A branch and bound algorithm to minimize completion time variance on a single processor
TL;DR: A branch and bound algorithm is presented and the same algorithm is extended to generate epsilon optimal solutions for large sized problems (i.e., number of jobs > 30) and results of simulated annealing are compared.
About: This article is published in Computers & Operations Research.The article was published on 2003-07-01. It has received 37 citations till now. The article focuses on the topics: Branch and bound & Branch and cut.
Citations
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TL;DR: A consistent pattern in the plot of WTV over mean of all possible sequences for a set of jobs is discovered, which can be used to evaluate the sacrifice of mean waiting time while pursuing WTV minimization.
47 citations
TL;DR: Carrier assignment models used in winner determination auctions for transportation procurement are extended to include shipper non-price objectives and carrier transit point costs, and solutions are developed for the new models.
Abstract: This paper extends carrier assignment models used in winner determination auctions for transportation procurement to include shipper non-price objectives and carrier transit point costs. The models are unlike traditional carrier assignment models which incorporate only carrier lane bids, and different from combinatorial auction models which focus on packets of lanes without considering transit point costs. We develop solutions, including metaheuristics, for the new models and through computational experimentation show that the algorithms work well and can be easily implemented.
38 citations
Cites background from "A branch and bound algorithm to min..."
...A branch-and-bound (B&B) complete search can be used to examine all possible assignments of the lanes to carriers for small test sizes, where the time performance of the algorithm depends largely on the bounding function used (Viswanathkumar and Srinivasan, 2002)....
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TL;DR: The proposed spreadsheet-based genetic algorithm approach is found to perform better than the previous GA, simulated annealing (SA) and Tabu search (TS) approaches for variance minimization in that it produces an optimal solution for all the test problems.
Abstract: This paper addresses an n-job, single-machine scheduling problem with an objective to minimize flow-time variance, a non-regular performance measure. A spreadsheet-based genetic algorithm (GA) approach is presented to solve the problem. A domain-independent general-purpose GA is used, which is an add-in to the spreadsheet software. The paper demonstrates an adaptation of the proprietary GA software to the problem of variance minimization. To test the performance of the proposed approach, test problems are taken from already published literature. The proposed approach is found to perform better than the previous GA, simulated annealing (SA) and Tabu search (TS) approaches for variance minimization in that it produces an optimal solution for all the test problems. Empirical analysis was carried out to study the effect of GA parameters, namely, the crossover rate, mutation rate, and population size.
20 citations
Cites background from "A branch and bound algorithm to min..."
...Viswanathkumar and Srinivasan [ 12 ] develop a branch-andbound algorithm to solve the CTV class of problems....
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TL;DR: A lower bound on CTV is developed for the static jobshop problem and a backward scheduling approach is proposed using the observations on the development of lower bound for hierarchical minimization of CTV and makespan.
18 citations
TL;DR: Two job scheduling algorithms, Weighted Verified Spiral and Weighted Simplified Spiral, are developed for the WWTV problems, and numerical testing shows that WVS and WSS significantly outperform existing WWTV algorithms.
16 citations
Cites methods from "A branch and bound algorithm to min..."
...A branch and bound algorithm to minimize CTV is given in (Viswanathkumar & Srinivasan, 2003) and a tabu search-based solution is developed in (Al-Turki, 2001)....
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References
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TL;DR: This heuristic procedure is proposed which is based on the complementary pair-exchange principle and provides improved results (in terms of objective-function value) when compared with other heuristics.
Abstract: In this paper we deal with an n-job, single-machine scheduling problem. All jobs are available from the start, and the objective is to minimize the variance of job flow-times. A heuristic procedure which is based on the complementary pair-exchange principle is proposed. It has been concluded that this heuristic procedure provides improved results (in terms of objective-function value) when compared with other heuristics. Our heuristic procedure has the complexity of O(n log n).
42 citations
TL;DR: The algorithm is a hybrid of a greedy approach, followed by a simulated annealing search of the V-shaped sequence solution space, which gives better solutions than the heuristics previously presented in the literature.
38 citations
TL;DR: Borders on the position of the smallest job in an optimal sequence are developed and a new heuristic method to solve the problem of scheduling jobs on a single machine is developed.
28 citations
"A branch and bound algorithm to min..." refers background or methods or result in this paper
...The heuristic of Manna and Prasad [12] has been run on the Pentium processor PC for problems with number of jobs up to 40....
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...For large problems (n=30 to 100) the solutions have been compared with simulated annealing [16], tabu search algorithms [17] and heuristic of Manna and Prasad [12] by computing the percentage deviations from the lower bounds....
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...Manna and Prasad [12] have reported in their work that their heuristic performs best when compared with other available heuristics in the literature and hence this heuristic has been chosen for comparison....
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...number of jobs from 55 to 100) gives much superior solutions when compared with heuristic of Manna and Prasad [12]....
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...[10], Ventura and Weng [11], Manna and Prasad [12]....
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TL;DR: A Lagrangian relaxation LR procedure is developed to find a lower bound LB to the optimal objective value of n-job, single-machine scheduling, and it is shown that the lower bounds obtained by the LR procedure are very close to the best known objective values.
Abstract: In this article the problem of minimizing the completion time variance in n-job, single-machine scheduling is considered. The release times for all jobs are assumed to be zero. A new quadratic integer programming formulation is introduced. A Lagrangian relaxation LR procedure is developed to find a lower bound LB to the optimal objective value. When the number of jobs is between 100 and 500, our computational study shows that the lower bounds obtained by the LR procedure are very close to the best known objective values. A new heuristic algorithm is also described. The first phase of the heuristic algorithm is a construction procedure whose purpose is to identify a good initial sequence. The second phase is an improvement procedure based on pairwise interchanges. The new heuristic algorithm provides improved solutions compared to the best known heuristic.
23 citations
TL;DR: A lower bound on minimum completion time variance given by De et al. (1992) is corrected using a simple proof and computational results on the lower bound are provided.
Abstract: This paper is concerned with the single machine scheduling problem where the objective is to minimize the variance of the job completion times. A lower bound on minimum completion time variance given by De et al. (1992) is corrected using a simple proof. Computational results on the lower bound are also provided.
2 citations