Conic programming models for production planning with clearing functions: Formulations and duality

•We address the problem of production planning for resources subject to congestion.•We show that several of the principal clearing function forms used in the literature are conic representable.•The conic programs yield excellent solutions in lower CPU times than the LP formulations. Concave clearing...

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Vydáno v:European journal of operational research Ročník 292; číslo 3; s. 953 - 966
Hlavní autoři: Gopalswamy, Karthick, Uzsoy, Reha
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.08.2021
Témata:
Capacity pricing
Congestion
Conic programming
Production planning
Congestion
Capacity pricing
Production planning
Conic programming
ISSN:0377-2217, 1872-6860
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Shrnutí:•We address the problem of production planning for resources subject to congestion.•We show that several of the principal clearing function forms used in the literature are conic representable.•The conic programs yield excellent solutions in lower CPU times than the LP formulations. Concave clearing functions that model the expected throughput of a production resource as a function of its planned workload have yielded promising results when used in production planning models. The most common of these models take the form of linear programs (LPs) obtained by piecewise linearization of the clearing function constraints, leading to large formulations and inaccurate estimates of dual prices for resources. We show that several clearing function forms considered in the literature to date can be reformulated as conic programs (CPs), for which efficient solution methods and an elegant duality theory analogous to that for linear programming exist. We derive expressions for the optimal values of the dual variables and present computational experiments showing that the dual prices obtained from the CP formulation are more accurate than those obtained from the piecewise linearized LP models. In addition, the CP solution outperforms the LP solutions with respect to nervousness.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2020.11.039