A Mixed integer second order cone programming reformulation for a congested location and capacity allocation problem on a supply chain network

Download
2013
Salimian, Mohammad
Supply chain network design involves location decisions for production facilities and distribution centers. We consider a make-to-order supply chain environment where distribution centers serve as crossdocking terminals. Long waiting times may occur at a cross-docking terminal, unless su cient handling capacity is installed. In this study, we deal with a facility location problem with congestion e ects at distribution centers. Along with location decisions, we make capacity allocation (service rate) and demand allocation decisions so that the total cost, including facility opening, transportation and congestion costs, is minimized. Response time to customer orders is a critical performance measure for a supply chain network. The decisions like where the plants and distribution centers are located a ect the response time of the system. Response time is more sensitive to these decisions in a make-to-order business environment. In a distribution network where distribution centers function as cross-docking terminals, capacity or the service rate decisions also a ect the response time performance. This study is closely related to a recent work Vidyarthi et al. (2009) which models distribution centers asM/G/1 queuing systems. They use the average waiting time formula ofM/G/1 queuing model. Thus, the average waiting time at a distribution center is a nonlinear function of the demand rate allocated to and the service rate available at the distribution center. The authors Vidyarthi et al. (2009) propose a linear approximation approach and a Lagrangian based heuristic for the problem. Di erent than the solution approach proposed in Vidyarthi et al. (2009), we propose a closed form formulation for the problem. In particular, we show that the waiting time function derived from M/G/1 queuing model can be represented via second order conic inequalities. Then, the problem becomes a mixed integer second order cone programming problem which can be solved by using commercial branch-and-bound software such as IBM ILOG CPLEX. Our computational tests show that proposed reformulation can be solved in reasonable CPU times for practical size instances.
Citation Formats
M. Salimian, “A Mixed integer second order cone programming reformulation for a congested location and capacity allocation problem on a supply chain network,” M.S. - Master of Science, Middle East Technical University, 2013.