A column generation heuristic for congested facility location problem with clearing functions

Nonlinear clearing functions, an idea initially suggested to reflect congestion effects in production planning, are used to express throughput of facilities prone to congestion in a facility location problem where each demand site is served by exactly one facility. The traditional constant capacity constraint for a facility is replaced with the nonlinear clearing function. The resulting nonlinear integer problem is solved by a column generation heuristic in which initial columns for the restricted master problem are generated by known existing algorithms and additional columns by a previously developed dynamic programming algorithm. Computational experimentation in terms of dual gap and CPU time based on both randomly generated and published data sets show not only clear dominance of the column generation over a Lagrangian heuristic previously developed, but also the high quality of results from the suggested heuristic for large problems.

[1]  Oded Berman,et al.  Facility Location Problems with Stochastic Demands and Congestion , 2002 .

[2]  Navneet Vidyarthi,et al.  Response time reduction in make-to-order and assemble-to-order supply chain design , 2009 .

[3]  Ali Amiri.  Solution procedures for the service system design problem , 1997, Comput. Oper. Res..

[4]  Kurt M. Bretthauer,et al.  Nonlinear programming for multiperiod capacity planning in a manufacturing system , 1997 .

[5]  Vladimir Marianov,et al.  Location of Multiple-Server Congestible Facilities for Maximizing Expected Demand, when Services are Non-Essential , 2003, Ann. Oper. Res..

[6]  Zvi Drezner,et al.  The multiple server location problem , 2007, J. Oper. Res. Soc..

[7]  Reha Uzsoy,et al.  Heuristics for capacity planning problems with congestion , 2009, Comput. Oper. Res..

[8]  Samir Elhedhli,et al.  Service System Design with Immobile Servers, Stochastic Demand, and Congestion , 2006, Manuf. Serv. Oper. Manag..

[9]  Vladimir Marianov,et al.  A probabilistic quality of service constraint for a location model of switches in ATM communications networks , 2000, Ann. Oper. Res..

[10]  Ward Whitt,et al.  The marshall and stoyan bounds for IMRL/G/1 queues are tight , 1982, Oper. Res. Lett..

[11]  F. Silva,et al.  A capacitated facility location problem with constrained backlogging probabilities , 2007 .

[12]  Stephen C. Graves,et al.  A Tactical Planning Model for a Job Shop , 1986, Oper. Res..

[13]  Ramaswami Sridharan,et al.  A Lagrangian Heuristic for the Capacitated Plant Location Problem with Side Constraints , 1991 .

[14]  Sampath Rajagopalan,et al.  Capacity planning with congestion effects , 2001, Eur. J. Oper. Res..

[15]  Gerald L. Thompson,et al.  A single source transportation algorithm , 1980, Comput. Oper. Res..

[16]  Reha Uzsoy,et al.  Planning Production and Inventories in the Extended Enterprise , 2011 .

[17]  Vladimir Marianov,et al.  PROBABILISTIC MAXIMAL COVERING LOCATION-ALLOCATION FOR CONGESTED SYSTEMS , 1998 .

[18]  Qian Wang,et al.  Algorithms for a Facility Location Problem with Stochastic Customer Demand and Immobile Servers , 2002, Ann. Oper. Res..

[19]  G. Nemhauser,et al.  Integer Programming , 2020 .

[20]  Robert C. Leachman,et al.  A general framework for modeling production , 1989 .

[21]  Uday S. Karmarkar,et al.  The Dynamic Lot-Sizing Problem with Startup and Reservation Costs , 1987, Oper. Res..

[22]  Reha Uzsoy,et al.  Exact and heuristic procedures for capacity expansion problems with congestion , 2008 .

[23]  Oded Berman,et al.  The Stochastic Queue p-Median Problem , 1987, Transp. Sci..

[24]  Jiamin Wang,et al.  Locating service facilities to reduce lost demand , 2002 .

[25]  D. Tirupati,et al.  Capacity planning in manufacturing networks with discrete options , 1989 .

[26]  James J. Solberg,et al.  Capacity Planning with a Stochastic Workflow Model , 1981 .

[27]  R. Uzsoy,et al.  Tractable nonlinear production planning models for semiconductor wafer fabrication facilities , 2006, IEEE Transactions on Semiconductor Manufacturing.

[28]  Dincer Konur,et al.  Competitive multi-facility location games with non-identical firms and convex traffic congestion costs , 2012 .

[29]  Vladimir Marianov,et al.  Location–Allocation of Multiple-Server Service Centers with Constrained Queues or Waiting Times , 2002, Ann. Oper. Res..

[30]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[31]  Kurt M. Bretthauer.  Capacity planning in networks of queues with manufacturing applications , 1995 .

[32]  Dincer Konur,et al.  Analysis of traffic congestion costs in a competitive supply chain , 2011 .

[33]  Di Yuan,et al.  An exact algorithm for the capacitated facility location problems with single sourcing , 1999, Eur. J. Oper. Res..

[34]  Reha Uzsoy,et al.  Production planning with resources subject to congestion , 2009 .

[35]  D. Serra,et al.  Probabilistic maximal covering location models for congested systems , 1994 .

[36]  Simin Huang,et al.  Distribution network design: Selection and sizing of congested connections , 2005 .

[37]  Oded Berman,et al.  Optimal Server Location on a Network Operating as an M/G/1 Queue , 1985, Oper. Res..

[38]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.