TY - JOUR
T1 - Theoretical framework for formulating MIP scheduling models with multiple and non-uniform discrete-time grids
AU - Velez, Sara
AU - Maravelias, Christos T.
N1 - Funding Information:
The authors would like to acknowledge financial support from the National Science Foundation under grant CBET-1066206.
Publisher Copyright:
© 2014 Elsevier Ltd.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2015/1/2
Y1 - 2015/1/2
N2 - We present a framework for the formulation of MIP scheduling models based on multiple and nonuniform discrete time grids. In a previous work we showed that it is possible to use different (possibly non-uniform) time grids for each task, unit, and material. Here, we generalize these ideas to account for general resources, and a range of processing characteristics such as limited intermediate storage and changeovers. Each resource has its own grid based on resource consumption and availability allowing resource constraints to be modeled more accurately without increasing the number of binary variables. We develop algorithms to define the unit-, task-, material-, and resource-specific grids directly from problem data. Importantly, we prove that the multi-grid formulation is able to find a schedule with the same optimal objective as the discrete-time single-grid model with an arbitrarily fine grid. The proposed framework leads to the formulation of models with reduced number of binary variables and constraints, which are able to find good solutions faster than existing models.
AB - We present a framework for the formulation of MIP scheduling models based on multiple and nonuniform discrete time grids. In a previous work we showed that it is possible to use different (possibly non-uniform) time grids for each task, unit, and material. Here, we generalize these ideas to account for general resources, and a range of processing characteristics such as limited intermediate storage and changeovers. Each resource has its own grid based on resource consumption and availability allowing resource constraints to be modeled more accurately without increasing the number of binary variables. We develop algorithms to define the unit-, task-, material-, and resource-specific grids directly from problem data. Importantly, we prove that the multi-grid formulation is able to find a schedule with the same optimal objective as the discrete-time single-grid model with an arbitrarily fine grid. The proposed framework leads to the formulation of models with reduced number of binary variables and constraints, which are able to find good solutions faster than existing models.
KW - Mixed-integer programming
KW - Process optimization
KW - Supply chain management
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U2 - 10.1016/j.compchemeng.2014.03.003
DO - 10.1016/j.compchemeng.2014.03.003
M3 - Article
AN - SCOPUS:84908287569
VL - 72
SP - 233
EP - 254
JO - Computers and Chemical Engineering
JF - Computers and Chemical Engineering
SN - 0098-1354
ER -