Heuristics for the Maximization of Operating Rooms Utilization Using Simulation

This paper addresses the problem of maximizing the utilization of operating rooms, which is translated to jobs scheduling in an identical parallel machine environment with sequence-dependent setup times and an objective of minimizing the makespan. The jobs’ processing times and setup times are stochastic for better depiction of the real world. This is a non-deterministic polynomial time (NP)-hard problem, and in this paper a new heuristic is developed and compared to existing ones using simulation and optimization. The results and analysis obtained from the computational experiments proved the superiority of the proposed algorithm Longest Expected Processing with Setup Time (LEPST) over the other algorithms presented.

[1]  K. Glazebrook.  Scheduling tasks with exponential service times on parallel processors , 1979 .

[2]  Michael Pinedo,et al.  Scheduling jobs on parallel machines with sequence-dependent setup times , 1997, Eur. J. Oper. Res..

[3]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[4]  Clyde L. Monma,et al.  On the Complexity of Scheduling with Batch Setup Times , 1989, Oper. Res..

[5]  Ghaith Rabadi,et al.  Heuristics for the Unrelated Parallel Machine Scheduling Problem with Setup Times , 2006, J. Intell. Manuf..

[6]  J. I.  The Design of Experiments , 1936, Nature.

[7]  Alain Guinet,et al.  Operating theatre planning. , 2003, Nursing mirror and midwives journal.

[8]  John Lu,et al.  Unrelated parallel machine scheduling with setup consideration and a total weighted completion time objective , 2001 .

[9]  J. Walrand,et al.  Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime , 1986, Journal of Applied Probability.

[10]  Rolf H. Möhring,et al.  Approximation in stochastic scheduling: the power of LP-based priority policies , 1999, JACM.

[11]  Genichi Taguchi,et al.  Taguchi methods : design of experiments , 1993 .

[12]  Greg N. Frederickson,et al.  Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan , 1981, JACM.

[13]  Wu Cheng,et al.  A genetic algorithm for minimizing the makespan in the case of scheduling identical parallel machines , 1999, Artif. Intell. Eng..

[14]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[15]  Jean-Paul M. Arnaout,et al.  Maximizing the utilization of operating rooms with stochastic times using simulation , 2008, 2008 Winter Simulation Conference.

[16]  F. Dexter.  A Strategy to Decide Whether to Move the Last Case of the Day in an Operating Room to Another Empty Operating Room to Decrease Overtime Labor Costs , 2000, Anesthesia and analgesia.

[17]  Pierre Ladet,et al.  OPERATING ROOMS SCHEDULING , 2006 .

[18]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[19]  Randall P. Sadowski,et al.  Simulation with Arena , 1998 .

[20]  Ravi Sethi,et al.  On the Complexity of Mean Flow Time Scheduling , 1977, Math. Oper. Res..

[21]  Gideon Weiss,et al.  Turnpike Optimality of Smith's Rule in Parallel Machines Stochastic Scheduling , 1992, Math. Oper. Res..

[22]  N. K. Kwak,et al.  Monte Carlo Simulation of Operating-Room and Recovery-Room Usage , 1972, Oper. Res..

[23]  Michael Pinedo,et al.  Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions , 1980, Journal of Applied Probability.

[24]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[25]  Ta R A Ja.  EXPECTED MAKESPAN MINIMIZATION ON IDENTICAL MACHINES IN TWO INTERCONNECTED QUEUES , 2001 .

[26]  L. N. Harris,et al.  Taguchi techniques for quality engineering, Philip J. Ross, Mcgraw-hill book company, 1988 , 1989 .

[27]  Ghaith Rabadi,et al.  A Dynamic Heuristic for the Stochastic Unrelated Parallel Machine Scheduling Problem , 2006 .

[28]  F. Dexter,et al.  An operating room scheduling strategy to maximize the use of operating room block time: computer simulation of patient scheduling and survey of patients' preferences for surgical waiting time. , 1999, Anesthesia and analgesia.