Solving Integer Programming Problems with a Variable Number of Switching Costs, Balking and Feedback

10.6186/IJIMS.2012.23.4.4

D. Arivudainambi；V. Poongothai

Optimization ； integer programming ； feedback ； switching costs ； cross trained

International Journal of Information and Management Sciences

23:4（2012 / 12 / 01）

395 - 407

英文

We consider a retail service facility with cross trained servers who can perform operations in both front room and back room depending on the length of the queue. Two essential models for service facility are discussed in this paper. The models are represented as a Markovian decision problem and solved using mixed integer programming techniques. Exact solution procedures are developed to solve the models and numerical study is conducted to see the impact of various parameters on performance.

1. Zhang, Hongbo,Shi, Dinghua(2011).Analysis of two queueing models with explicit rate operators and stationary distributions.International Journal of Information and Management Sciences,22,177-188.
   連結：
2. Berman, O.,Ianovsky, E.(2008).Optimal management of cross-trained workers, using Markov decision approach.International Journal of Operational Research,3,154-182.
3. Berman, O.,Larson, K. P.(2004).A queueing control model for retail services having back room operations and cross-trained workers.Computers and Operations Research,31,201-222.
4. Berman, O.,Sapna, K. P.(2005).Optimal control of servers in front and back rooms with correlated work.IIE Transactions,37,167-173.
5. Berman, O.,Wang, J.,Sapna, K. P.(2005).Optimal management of cross-trained workers in services with negligible switching costs.European Journal of Operational Research,167,349-369.
6. Brusco, M. J.,Johns, T. R.(1998).Staffing a multiskilled workforce with varying levels of producitivity: An analysis of cross training policies.Decision Sciences,29,499-515.
7. Cezik, M.,L'' Ecuyer, P.(2008).Staffing multiskill call centers via linear programming and simulation.Management Science,54,310-323.
8. Choudhury, G.,Paul, M.(2005).A two phase queueing system with bernoulli feedback.Information and Management Sciences,16,35-52.
9. Fowler, J. W.,Wirojanagud, P.(2008).Heuristics for workforce planning with worker differences.European Journal of Operational Research,190,724-740.
10. Haight, F. A.(1957).Queueing with balking.Biometrika,44,360-369.
11. Jain, N. K.,Rakesh, Kumar(2007).Transient solution of a catastrophic-cum- restorative queuing problem with correlated arrivals and variable service capacity.International Journal of Information and Management Sciences,18,461-465.
12. Kitaev, M. Y.,Serfozo, R. F.(1999).M|M|1 queues with switching costs and hysteretic optimal control.Operations Research,47,310-312.
13. Krishna Kumar, B.,Arivudainambi, D.(2001).Transient solution of an M/M/C queue with heterogeneous servers and balking.Information and Management Sciences,12,15-27.
14. Moder, J. J.,Phillips, C. R., Jr.(1962).Queueing with fixed and variable channels.Operations Research,10,218-231.
15. Oniszczuk, W.(2010).Loss tandem networks with blocking - a semi-Markov approach.Bulletin of the Polish Academy of Sciences Technical Sciences,58,673-681.
16. Pandelis, D. G.(2008).Optimal control of flexible servers in two tandem queues with operating costs.Probability in the Engineering and Informational Sciences,22,218-231.
17. Santhakumaran, A.,Thangaraj, V.(2000).A single server queue with impatient and feedback customers.International Journal of Information and Management Sciences,11,71-79.
18. Serfozo, R. F.(1984).Optimal control of random walks, birth and death processes and queues.Advances in Applied Probability,13,61-83.
19. Serfozo, R. F.,Lu, F. V.(1984).M|M|1 Queueing decision processes with monotone hysteretic policies.Operations Research,32,1116-1132.
20. Slomp, J.,Bokhorst Jos, A. C.,Molleman, E.(2005).Cross training in a cellular manafacturing environment.Computers and Industrial Engineering,48,609-624.
21. Takacs, L.(1963).A single-server queue with feedback.The Bell System Technical Journal,42,502-519.
22. Terekhov, D.,Beck, J. C.(2009).An extended queueing control model for facilities with front room and back room operations and mixed-skilled workers.European Journal of Operational Research,198,223-231.
23. Vielma, J. P.,Ahmed, S.,Nemhauser, G. L.(2012).Mixed integer linear programming formulations for probabilistic constraints.Operations Research Letters,40,153-158.
24. Wang, J.(2009).An optimal deterministic control policy of servers in front and back rooms with a variable number of switching points and switching costs.Science in China Series F : Information Science,52,1113-1119.
25. Yadin, M.,Naor, P.(1963).On queueing systems with variable service capacities.Naval Research Logistics Quarterly,14,43-54.