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MYOPIC POLICIES FOR NON-PREEMPTIVE SCHEDULING OF JOBS WITH DECAYING VALUE

Published online by Cambridge University Press:  28 November 2016

Neal Master ,
Carri W. Chan  and
Nicholas Bambos
Neal Master
Affiliation:
Department of Electrical Engineering, Stanford University, Stanford, California, USA E-mail: [email protected]
Carri W. Chan
Affiliation:
Decision, Risk, and Operations, Columbia Business School, New York, New York, USA E-mail: [email protected]
Nicholas Bambos
Affiliation:
Department of Management Sciences & Engineering and Department of Electrical Engineering, Stanford University, Stanford, California, USA E-mail: [email protected]
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Abstract

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In many scheduling applications, minimizing delays is of high importance. One adverse effect of such delays is that the reward for completion of a job may decay over time. Indeed in healthcare settings, delays in access to care can result in worse outcomes, such as an increase in mortality risk. Motivated by managing hospital operations in disaster scenarios, as well as other applications in perishable inventory control and information services, we consider non-preemptive scheduling of jobs whose internal value decays over time. Because solving for the optimal scheduling policy is computationally intractable, we focus our attention on the performance of three intuitive heuristics: (1) a policy which maximizes the expected immediate reward, (2) a policy which maximizes the expected immediate reward rate, and (3) a policy which prioritizes jobs with imminent deadlines. We provide performance guarantees for all three policies and show that many of these performance bounds are tight. In addition, we provide numerical experiments and simulations to compare how the policies perform in a variety of scenarios. Our theoretical and numerical results allow us to establish rules-of-thumb for applying these heuristics in a variety of situations, including patient scheduling scenarios.

Keywords

operations researchstochastic dynamic programmingstochastic modelling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 1 , January 2018 , pp. 1 - 36
Copyright
Copyright © Cambridge University Press 2016 

References

1. Argon, N.T., Ziya, S., & Righter, R. (2008). Scheduling impatient jobs in a clearing system with insights on patient triage in mass casualty incidents. Probability in the Engineering and Informational Sciences 22(03): 301–332.Google Scholar
2. Argon, N.T., Ziya, S., & Winslow, J.E. (2011). Triage in the aftermath of mass-casualty incidents. Hoboken, NJ: Wiley Encyclopedia of Operations Research and Management Science.Google Scholar
3. Aylwin, C.J., König, T.C., Brennan, N.W., Shirley, P.J., Davies, G., Walsh, M.S., & Brohi, K. (2007). Reduction in critical mortality in urban mass casualty incidents: Analysis of triage, surge, and resource use after the london bombings on July 7, 2005. The Lancet 368(9554): 2219–2225.Google Scholar
4. Bertsekas, D.P. (2012). Dynamic programming and optimal control vol. II: Approximate dynamic programming. Belmont, MA: Athena Scientific.Google Scholar
5. Buist, M.D., Moore, G.E., Bernard, S.A., Waxman, B.P., Anderson, J.N., & Nguyen, T.V. (2002). Effects of a medical emergency team on reduction of incidence of and mortality from unexpected cardiac arrests in hospital: preliminary study. British Medical Journal 324: 7334.Google Scholar
6. Chan, C.W. & Farias, V.F. (2009). Stochastic depletion problems: Effective myopic policies for a class of dynamic optimization problems. Mathematics of Operations Research 34(2): 333–350.Google Scholar
7. Chan, C.W., Farias, V.F., & Escobar, G. (2015). The impact of delays on service times in the intensive care unit. Columbia Business School, Working Paper.Google Scholar
8. Chan, C.W., Green, L.V., Lu, Y., Leahy, N., & Yurt, R. (2013). Prioritizing burn-injured patients during a disaster. Manufacturing & Service Operations Management 15(2): 170–190.Google Scholar
9. Chan, P.S., Krumholz, H.M., Nichol, G., Nallamothu, B.K., & the American Heart Association National Registry of Cardiopulmonary Resuscitation Investigators. (2008). Delayed time to defibrillation after in-hospital cardiac arrest. The New England Journal of Medicine 358: 9–17.Google Scholar
10. Cormen, T.H., Leiserson, C.E., Rivest, R.L., & Stein, C. (2009). Introduction to algorithms. Cambridge, MA: MIT Press.Google Scholar
11. Cushman, J.G., Pachter, H.L., & Beaton, H.L. (2003). Two New York city hospitals surgical response to the September 11, 2001, terrorist attack in New York city. Journal of Trauma and Acute Care Surgery 54(1): 147–155.CrossRefGoogle Scholar
12. Dalal, A.C. & Jordan, S. (2005). Optimal scheduling in a queue with differentiated impatient users. Performance Evaluation 59(1): 73–84.CrossRefGoogle Scholar
13. Dewan, S. & Mendelson, H. (1990). User delay costs and internal pricing for a service facility. Management Science 36(12): 1502–1517.Google Scholar
14. Dua, A. & Bambos, N. (2007). Downlink wireless packet scheduling with deadlines. Mobile Computing, IEEE Transactions on 6(12): 1410–1425.Google Scholar
15. Dua, A., Chan, C.W., Bambos, N., & Apostolopoulos, J. (2010). Channel, deadline, and distortion (CD 2) aware scheduling for video streams over wireless. IEEE Transactions on Wireless Communications 9(3): 1001–1011.Google Scholar
16. Federgruen, A. & Wang, M. (2015). Inventory models with shelf-age and delay-dependent inventory costs. Operations Research 63(3): 701–715.CrossRefGoogle Scholar
17. Frykberg, E.R. (2004). Principles of mass casualty management following terrorist disasters. Annals of Surgery 239(3): 319.Google Scholar
18. Gallup, Inc. (2001). Operating room directors study. Conducted for Surgical Information Systems.Google Scholar
19. Gamarnik, D. (2010). Fluid models of queueing networks. Hoboken, NJ: Wiley Encyclopedia of Operations Research and Management Science.Google Scholar
20. Gittins, J., Glazebrook, K., & Weber, R. (2011). Multi-armed bandit allocation indices. Chichester, UK: John Wiley & Sons.CrossRefGoogle Scholar
21. Iserson, K.V. & Moskop, J.C. (2007). Triage in medicine, part I: Concept, history, and types. Annals of Emergency Medicine 49(3): 275–281.CrossRefGoogle Scholar
22. Jakeman, C.M. (1994). Scheduling needs of the food processing industry. Food Research International 27(2): 117–120.Google Scholar
23. Kim, J.-H. & Chwa, K.-Y. (2004). Scheduling broadcasts with deadlines. Theoretical Computer Science 325(3): 479–488.CrossRefGoogle Scholar
24. King, B. & Jatoi, I. (2005). The mobile army surgical hospital (mash): A military and surgical legacy. Journal of the National Medical Association 97(5): 648.Google Scholar
25. Linstone, H.A. & Turoff, M. (1975). The Delphi method: Techniques and applications, vol. 29; Reading, MA: Addison-Wesley.Google Scholar
26. Luca, G.D., Suryapranata, H., Ottervanger, J.P., & Antman, E.M. (2004). Time delay to treatment and mortality in primary angioplasty for acute myocardial infarction: Every minute of delay counts. Circulation 109: 1223–1225.CrossRefGoogle ScholarPubMed
27. Mandelbaum, A. & Stolyar, A.L. (2004). Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule. Operations Research 52(6): 836–855.Google Scholar
28. Martello, S. & Toth, P. (1990). Knapsack problems: algorithms and computer implementations. New York, NY: John Wiley & Sons, Inc.Google Scholar
29. Master, N. & Bambos, N. (2014). Power control for wireless streaming with HOL packet deadlines. In 2014 IEEE International Conference on Communications (ICC). IEEE, pp. 2263–2269.Google Scholar
30. Master, N. & Bambos, N. (2015). Service rate control for jobs with decaying value. In 2015 American Control Conference (ACC). IEEE, pp. 3255–3260.Google Scholar
31. McQuillan, P., Pilkington, S., Allan, A., Taylor, B., Short, A., Morgan, G., Nielsen, M., Barrett, D., & Smith, G. (1998). Confidential inquiry into quality of care before admission to intensive care. British Medical Journal 316: 1853–1858.Google Scholar
32. Mihaylova, B., Briggs, A., O'Hagan, A., & Thompson, S.G. (2011). Review of statistical methods for analysing healthcare resources and costs. Health Economics 20(8): 897–916.Google Scholar
33. Mills, A.F., Argon, N.T., & Ziya, S. (2013). Resource-based patient prioritization in mass-casualty incidents. Manufacturing & Service Operations Management 15(3): 361–377.Google Scholar
34. Moskop, J.C. & Iserson, K.V. (2007). Triage in medicine, part II: Underlying values and principles. Annals of Emergency Medicine 49(3): 282–287.Google Scholar
35. Patrick, J., Puterman, M.L., & Queyranne, M. (2008). Dynamic multipriority patient scheduling for a diagnostic resource. Operations Research 56(6): 1507–1525.Google Scholar
36. Poon, E.G., Gandhi, T.K., Sequist, T.D., Murff, H.J., Karson, A.S., & Bates, D.W. (2004). ‘I wish I had seen this test result earlier!’: Dissatisfaction with test result management systems in primary care. Archives of Internal Medicine 164: 2223–2228.Google Scholar
37. Sacco, W.J., Navin, D.M., Fiedler, K.E., Waddell, I.I., Robert, K., Long, W.B., & Buckman, R.F. (2005). Precise formulation and evidence-based application of resource-constrained triage. Academic Emergency Medicine 12(8): 759–770.Google ScholarPubMed
38. Sharek, P.J., Parast, L.M., Leong, K., Coombs, J., Earnestand, K., & Sullivan, J., Frankel, L.R., & Roth, S.J. (2007). Effect of a rapid response team on hospital-wide mortality and code rates outside the ICU in a children's hospital. Journal of the American Medical Association 298: 2267–2274.CrossRefGoogle ScholarPubMed
39. Spangler, W.E., Strum, D.P., Vargas, L.G., & May, J.H. (2004). Estimating procedure times for surgeries by determining location parameters for the lognormal model. Health care management science 7(2): 97–104.Google Scholar
40. Strum, D.P., May, J.H., & Vargas, L.G. (2000). Modeling the uncertainty of surgical procedure times: Comparison of log-normal and normal models. Anesthesiology 92(4): 1160–1167.CrossRefGoogle ScholarPubMed
41. Turégano-Fuentes, F., Caba-Doussoux, P., Jover-Navalón, J.M., Martín-Pérez, E., Fernández-Luengas, D., Diez-Valladares, L., Perez-Diaz, D., Yuste-Garcia, P., Guadalajara Labajo, H., Rios-Blanco, R., Hernando-Trancho, F., García-Moreno Nisa, F., Sanz-Sánchez, M., García-Fuentes, C., Martíinez-Virto, A., León-Baltasar, J. L., Vazquez-Estévez, J. (2008). Injury patterns from major urban terrorist bombings in trains: The madrid experience. World Journal of Surgery 32(6): 1168–1175.Google Scholar
42. Turégano-Fuentes, F., Pérez-Díaz, D., Sanz-Sánchez, M., & Alonso, J.O. (2008). Overall assessment of the response to terrorist bombings in trains, madrid, 11 March 2004. European Journal of Trauma and Emergency Surgery 34(5): 433–441.Google Scholar
43. Van Mieghem, J.A. (2003). Commissioned paper: Capacity management, investment, and hedging: Review and recent developments. Manufacturing & Service Operations Management 5(4): 269–302.Google Scholar
44. Wachtel, R.E. & Dexter, F. (2009). Reducing tardiness from scheduled start times by making adjustments to the operating room schedule. Anesthesia & Analgesia 108(6): 1902–1909.Google Scholar
45. Walrand, J. (1988). An introduction to queuing networks. Englewood Cliffs, NJ: Prentice–Hall, Inc.Google Scholar
46. Weber, R.R. & Weiss, G. (1990). On an index policy for restless bandits. Journal of Applied Probability 27: 637–648.Google Scholar
47. Whittle, P. (1988). Restless bandits: Activity allocation in a changing world. Journal of Applied Probability 25: 287–298.Google Scholar
48. Xie, M. & Lai, C.D. (1996). Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliability Engineering & System Safety 52(1): 87–93.CrossRefGoogle Scholar
49. Zheng, F., Fung, S., P.Y., Chan, W.-T., Chin, F.Y.L., Poon, C.K., & Wong, P.W.H. (2006). Improved on-line broadcast scheduling with deadlines. In Computing and Combinatorics Conf. Springer, 320–329.Google Scholar