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2 results

  • 4 - Single-Stage Environment

  • from Part II - Basic Methods
  • Christos T. Maravelias, Princeton University, New Jersey
  • Book:
    Chemical Production Scheduling
    Published online:
    01 May 2021
    Print publication:
    06 May 2021, pp 98-127

  • Summary

    In this chapter, we discuss problems in the single-stage or parallel-units environment. The problem statement is presented in Section 4.1. Three types of models are presented in Section 4.2 (sequence-based), Section 4.3 (continuous time grid-based), and Section 4.4 (discrete time grid-based). In Section 4.5, we present how batching decisions can be handled, and in Section 4.6 we discuss how the three types of models can be extended to handle a new feature, namely, general shared resources. Finally, in Section 4.7 we present extensions on the modeling of general resource constraints using discrete modeling of time. Building upon the material in Chapter 3, we illustrate how some of the modeling techniques introduced for single-unit problems can be extended to account for multiple units. Our goal is to outline some general ideas that the reader can apply to a wider range of problems.We focus on (1) problem features that are new, compared to the ones in single-unit problems (i.e., batching decisions and general shared resources); and (2) new modeling techniques that are necessary to account for these features.

  • On Minimizing Total Tardiness in a Serial Batching Problem

  • Philippe Baptiste, Antoine Jouglet
  • Journal:
    RAIRO - Operations Research / Volume 35 / Issue 1 / January 2001
    Published online by Cambridge University Press:
    15 August 2002, pp. 107-115
    Print publication:
    January 2001

  • We study the problem of scheduling jobs on a serial batching machineto minimize total tardiness. Jobs of the same batch start and arecompleted simultaneously and the length of a batch equals the sum ofthe processing times of its jobs. When a new batch starts, a constantsetup time s occurs. This problem 1| s-batch| ∑Ti isknown to be NP-Hard in the ordinary sense. In this paper we show thatit is solvable in pseudopolynomial time by dynamic programming.