IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i5p1178-d1082476.html
   My bibliography  Save this article

An Inverse Optimal Value Approach for Synchronously Optimizing Activity Durations and Worker Assignments with a Project Ideal Cost

Author

Listed:
  • Lili Zhang

    (School of Maritime Economics and Management, Dalian Maritime University, Dalian 116026, China)

  • Zhengrui Chen

    (School of Business, Dalian University of Technology, Panjin 124221, China)

  • Dan Shi

    (School of Business, Dalian University of Technology, Panjin 124221, China)

  • Yanan Zhao

    (School of Economics and Management, Liaoning Petrochemical University, Fushun 113001, China)

Abstract

Most companies survive the pain of cost and schedule overruns because of inaccurate project activity time settings. In order to deliver a project with a target cost and on schedule, this research proposes an inverse optimal value approach to optimize activity durations and the corresponding worker assignments synchronously to make the optimal project cost infinitely close to an ideal cost. The leader model reflects cost orientation and adjustability of activity durations, the follower model reflects the complexity of activity sequence, critical path completion time, cost pressure, skill matching, energy consumption, and other costs. Through upper-level and lower-level feedback and interaction of activity durations and worker assignments it is possible to deliver a project with an ideal cost. With considerations of the mathematical model characteristics of bi-level programming, nonlinearity, NP hard, and MAX functions, an improved genetic algorithm combining adaptive artificial fish swarms is designed. From the comparison results of random examples and an actual example, the error rate of the optimal value of the improved algorithm is acceptable. Numerical experiments show that the inverse optimal approach can deliver a project without delay and with an ideal cost. The inverse optimization method is more in line with the idea of target management, and can help managers achieve the purpose of cost control.

Suggested Citation

  • Lili Zhang & Zhengrui Chen & Dan Shi & Yanan Zhao, 2023. "An Inverse Optimal Value Approach for Synchronously Optimizing Activity Durations and Worker Assignments with a Project Ideal Cost," Mathematics, MDPI, vol. 11(5), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1178-:d:1082476
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/5/1178/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/5/1178/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chow, Joseph Y.J. & Ritchie, Stephen G. & Jeong, Kyungsoo, 2014. "Nonlinear inverse optimization for parameter estimation of commodity-vehicle-decoupled freight assignment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 67(C), pages 71-91.
    2. Timothy C. Y. Chan & Taewoo Lee & Daria Terekhov, 2019. "Inverse Optimization: Closed-Form Solutions, Geometry, and Goodness of Fit," Management Science, INFORMS, vol. 65(3), pages 1115-1135, March.
    3. Joel Goh & Nicholas G. Hall, 2013. "Total Cost Control in Project Management via Satisficing," Management Science, INFORMS, vol. 59(6), pages 1354-1372, June.
    4. Hesham K. Alfares, 2022. "Plant shutdown maintenance workforce team assignment and job scheduling," Journal of Scheduling, Springer, vol. 25(3), pages 321-338, June.
    5. Zhichao Zheng & Karthik Natarajan & Chung-Piaw Teo, 2016. "Least Squares Approximation to the Distribution of Project Completion Times with Gaussian Uncertainty," Operations Research, INFORMS, vol. 64(6), pages 1406-1421, December.
    6. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    7. Lim, Dong-Joon, 2016. "Inverse DEA with frontier changes for new product target setting," European Journal of Operational Research, Elsevier, vol. 254(2), pages 510-516.
    8. Anil Aswani & Zuo-Jun Max Shen & Auyon Siddiq, 2019. "Data-Driven Incentive Design in the Medicare Shared Savings Program," Operations Research, INFORMS, vol. 67(4), pages 1002-1026, July.
    9. W Lo & M-E Kuo, 2013. "Cost impact of float loss on a project with adjustable activity durations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(8), pages 1147-1156, August.
    10. John R. Birge & Ali Hortaçsu & J. Michael Pavlin, 2017. "Inverse Optimization for the Recovery of Market Structure from Market Outcomes: An Application to the MISO Electricity Market," Operations Research, INFORMS, vol. 65(4), pages 837-855, August.
    11. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lili Zhang & Wenhao Guo, 2023. "Inverse Optimization Method for Safety Resource Allocation and Inferring Cost Coefficient Based on a Benchmark," Mathematics, MDPI, vol. 11(14), pages 1-15, July.
    2. Adrian Marius Deaconu & Daniel Tudor Cotfas & Petru Adrian Cotfas, 2023. "Advanced Optimization Methods and Applications," Mathematics, MDPI, vol. 11(9), pages 1-7, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rishabh Gupta & Qi Zhang, 2022. "Decomposition and Adaptive Sampling for Data-Driven Inverse Linear Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2720-2735, September.
    2. Jonathan Yu-Meng Li, 2021. "Inverse Optimization of Convex Risk Functions," Management Science, INFORMS, vol. 67(11), pages 7113-7141, November.
    3. Merve Bodur & Timothy C. Y. Chan & Ian Yihang Zhu, 2022. "Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1471-1488, May.
    4. Susan Jia Xu & Mehdi Nourinejad & Xuebo Lai & Joseph Y. J. Chow, 2018. "Network Learning via Multiagent Inverse Transportation Problems," Service Science, INFORMS, vol. 52(6), pages 1347-1364, December.
    5. Nur Kaynar & Auyon Siddiq, 2023. "Estimating Effects of Incentive Contracts in Online Labor Platforms," Management Science, INFORMS, vol. 69(4), pages 2106-2126, April.
    6. Chen, Lu & Chen, Yuyi & Langevin, André, 2021. "An inverse optimization approach for a capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1087-1098.
    7. Javad Tayyebi & Ali Reza Sepasian, 2020. "Partial inverse min–max spanning tree problem," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1075-1091, November.
    8. Hughes, Michael S. & Lunday, Brian J., 2022. "The Weapon Target Assignment Problem: Rational Inference of Adversary Target Utility Valuations from Observed Solutions," Omega, Elsevier, vol. 107(C).
    9. Ghobadi, Kimia & Mahmoudzadeh, Houra, 2021. "Inferring linear feasible regions using inverse optimization," European Journal of Operational Research, Elsevier, vol. 290(3), pages 829-843.
    10. Shi Yu & Haoran Wang & Chaosheng Dong, 2020. "Learning Risk Preferences from Investment Portfolios Using Inverse Optimization," Papers 2010.01687, arXiv.org, revised Feb 2021.
    11. Timothy C. Y. Chan & Katharina Forster & Steven Habbous & Claire Holloway & Luciano Ieraci & Yusuf Shalaby & Nasrin Yousefi, 2022. "Inverse optimization on hierarchical networks: an application to breast cancer clinical pathways," Health Care Management Science, Springer, vol. 25(4), pages 590-622, December.
    12. El Mehdi, Er Raqabi & Ilyas, Himmich & Nizar, El Hachemi & Issmaïl, El Hallaoui & François, Soumis, 2023. "Incremental LNS framework for integrated production, inventory, and vessel scheduling: Application to a global supply chain," Omega, Elsevier, vol. 116(C).
    13. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    14. Andreas Lanz & Gregor Reich & Ole Wilms, 2022. "Adaptive grids for the estimation of dynamic models," Quantitative Marketing and Economics (QME), Springer, vol. 20(2), pages 179-238, June.
    15. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    16. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    17. Lucio Bianco & Massimiliano Caramia & Stefano Giordani & Veronica Piccialli, 2016. "A Game-Theoretic Approach for Regulating Hazmat Transportation," Transportation Science, INFORMS, vol. 50(2), pages 424-438, May.
    18. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    19. Cerulli, Martina & Serra, Domenico & Sorgente, Carmine & Archetti, Claudia & Ljubić, Ivana, 2023. "Mathematical programming formulations for the Collapsed k-Core Problem," European Journal of Operational Research, Elsevier, vol. 311(1), pages 56-72.
    20. Chan Y. Han & Brian J. Lunday & Matthew J. Robbins, 2016. "A Game Theoretic Model for the Optimal Location of Integrated Air Defense System Missile Batteries," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 405-416, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1178-:d:1082476. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.