Showing papers on "Single-machine scheduling published in 1991"
TL;DR: The problem of finding a schedule that minimizes the sum of weighted deviations of the job completion times from a given common due date d is NP-hard as mentioned in this paper, even if all job weights are equal.
135 citations
TL;DR: This paper considers the use of three local search strategies within a tabu search (TS) method for the approximate solution of a single machine scheduling problem and constructs a TS method that employs both swap and insert moves.
Abstract: In this paper we discuss the use of three local search strategies within a tabu search (TS) method for the approximate solution of a single machine scheduling problem. The problem consists of minimizing the sum of the set-up costs and linear delay penalties whenN jobs, arriving at time zero, are to be scheduled for sequential processing on a continuously available machine. Following a review of a previous study of this problem, we first consider a TS method that uses the common approach of making a succession of pairwise job exchanges, or swaps, to move from one trial solution to another. Next, we consider the use of insert moves to define the local neighborhood of each trial solution. These moves consist of transferring a single job from one position to another in the schedule. Finally, we construct a TS method (TS-hybrid) that employs both swap and insert moves. Experiments with benchmark problems of up to 60 jobs illustrate that there is an advantage in using more than one strategy to move from one trial solution to another within a TS method.
116 citations
TL;DR: The main result is a complete description of the minimal linear system defining P when the precedence constraints are series-parallel, which consists of two classes of facet-inducing inequalities, associated with series and parallel compositions, respectively.
Abstract: We consider nonpreemptive single-machine scheduling subject to precedence constraints. We define feasible schedules by the vector of the job completion times and study the structure of the convex hull of all feasible schedules, called the scheduling polyhedron P. We derive classes of valid inequalities for P, and necessary and sufficient conditions under which they are facet-inducing. Our main result is a complete description of the minimal linear system defining P when the precedence constraints are series-parallel. Moreover, this system consists of two classes of facet-inducing inequalities, associated with series and parallel compositions, respectively. If the precedence constraints are not series-parallel, we present another class of facet-inducing inequalities for P, associated with induced Z-subgraphs. We also show that the convex hull of all preemptive feasible schedules is identical to P if and only if the precedence constraints form an out-forest.
92 citations
TL;DR: A greedy randomized adaptive search procedure (GRASP) is presented for an unusually difficult single machine scheduling problem with flow time and earliness penalties and constructs an optimal solution typically within 10 s of CPU time on a personal computer for 58 out of the 60 problems tested with 30 jobs.
89 citations
TL;DR: It is shown that the decision form of the problem dealt with is NP-complete in the strong sense for the case of identical release date reduction rates and some efficiently solvable cases and an approximate algorithm are shown.
66 citations
TL;DR: New heuristic dominance rules and a flexible decomposition heuristic are developed for the problem of minimizing weighted tardiness on a single processor, basically relaxations of optimal solution algorithms that could easily be adapted for use in the solution of other scheduling problems.
Abstract: New heuristic dominance rules and a flexible decomposition heuristic are developed for the problem of minimizing weighted tardiness on a single processor Extensive computational experience demonstrates that, when our new heuristic dominance rules were incorporated into an optimal algorithm, optimal or nearly optimal solutions were obtained quickly In fact, solution times were orders of magnitude faster than those using the optimal algorithm alone On larger problems, our decomposition heuristic obtained better solutions than previous heuristics Furthermore, on 50-job problems our decomposition heuristic obtained an optimal solution over ten times more often on the average than the best competing heuristic (22% versus 2% of the time) Since both our approaches are basically relaxations of optimal solution algorithms, they could easily be adapted for use in the solution of other scheduling problems
34 citations
TL;DR: The effectiveness of the algorithm is evaluated and it is shown that in many cases the algorithm picks an optimal order.
24 citations
TL;DR: The n-job, single-machine total tardiness problem is considered and a branching algorithm based on three theorems is proposed to generate a reduced set of candidate sequences.
Abstract: The n-job, single-machine total tardiness problem is considered in this paper. A branching algorithm based on three theorems is proposed to generate a reduced set of candidate sequences. The computational results indicate that the proposed algorithm provides a smaller set of candidate sequences than the DP algorithm of Schrage and Baker.
19 citations
TL;DR: A set of stochastic jobs is to be processed on a single machine that is subject to breakdown, and it is demonstrated the existence of a nonpreemptive policy that is optimal in the class of all preemptive ones.
Abstract: A set of stochastic jobs is to be processed on a single machine that is subject to breakdown. All jobs make progress as they are processed in the absence of machine breakdowns. However, breakdowns cause setbacks to (possibly) all jobs in the system, except those that have already been completed. With machines subject only to fairly mild restrictions on this “damage” process, we demonstrate the existence of a nonpreemptive policy that is optimal in the class of all preemptive ones.
14 citations
TL;DR: A worst-case performance of the shortest-processing-time (SPT) heuristic in minimizing a quadratic function of job lateness for single machine scheduling is analyzed and it is shown that the SPT sequence is asymptotically optimal.
Abstract: This paper analyses a worst-case performance of the shortest-processing-time (SPT) heuristic in minimizing a quadratic function of job lateness for single machine scheduling. A sufficient condition on processing-plus-wait due dates is found for the SPT sequence to be optimal. A worst-case lower bound to the optimal solution is derived from the SPT sequence. It is then shown that the SPT sequence is asymptotically optimal. Extensive computational experiments suggest that the SPT heuristic may be a good choice for just-in-time production.
11 citations
TL;DR: This paper considers the problem of minimizing the total job processing cost plus the average flow cost, and the tolerance ranges of job processing times are determined so that the optimal sequence remains unchanged.
TL;DR: Efficient algorithms that generate a detailed operation plan for satellite-switched time-division multiple access (SS/TDMA) systems are proposed and are shown to be applicable to practical systems operating with transponder hopping and multidestination bursts.
Abstract: Efficient algorithms that generate a detailed operation plan for satellite-switched time-division multiple access (SS/TDMA) systems are proposed. A burst time plan generation problem is analyzed and two algorithms for burst scheduling are presented. The first method is an algorithm based upon a bin pack problem. The other algorithm schedules new bursts while reassigning already scheduled bursts by a single machine scheduling model. These algorithms are shown to be applicable to practical systems operating with transponder hopping and multidestination bursts. Simulation results for a number of example problems are presented. >