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Introduction, section snippets.

## Cited by (116)

## International Journal of Production Economics

Solving surgical cases assignment problem by a branch-and-price approach ☆.

## General integer programming

Human and instruments resources are always

## Framework of branch-and-price procedure

## Set partitioning general problem (GP) corresponding to general integer problem (GIP)

1 if surgical case i is assigned to plan j ; 0 otherwise;

1 if plan j is scheduled on day d ; 0 otherwise;

1 if operating room k is used by plan j ; 0 otherwise.

## Framework of heuristic procedure based on column generation

## Selection strategy of node and branching variable

## Experimental results

Hardware for running the algorithm : IBM ThinkPad T23 (CPU: PM 1.6 GHz, Memory: 256 MB).

Software development environment : Microsoft VC++ 6.0

## Conclusion and perspective

## Reference (18)

## A data-driven approach to include availability of ICU beds in the planning of the operating room

## A discrete squirrel search algorithm for the surgical cases assignment problem

## A robust multiobjective integrated master surgery schedule and surgical case assignment model at a publicly funded hospital

## An approximate dynamic programming approach to the admission control of elective patients

## Surgery scheduling in outpatient procedure centre with re-entrant patient flow and fuzzy service times

## A two level metaheuristic for the operating room scheduling and assignment problem

## Local search heuristics for a surgical case assignment problem

## A simulation based approximate dynamic programming approach to multi-class, multi-resource surgical scheduling

## Scheduling elective surgeries with sequence-dependent setup times to multiple operating rooms using constraint programming

## Integrated operating room planning and scheduling problem with assistant surgeon dependent surgery durations

## A hybrid optimization algorithm for surgeries scheduling

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## JSmol Viewer

## 1. Introduction

- X jk = { 1 i f c u t t i n g s e t j i s a s s i g n e d t o s u g a r c a n e f i e l d k 0 o t h e r w i s e
- Y ij = { 1 i f w o r k e r i i s a s s i g n e d t o c u t t i n g s e t j 0 o t h e r w i s e
- Wi = { 1 i f w o r k e r i i s i n u s e d 0 o t h e r w i s e
- Z k = { 1 i f s u g a r c a n e f i e l d i s a s s i g n e d b y a t l e a s t o n e c u t t i n g s e t 0 o t h e r w i s e
- H jk = Hours required to cut sugarcane in field k using harvester j
- Q jk = Hours required to travel from j to k
- M j = Real fuel consumption rate of harvester j (baht/hours)
- N j = Real cutting speed of harvester j (rai/hours)

## 3. Proposed Heuristic

- Shim, S.-O.; Park, K.; Choi, S. Innovative Production Scheduling with Customer Satisfaction Based Measurement for the Sustainability of Manufacturing Firms. Sustainability 2017 , 9 , 2249. [ Google Scholar ] [ CrossRef ]
- Shim, S.-O.; Park, K. Technology for Production Scheduling of Jobs for Open Innovation and Sustainability with Fixed Processing Property on Parallel Machines. Sustainability 2016 , 8 , 904. [ Google Scholar ] [ CrossRef ]
- Jeong, B.J.; Kim, Y.-D.; Shim, S.-O. Algorithms for a two-machine flow shop problem with jobs of two classes. Int. Trans. Oper. Res. 2018 . [ Google Scholar ] [ CrossRef ]
- Joo, B.J.; Shim, S.-O.; Chua, T.J.; Cai, T.X. Multi-level job scheduling under processing time uncertainty. Comput. Ind. Eng. 2018 , 120 , 480–487. [ Google Scholar ] [ CrossRef ]
- Jeong, B.J.; Shim, S.-O. Heuristic algorithms for two-machine re-entrant flow shop scheduling problem with jobs of two classes. J. Adv. Mech. Des. Syst. Manuf. 2017 , 11 , 1–14. [ Google Scholar ] [ CrossRef ]
- Ross, G.T.; Soland, R.M. A branch and bound algorithm for the generalized Assignment problem. Math. Program. 1975 , 8 , 91–103. [ Google Scholar ] [ CrossRef ]
- Fisher, M.L.; Jaikumar, R. A generalized assignment heuristic for vehicle routing. Networks 1981 , 11 , 109–124. [ Google Scholar ] [ CrossRef ]
- Chu, P.C.; Beasley, J.E. A genetic algorithm for the generalized assignment problem. Comput. Oper. Res. 1997 , 24 , 17–23. [ Google Scholar ] [ CrossRef ]
- Osorio, M.A.; Laguna, M. Logic cuts for multi-level generalized assignment problems. Eur. J. Oper. Res. 2003 , 151 , 238–246. [ Google Scholar ] [ CrossRef ]
- Alfares, H.K. Optimum work force scheduling under the (14,21) days-off timetable. Adv. Decis. Sci. 2002 , 6 , 191–199. [ Google Scholar ]
- Elshafei, M.; Alfares, H.K. A dynamic programming algorithm for days-off scheduling with sequence dependent labor costs. J. Sched. 2008 , 11 , 85–93. [ Google Scholar ] [ CrossRef ]
- Ghoniem, A.; Flamand, T.; Haouari, M. Exact solution methods for a generalized assignment problem with location/allocation considerations. INFORMS J. Comput. 2016 , 28 , 589–602. [ Google Scholar ] [ CrossRef ]
- Laguna, M.; Kelly, J.P.; Gonzalez Velarde, J.L.; Glover, F. Tabu search for the multilevel generalized assignment problem. Eur. J. Oper. Res. 1995 , 82 , 176–189. [ Google Scholar ] [ CrossRef ]
- Kaewman, S.; Srivarapongse, T.; Theeraviriya, T.; Jirasirilerd, G. Differential Evolution Algorithm for Multilevel Assignment Problem: A Case Study in Chicken Transportation. Math. Comp. Appl. 2018 , 23 , 55. [ Google Scholar ] [ CrossRef ]
- Woźniak, M.; Połap, D. Bio-inspired methods modeled for respiratory disease detection from medical images. Swarm Evolut. Comp. 2018 , 41 , 69–96. [ Google Scholar ] [ CrossRef ]
- Woźniak, M.; Połap, D. Adaptive neuro-heuristic hybrid model for fruit peel defects detection. Neural Netw. 2018 , 98 , 16–33. [ Google Scholar ] [ CrossRef ] [ PubMed ]
- Woźniak, M.; Połap, D. Hybrid neuro-heuristic methodology for simulation and control of dynamic systems over time interval. Neural Netw. 2017 , 93 , 45–56. [ Google Scholar ] [ CrossRef ] [ PubMed ]
- Thongkham, M.; Kaewman, S. Methodology to Solve the Combination of the Generalized Assignment Problem and the Vehicle Routing Problem: A Case Study in Drug and Medical Instrument Sales and Service. Adm. Sci. 2019 , 9 , 3. [ Google Scholar ] [ CrossRef ]
- Savelsbergh, M. A branch-and-price algorithm for the generalized assignment problem. Oper. Res. 1997 , 45 , 831–841. [ Google Scholar ] [ CrossRef ]
- Cohen, R.; Katzir, L.; Raz, D. An efficient approximation for the generalized assignment problem. Inf. Process. Lett. 2006 , 100 , 162–166. [ Google Scholar ] [ CrossRef ]
- López Cruz, I.L.; van Willigenburg, L.G.; van Straten, G. Optimal control of nitrate in lettuce by a hybrid approach: Differential evolution and adjustable control weight gradient algorithms. Comput. Electron. Agric. 2003 , 40 , 179–197. [ Google Scholar ] [ CrossRef ]
- Woodcock, A.J.; Wilson, J.M. A hybrid tabu search/branch and bound approach to solving the generalized assignment problem. Eur. J. Oper. Res. 2010 , 207 , 566–578. [ Google Scholar ] [ CrossRef ]
- Osman, I.H. Heuristics for the generalized assignment problem: Simulated annealing and tabu search approaches. Oper. Res. Spektrum 1995 , 17 , 211–225. [ Google Scholar ] [ CrossRef ]
- Diaz, J.A.; Fernandez, E. A Tabu search heuristic for the generalized assignment problem. Eur. J. Oper. Res. 2001 , 132 , 22–38. [ Google Scholar ] [ CrossRef ]
- McKendall, A.; Li, C. A tabu search heuristic for a generalized quadratic assignment problem. J. Ind. Prod. Eng. 2017 , 34 , 221–231. [ Google Scholar ] [ CrossRef ]
- Ghoniem, A.; Flamand, T.; Haouari, M. Optimization based very large-scale neighborhood search for generalized assignment problems with location/allocation considerations. INFORMS J. Comp. 2016 , 28 , 575–588. [ Google Scholar ] [ CrossRef ]
- Özbakir, L.; Baykasoglu, A.; Tapkan, P. Bees algorithm for generalized assignment problem. Appl. Math. Comput. 2010 , 215 , 3782–3795. [ Google Scholar ] [ CrossRef ]
- Tasgetiren, M.F.; Suganthan, P.N.; Chua, T.J.; Al-Hajri, A. Differential evolution algorithms for the generalized assignment problem. In Proceedings of the 2009 IEEE Congress on Evolutionary Computation, Trondheim, Norway, 18–21 May 2009. [ Google Scholar ]
- Sethanan, K.; Pitakaso, R. Improved differential evolution algorithms for solving generalized assignment problem. Expert Syst. Appl. 2016 , 45 , 450–459. [ Google Scholar ] [ CrossRef ]
- Pitakaso, R. Differential evolution algorithm for simple assembly line balancing type 1 (SALBP-1). J. Ind. Prod. Eng. 2015 , 32 , 104–114. [ Google Scholar ] [ CrossRef ]
- Sethanan, K.; Pitakaso, R. Differenevolution algorithm for simple assembly line balancing with a limit on the number of machine types. Eng. Optim. 2015 , 48 , 253–271. [ Google Scholar ] [ CrossRef ]
- Dechampai, D.; Tanwanichkul, L.; Sethanan, K.; Pitakaso, R. A differential evolution algorithm for the capacitated VRP with flexibility of mixing pickup and delivery services and the maximum duration of a route in poultry industry. J. Intell. Manuf. 2015 , 28 , 1357–1376. [ Google Scholar ] [ CrossRef ]
- Akararungruangkul, R.; Kaewman, S. Modified Differential Evolution Algorithm Solving the Special Case of Location Routing Problem. Math. Comput. Appl. 2018 , 23 , 34. [ Google Scholar ] [ CrossRef ]
- Sethanan, K.; Pitakaso, R. Differential evolution algorithms for scheduling raw milk transportation. Comput. Electron. Agric. 2016 , 121 , 245–259. [ Google Scholar ] [ CrossRef ]
- Boon, E.T.; Ponnambalam, S.G.; Kanagara, G. Differential evolution algorithm with local search for capacitated vehicle routing problem. Int. J. Bio-Inspired Comput. 2013 , 7 , 321–342. [ Google Scholar ]
- Połap, D.; Woz’niak, M. Polar Bear Optimization Algorithm: Meta-Heuristic with Fast Population Movement and Dynamic Birth and Death Mechanism. Symmetry 2017 , 9 , 203. [ Google Scholar ] [ CrossRef ]
- Mirjalili, S. Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. Appl. 2016 , 27 , 1053. [ Google Scholar ] [ CrossRef ]
- Sun, W.-Z.; Wang, J.-S.; Wei, X. An Improved Whale Optimization Algorithm Based on Different Searching Paths and Perceptual Disturbance. Symmetry 2018 , 10 , 210. [ Google Scholar ] [ CrossRef ]
- Yun, J.J.; Jeong, E.; Lee, Y.; Kim, K. The Effect of Open Innovation on Technology Value and Technology Transfer: A Comparative Analysis of the Automotive, Robotics, and Aviation Industries of Korea. Sustainability 2018 , 10 , 2459. [ Google Scholar ] [ CrossRef ]
- Yun, J.J.; Won, D.; Park, K. Dynamics from open innovation to evolutionary change. J. Open Innov. Technol. Mark. Complex. 2016 , 2 , 1–22. [ Google Scholar ] [ CrossRef ]

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## Sequencing surgical cases in a day-care environment: An exact branch-and-price approach

2009, Computers & Operations Research

## Related Papers

Workshop on Mixed Integer Nonlinear …

Computational Optimization and Applications

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## Healthcare scheduling in optimization context: a review

- Zahraa A. Abdalkareem ORCID: orcid.org/0000-0003-0326-2519 1 , 5 ,
- Amiza Amir 1 ,
- Mohammed Azmi Al-Betar 2 , 3 ,
- Phaklen Ekhan 1 &
- Abdelaziz I. Hammouri 4

Health and Technology volume 11 , pages 445–469 ( 2021 ) Cite this article

## Working on a manuscript?

Healthcare scheduling papers between 2010-2020

## 2 Patient admission scheduling problem (PASP)

## 2.1 Definition of patient admission scheduling problem (PASP)

## 2.2 PASP Formulation

Nigh: The variables representing time horizon for individual patient located in the hospital

Transfer: Moving admitted patient from room to another during her/his stay.

HC1: The availability of the room ( \(R_j\) ).

HC3: Time horizon should be continuous.

HC5: Gender schema should be carried out.

HC6: The patient should be allocated to a department which is is acceptable to his/her age.

HC7: Mandatory room properties should be available in the assignment rooms.

Furthermore, the soft constraints for this problem could be summarized as follow:

SC5: Transfer, the unplanned transfers should be minimised.

## 2.2.1 Patient admission scheduling problem under uncertainty (PASU) version 2

HC2: Patient Age (PA), patients should be assigned to a department that accept his/her age.

SC1: Room Gender (RG), gender policy room should be fulfilled.

SC2: Room Preference (RP), patient prefer to be allocated room with special preference.

SC3: Transfer (Tr), transfer inpatient from room to another during her stay is undesirable.

Delay (De): delay patients admission.

## 2.3 PASU formulation in mathematics

R : the set of rooms and \(c_{r}\) is the capacity of room \(r\in R\) .

\(R_{SG}\) : the subset of rooms with policy SG . Additionally we have

\(D_{p}\) : is a set of days in which a patient \(p\in P\) is present in the hospital.

The components of the objective function PRC , RG ,and OR is defined as follow:

## 2.4 Dynamic patient admission scheduling with operating room constraints, flexible horizons, and patient delay (version 3)

The basic concept of the first phase is as following [ 18 ]:

The basic concept of the second phase (operating room notions) is as follow:

## 2.5 Dynamic patient admission scheduling with operating room constraints, flexible horizons, and patient delay (version 3) formulation in mathematics

## 2.6 PASP Data sets versions

Example for PASP original version data set

## 2.7 PASP-based optimization methods

## 2.8 Discussion

## 3 Nurse rostering problem

## 3.1 Nurse scheduling problem definition

## 3.2 Nurse rostering problem versions

## 3.2.1 NRP version1 (INRC-I)

Roster: List which is made for several days for each ward in the healthcare institution.

Shift/rotation types: Appointed a nurse with specific skill based on period of time.

The number of nurses required for each day and for each type of shift is provided.

## 3.3 NRP Datasets versions

## 3.4 NRP-based Optimization Methods

## 3.5 Discussion

## 4 Operating room scheduling

## 4.1 Operating room scheduling problem definition

## 4.2 Operating room scheduling versions

## Open scheduling strategy

## Block scheduling strategy

## Modified block scheduling strategy

## 4.3 OR Advanced scheduling (version 1)

## 4.4 Allocation scheduling (version 2)

## 4.5 Operating room scheduling mathematical formulation

## 4.6 Operating room scheduling data sets

## 4.7 Operating room scheduling in optimization

## 4.7.1 Surgery scheduling problem in optimization

## 4.8 Discussion

## 5 Other healthcare scheduling and planning problems

## 6 Conclusion and future work

Study and analysed the robustness of each algorithm that has been applied to each problem.

Build a scheduling system for the hospital, which covers the entire hospital dynamically.

https://people.cs.kuleuven.be/wim.vancroonenburg/pas/

Article MathSciNet Google Scholar

Hall RW, et al. Handbook of healthcare system scheduling. Springer; 2012.

Article MathSciNet MATH Google Scholar

Gunawan A, Lau HC. Master physician scheduling problem. J Oper Res Soc. 2013;64(3):410–25.

Fikar C, Hirsch P. Home health care routing and scheduling: A review. Comp Oper Res. 2017;77:86–95.

## Author information

Zahraa A. Abdalkareem, Amiza Amir & Phaklen Ekhan

Department of Computer Information Systems , Al-Balqa Applied University , 19117, Al- Salt, Jordan

Department of Islamic English studies , Alimam Aladham university college , Baghdad, Iraq

You can also search for this author in PubMed Google Scholar

## Corresponding authors

Correspondence to Zahraa A. Abdalkareem , Mohammed Azmi Al-Betar or Abdelaziz I. Hammouri .

## Ethics declarations

The authors declare that they have no conflict of interest.

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## About this article

DOI : https://doi.org/10.1007/s12553-021-00547-5

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- Metaheurstic
- Meta-heurstics
- Nurse scheduling
- Patient admission scheduling
- Patient to bed assignment
- Operating room scheduling
- Operating theater
- Surgery scheduling
- Surgical scheduling
- Physician scheduling
- Healthcare scheduling

An official website of the United States government

## Solving Operating Room Scheduling Problem Using Artificial Bee Colony Algorithm

## 1. Introduction

## 2. Mathematical Model

Notations used in this article.

## 3. Heuristics

## 3.1. Modified EDD Heuristic (MEDD)

The flow chart of the modified earliest due date (MEDD) heuristic.

## MEDD Heuristic

Step 5. Apply RecoveryScheme (described in Section 4.3 ) to schedule π .

## 3.2. Modified LPT Heuristic (MLPT)

The flow chart of modified longest processing time (MLPT) heuristic.

## MLPT Heuristic

Step 7. Apply RecoveryScheme (described in Section 4.3 ) to schedule π .

## 4. Artificial Bee Colony (ABC) Algorithm

## 4.1. Coding Scheme

## 4.2. Initialization

## Randomly Generate Solution Scheme

Step 3. Apply RecoveryScheme (described in Section 4.3 ) to generate a feasible solution π .

## 4.3. RecoveryScheme

## 4.4. Local Search Schemes

## 4.4.1. Internal Swap

Step 1: For a given schedule π , randomly choose two surgeries x , y x , y ∈ B

Step 3: Apply RecoveryScheme to schedule π .

## 4.4.2. External Swap

Step 2: If D x > H , then swap x and y and update schedule π . Otherwise, go back to step 1.

## 4.4.3. InternalInsertion

## 4.4.4. ExternalInsertion

## 4.4.5. ExplorationProcess

Step 5. Perform ExternalInsertion on schedule

## 4.4.6. ExploitationProcess

Step 2. Apply ExternalSwap. If a smaller cost is found, then go to step 2; otherwise, go to step 3.

Step 4. Apply InternalSwap. If a smaller cost is found, then go to step 4; otherwise, go to step 5.

Step 5. Terminate ExploitationProcess.

## 4.5. Fitness Value and Selection

## 4.6. Elitism Strategy

## Elitism Strategy

## 4.7. The Implementation of the Proposed ABC Algorithm

The flow chart of the artificial bee colony (ABC) algorithm.

Step 8: Terminate the ABC algorithm and report the final best solution in EliteSolutions.

## 5. Computational Results

Hardware for running the algorithm: ASUS TeK (AMD Ryzen 7 4700 U 2.00 GHz, memory: 8 GB).

Algorithm development environment: Microsoft Visual C + + 2019.

Software for running the MIP model: AMPL with CPLEX 11.2 solver.

The testing data were generated as follows:

The cost ratio of ordinary working hours and overtime ones was set to α = 1.5.

From Monday to Friday ( A l d ),

Regular opening hours from Monday to Friday ( R T k d ):

Operating room 6: (8,-,5,4,7), where “-“ means the operating room is not available.

Maximum overtime hours from Monday to Friday ( O T k d . ):

Operating room 6: (0,-,2,2,0), where “-“ means the operating room is not available.

The performance of the heuristics and the ABC algorithm for small problem instances.

The performance of the heuristics and the ABC algorithm for large problem instances.

The computational time of the MIP model, heuristics, and the ABC algorithm.

The result is the average of 20 randomly generated problem instances.

The converge curves of the proposed ABC.

## 6. Conclusions and Future Work

## Author Contributions

## Institutional Review Board Statement

## Informed Consent Statement

Data availability statement, conflicts of interest.

The authors declare no conflict of interest.

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developed a branch-and-price approach to solving a surgery assignment problem.

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Solving surgical cases assignment problem by a branch-and-price approach. 112(1): 96-108. Fei, H., Chu, C., Meskens, N.J.A.o.O.R., 2009.