Capacitated lot sizing with setup times
Management Science
A cutting plane approach to capacitated lot-sizing with start-up costs
Mathematical Programming: Series A and B
The OPL optimization programming language
The OPL optimization programming language
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Lot sizing and furnace scheduling in small foundries
Computers and Operations Research
Computers and Operations Research
Computers and Operations Research
Computers and Operations Research
Lot sizing and sequencing optimisation at an animal-feed plant
Computers and Industrial Engineering
Infeasibility handling in genetic algorithm using nested domains for production planning
Computers and Operations Research
Computers and Industrial Engineering
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We consider the single machine capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup costs and non-zero setup times, with the additional feature that setups may be carried over from one period to the next, and that setups are preserved over idle periods. We provide an exact formulation of this problem as a mixed-integer program.It is well known that the CLSP is NP-hard. Therefore, we have also developed a heuristic for solving large problem instances. This is coupled with a procedure for obtaining a lower bound on the optimal solution. We carry out a computational study to test the accuracy of several different lower bounding linear relaxations and the approximate solution obtained by the heuristic. In our study, the average deviation of the heuristic solution from the corresponding exact solution depends on the size of the problem and ranges from 10 to 16%. The heuristic is more effective when there are many more products than there are planning periods. This is a desirable property from a practical viewpoint since most firms are likely to implement such a procedure on a rolling horizon basis, solving the problem repeatedly for a few periods at a time.