Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Method: Part Ii, the Multi-Station Case

Economics Working Paper No. 314

35 Pages Posted: 11 Nov 1998

See all articles by Dimitris Bertsimas

Dimitris Bertsimas

Massachusetts Institute of Technology (MIT) - Sloan School of Management

José Niño Mora

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Abstract

We address the problem of scheduling a multi-station multiclass queueing network (MQNET) with server changeover times to minimize steady-state mean job holding costs. We present new lower bounds on the best achievable cost that emerge as the values of mathematical programming problems (linear, semidefinite, and convex) over relaxed formulations of the system's achievable performance region. The constraints on achievable performance defining these formulations are obtained by formulating system's equilibrium relations. Our contributions include: (1) a flow conservation interpretation and closed formulae for the constraints previously derived by the potential function method; (2) new work decomposition laws for MQNETs; (3) new constraints (linear, convex, and semidefinite) on the performance region of first and second moments of queue lengths for MQNETs; (4) a fast bound for a MQNET with N customer classes computed in N steps; (5) two heuristic scheduling policies: a priority-index policy, and a policy extracted from the solution of a linear programming relaxation.

JEL Classification: C61, C63

Suggested Citation

Bertsimas, Dimitris and Niño Mora, José, Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Method: Part Ii, the Multi-Station Case. Economics Working Paper No. 314. Available at SSRN: https://ssrn.com/abstract=135288 or http://dx.doi.org/10.2139/ssrn.135288

Dimitris Bertsimas (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

E53-359
Cambridge, MA 02142
United States
617-253-4223 (Phone)
617-258-7579 (Fax)

José Niño Mora

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
(34-3) 542 26 73 (Phone)
(34-3) 542 17 46 (Fax)

Register to save articles to
your library

Register

Paper statistics

Downloads
100
Abstract Views
2,176
rank
267,044
PlumX Metrics