Topic
Single-machine scheduling
About: Single-machine scheduling is a research topic. Over the lifetime, 2473 publications have been published within this topic receiving 56288 citations.
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TL;DR: This article presents a dynamic programming algorithm for scheduling, on a single machine, production of multiple items with time-varying deterministic demands that casts the optimal schedule as a shortest path through a network embedded in a state space.
Abstract: This article presents a dynamic programming algorithm for scheduling, on a single machine, production of multiple items with time-varying deterministic demands. We formulate the scheduling problem with the objective of minimizing the sum of changeover and inventory holding costs. The formulation is appealing in that it represents changeover costs directly instead of by the familiar approximate technique of including setup costs in the objective. Our algorithm, which we developed using an approach similar to C. R. Glassey's that minimizes the total number of changeovers, casts the optimal schedule as a shortest path through a network embedded in a state space. It generates optimal schedules under two assumptions. First, we assume that in each time period within the planning horizon, the machine must either be shut down or be producing some one item for the entire time period. Second, we assume that inventory holding costs are representable as a nondecreasing function of aggregate inventory. We provide a nu...
55 citations
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TL;DR: An in-depth theoretical, algorithmic, and computational study of a linear programming (LP) relaxation to the precedence constrained single-machine scheduling problem 1|prec|S jw jC j to minimize a weighted sum of job completion times.
Abstract: We present an in-depth theoretical, algorithmic, and computational study of a linear programming (LP) relaxation to the precedence constrained single-machine scheduling problem 1|prec|S jw jC jto minimize a weighted sum of job completion times. On the theoretical side, we study the structure of tight parallel inequalities in theLP relaxation and show thatevery permutation schedule that is consistent with Sidney's decomposition has total cost no more than twice the optimum. On the algorithmic side, we provide a parametric extension to Sidney's decomposition and show that a finest decomposition can be obtained by essentially solving a parametric minimum-cut problem. Finally, we report results obtained by an algorithm based on these developments on randomly generated instances with up to 2,000 jobs.
55 citations
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TL;DR: It is shown that complex scheduling problems like general shop problems, problems with multi-processor tasks, problemsWith multi-purpose machines, and problems with changeover times can be reduced to single-machine problems with positive and negative time-lags between jobs.
55 citations
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TL;DR: This paper focuses on the single-machine problems with objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost and shows that the problems remain polynomially solvable under the proposed model.
55 citations
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TL;DR: A polynomial-time algorithm is provided to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes the weighted number of tardy jobs, and due date assignment, makespan, and total resource consumption costs.
Abstract: With the increased emphasis on the effective management of operational issues in supply chains, the timely delivery of products has become even more important. Companies have to quote attainable delivery dates and then meet these, or face large tardiness penalties. We study systems that can be modeled by single-machine scheduling problems with due date assignment and controllable job-processing times, which are either linear or convex functions of the amount of a continuously divisible and nonrenewable resource that is allocated to the task. The due date assignment methods studied include the common due date, the slack due date, which reflects equal waiting time allowance for the jobs, and the most general method of unrestricted due dates, when each job may be assigned a different due date. For each combination of due date assignment method and processing-time function, we provide a polynomial-time algorithm to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes the weighted number of tardy jobs, and due date assignment, makespan, and total resource consumption costs.
55 citations