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 sucient handling
capacity is installed. In this study, we deal with a facility location problem with congestion
eects 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 aect 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 aect 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.
Dierent 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.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12615407/index.pdf |
| Date | 01 January 2013 |
| Creators | Mohammad, Salimian |
| Contributors | Gural, Sinan |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | Access forbidden for 1 year |
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