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An integrated machine scheduling and personnel allocation problem for large-scale industrial facilities using a rolling horizon framework

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Abstract

In this study we present an optimization problem where machine scheduling and personnel allocation decisions are solved simultaneously. The machine scheduling consists of solving a variant of the job shop problem where jobs are allocated in batches and multitasking is allowed. On the other hand, the personnel allocation problem searches for the optimal allocation of human resources to support the facility operation. Although these problems have been extensively studied independently in the literature, the integrated problem has very limited studies, in particular for large-scale industrial environments. We introduce a mathematical formulation for this problem and propose a solution method to evaluate optimal solutions more efficiently. We also implement a rolling horizon framework to test our approach using real-world based instances extracted from an analytical service facility. The results show that, overall improvements of up to 11.6% are achieved compared to the case where no personnel allocation decisions are considered within the scheduling problem.

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References

  • Ahmadi-Javid A, Hooshangi-Tabrizi P (2017) Integrating employee timetabling with scheduling of machines and transporters in a job-shop environment: a mathematical formulation and an anarchic society optimization algorithm. Comput Oper Res 84:73–91

    Article  MathSciNet  Google Scholar 

  • Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms and applications. Prentice Hall, Upper Saddle River

    MATH  Google Scholar 

  • Artigues C, Gendreau M, Rousseau L, Vergnaud A (2009) Solving an integrated employee timetabling and job-shop scheduling problem via hybrid branch-and-bound. Comput Oper Res 36:2330–2340

    Article  Google Scholar 

  • Ashley DW (1993) A spreadsheet optimization system for library staff scheduling. Comput Oper Res 22:615–624

    Article  Google Scholar 

  • Balas E, Simonetti N, Vazacopoulos A (2008) Job shop scheduling with setup times, deadlines and precedence constraints. J Sched 11:253–262

    Article  MathSciNet  Google Scholar 

  • Bassett MH, Pekny JF, Reklaitis GV (1996) Decomposition techniques for the solution of large-scale scheduling problems. AIChE J 42:3373–3384

    Article  Google Scholar 

  • Brucker P, Qu R, Burke E (2011) Personnel scheduling: models and complexity. Eur J Oper Res 210:467–473

    Article  MathSciNet  Google Scholar 

  • Cerda J, Henning GP, Grossmann IE (1997) A mixed-integer linear programming model for short-term scheduling of single-stage multiproduct batch plants with parallel lines. Ind Eng Chem Res 36:1695–1707

    Article  Google Scholar 

  • Chand S, Traub R, Uzsoy R (1997) Rolling horizon procedures for the single machine deterministic total completion time scheduling problem with release dates. Ann Oper Res 70:115–125

    Article  Google Scholar 

  • Daniels R, Mazzola J, Shi D (2004) Flow shop scheduling with partial resource flexibility. Manage Sci 50:658–669

    Article  Google Scholar 

  • Daniels RL, Mazzola JB (1994) Flow shop scheduling with resource flexibility. Oper Res 42:504–522

    Article  Google Scholar 

  • Dunning I, Huchette J, Lubin M (2017) JuMP: a modeling language for mathematical optimization. SIAM Rev 59(2):295–320

    Article  MathSciNet  Google Scholar 

  • Erhard M, Schoenfelder J, Fugener A, Brunner JO (2018) State of the art in physician scheduling. Eur J Oper Res 265:1–18

    Article  MathSciNet  Google Scholar 

  • Ernst A, Jiang H, Krishnamoorthy M, Sier D (2004) Staff scheduling and rostering: a review of applications, methods and models. Eur J Oper Res 153:3–27

    Article  MathSciNet  Google Scholar 

  • Fang J, Xi Y (1997) A rolling horizon job shop rescheduling strategy in the dynamic environment. Int J Adv Manuf Technol 13:227–232

    Article  Google Scholar 

  • Frihat M, Sadfi C, Hadj-Alouane A (2014) Optimization of integrated employee timetabling and hybrid job shop scheduling under time lag constraints. In: Proceedings—2014 international conference on control, decision and information technologies, CoDIT 2014, pp 282–287

  • Graham RL (1966) Bounds for certain multiprocessing anomalies. Bell Syst Tech J 45:1563–1581

    Article  Google Scholar 

  • Guyon O, Lemaire P, Pinson E, Rivreau D (2014) Solving an integrated job-shop problem with human resource constraints. Ann Oper Res 23:147–171

    Article  MathSciNet  Google Scholar 

  • Jamili A (2016) Robust job shop scheduling problem: mathematical models, exact and heuristic algorithms. Exper Syst Appl 55:341–350

    Article  Google Scholar 

  • Kuhn HW (1955) The Hungarian method for the assignment problem. Naval Res Logist 2:83–97

    Article  MathSciNet  Google Scholar 

  • Lagzi S, Fukasawa R, Ricardez-Sandoval L (2017a) A multitasking continuous time formulation for short-term scheduling of operations in multipurpose plants. Comput Chem Eng 97:135–146

    Article  Google Scholar 

  • Lagzi S, Lee DY, Fukasawa R, Ricardez-Sandoval L (2017b) A computational study of continuous and discrete time formulations for a class of short-term scheduling problems for multipurpose plants. Ind Eng Chem Res 56:8940–8953

    Article  Google Scholar 

  • Lenstra JK, Kan AHGR (1978) Complexity of scheduling under precedence constraints. Oper Res 26:22–35

    Article  MathSciNet  Google Scholar 

  • Liu SQ, Kozan E (2016) Parallel-identical-machine job-shop scheduling with different stage-dependent buffering requirements. Comput Oper Res 74:31–41

    Article  MathSciNet  Google Scholar 

  • Mendez CA, Cerda J, Grossmann IE, Harjunkoski I, Fahl M (2006) State-of-the-art review of optimization methods for short-term scheduling of batch processes. Comput Chem Eng 30:913–946

    Article  Google Scholar 

  • Morton TE, Pentico DW (1993) Heuristic scheduling systems. Wiley-Interscience, New York

    Google Scholar 

  • Raman N, Talbot F (1993) The job shop tardiness problem: a decomposition approach. Eur J Oper Res 69:187–199

    Article  Google Scholar 

  • Patil B, Fukasawa R, Ricardez-Sandoval L (2015) Scheduling of operations in a large-scale scientific services facility via multicommodity flow and an optimization-based algorithm. Ind Eng Chem Res 54:1628–1639

    Article  Google Scholar 

  • Potts CN, Kovalyov MY (2000) Scheduling with batching: a review. Eur J Oper Res 120:228–249

    Article  MathSciNet  Google Scholar 

  • Santos F, Fukasawa R, Ricardez-Sandoval L (2018) An integrated personnel allocation and machine scheduling problem for industrial size multipurpose plants. In: ADCHEM—Advanced control of chemical processes, pp 156–161

  • Schulze M, Zimmermann J (2017) Staff and machine shift scheduling in a german potash mine. J Sched 20:635–656

    Article  MathSciNet  Google Scholar 

  • Serafini P (1996) Scheduling jobs on several machines with the job splitting property. Oper Res 44:617–628

    Article  Google Scholar 

  • Singer M (2001) Decomposition methods for large job shops. Comput Oper Res 28:193–207

    Article  MathSciNet  Google Scholar 

  • Stevenson Z, Fukasawa R, Ricardez-Sandoval L (2020a) Evaluating periodic rescheduling policies using a rolling horizon framework in an industrial-scale multipurpose plant. Journal of Scheduling 23(3):397–410

    Article  MathSciNet  Google Scholar 

  • Stevenson Z, Fukasawa R, Ricardez-Sandoval L (2020b) A dynamic approach to selecting time points for short-term scheduling with application to multipurpose facilities. Ind & Eng Chem Res 59:9180–9197

    Article  Google Scholar 

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Acknowledgements

The financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Ontario Centers for Excellence (OCE), and the industrial partner in the analytical services sector are gratefully acknowledged.

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Authors and Affiliations

  1. Combinatorics and Optimization Department, University of Waterloo, Waterloo, Canada

    Fernando Santos & Ricardo Fukasawa

  2. Chemical Engineering Department, University of Waterloo, Waterloo, Canada

    Luis Ricardez-Sandoval

Authors
  1. Fernando Santos
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  2. Ricardo Fukasawa
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  3. Luis Ricardez-Sandoval
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Correspondence to Luis Ricardez-Sandoval.

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Santos, F., Fukasawa, R. & Ricardez-Sandoval, L. An integrated machine scheduling and personnel allocation problem for large-scale industrial facilities using a rolling horizon framework. Optim Eng 22, 2603–2626 (2021). https://doi.org/10.1007/s11081-020-09542-7

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  • DOI: https://doi.org/10.1007/s11081-020-09542-7

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