic algorithm.
This paper considers the single machine scheduling problem with precedence constraints and deteriorating jobs. A mathematical model based on binary integer programming (BIP) is developed. By these precedence constraints, jobs can not start before completion of its all predecessors. The represented model is in two steps, in step one the earliest starting time of each job is computed, then the re...متن کامل
This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. The objective is to find a feasible job sequence that minimizes the number of tardy jobs. On the basis of an original mathematical integer programming formulation, this paper shows how both good-quality lower and up...متن کامل
Minimizing the number of tardy jobs for the single machine scheduling problem: MIP-based lower and upper bounds
This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. The objective is to find a feasible job sequence that minimizes the number of tardy jobs. On the basis of an original mathematical integer programming formulation, this paper shows how good-quality lower and upper b...متن کامل
In this paper, an exact geometric algorithm is presented for solving two-job sequencing and scheduling problems in flexible flow shop and job shop environments while the resources are (un)available in some time periods and processors (un)availability is the same in all work centers. This study seems utterly new and it is applicable to any performance measure based on the completion time. The in...متن کامل
Minimizing the Number of Tardy Jobs in a Permutation Flowshop Scheduling Problem with Setup Times and Time Lags Constraints
This paper studies the permutation flowshop scheduling problem with sequence dependent setup times and time lags constraints minimizing the number of tardy jobs. Dependent setup times are defined as the work to prepare the machines between two successive jobs. Time lags are defined as intervals of time that must exist between every couple of successive operations of the same job. Two mathematic...متن کامل
دوره 29 شماره 1
صفحات 15- 34
تاریخ انتشار 2018-03
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