A resilience optimization approach for workforce-inventory control dynamics under uncertainty. (English) Zbl 1305.90233
Summary: The presence of uncertainties in manufacturing systems and supply chains can cause undesirable behavior. Failure to account for these in the design phase can further impair the capability of systems to respond to changes effectively. In this work, we consider a dynamic workforce-inventory control problem wherein inventory planning, production releases, and workforce hiring decisions need to be made. The objective is to develop planning rules to achieve important requirements related to dynamic transient behavior when system parameters are imprecisely known. To this end, we propose a resilience optimization model for the problem and develop a novel local search procedure that combines the strengths of recent developments in robust optimization technology and small signal stability analysis of dynamic systems. A numerical case study of the problem demonstrates significant improvements of the proposed solution in controlling fluctuations and high variability found in the system’s inventory, work-in-process, and workforce levels. Overall, the proposed model is shown to be computationally efficient and effective in hedging against model uncertainties.
MSC:
| 90B50 | Management decision making, including multiple objectives |
| 90B35 | Deterministic scheduling theory in operations research |
| 68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |
References:
| [1] | Ansof, H., & Slevin, D. (1968). An appreciation of industrial dynamics. Management Science, 14, 91-106. |
| [2] | Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52, 35-53. · Zbl 1165.90565 |
| [3] | Blanchini, F., Rinaldi, F., & Ukovich, W. (1997). A network design problem for a distribution system with uncertain demands. SIAM Journal on Optimization, 7, 560-578. · Zbl 0878.90055 · doi:10.1137/S1052623494266262 |
| [4] | Bertsimas, D., & Thiele, A. (2006). A robust optimization approach to inventory theory. Operations Research, 54(1), 150-168. · Zbl 1167.90314 · doi:10.1287/opre.1050.0238 |
| [5] | Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions to uncertain programs. Operations Research Letters, 25, 1-13. · Zbl 0941.90053 · doi:10.1016/S0167-6377(99)00016-4 |
| [6] | Christensen, J., & Brogan, W. (1971). Modeling and optimal control of production processes. International Journal of Systems Science, 1, 247-255. · Zbl 0212.51501 · doi:10.1080/00207727108920234 |
| [7] | Dong, Z., Pang, C., & Zhang, P. (2005). Power system sensitivity analysis for probabilistic small signal stability assessment in a deregulated environment. International Journal of Control, Automation, and Systems, 3(2), 355-362. |
| [8] | Edgehill, J., Olsmats, C., & Towill, D. (1988). Industrial case study on the dynamics and sensitivity of a close-coupled production-distribution system. International Journal of Production Research, 26(10), 1681-1693. · doi:10.1080/00207548808947982 |
| [9] | Forrester, J. W. (1961). Industrial Dynamics. Cambridge, MA: The M.I.T Press. |
| [10] | Goh, J., & Sim, M. (2011). Robust optimization made easy with ROME. Operations Research, 59(4), 973-985. · Zbl 1235.90107 |
| [11] | Kuo, B., & Golnaraghi, F. (2009). Automatic Control Systems (9th ed.). New Jersey: Wiley. |
| [12] | Ortega, M., & Lin, L. (2004). Control theory applications to the production-inventory problem: A review. International Journal of Production Research, 42(11), 2303-2322. · Zbl 1060.90011 |
| [13] | Min, H., Beyeler, W., Brown, T., Son, Y., & Jones, A. (2007). Toward modeling and simulation of critical national infrastructure interdependencies. IIE Transactions, 39(1), 57-71. |
| [14] | Nemirovski, A. (1993). Several NP-hard problems arising in robust stability analysis. Mathematics of Control, Signals, and Systems, 6(2), 99-105. · Zbl 0792.93100 · doi:10.1007/BF01211741 |
| [15] | Mitroff, I., & Alpaslan, M. (2003). Preparing for evil. Harvard Business Review, 81(4), 109-115. |
| [16] | Özveren, C., & Sterman, J. (1989). Control theory heuristics for improving the behavior of economic models. System Dynamics Review, 5(2), 130-147. · doi:10.1002/sdr.4260050204 |
| [17] | Pishvaee, M., Rabbani, M., & Torabi, S. (2011). A robust optimization approach to closed-loop supply chain network design under uncertainty. Applied Mathematical Modelling, 35, 637-649. · Zbl 1205.90056 · doi:10.1016/j.apm.2010.07.013 |
| [18] | Porter, B., & Bradshaw, A. (1974). Modal control of production-inventory systems using piecewise-constant control policies. International Journal of Systems Science, 5, 733-742. · Zbl 0286.90023 · doi:10.1080/00207727408920137 |
| [19] | Qiu, J., Shahidehpour, S., & Schuss, Z. (1989). Effect of small random perturbations on power system dynamics and its reliability evaluation. IEEE Transactions on Power Systems, 4, 197-204. · doi:10.1109/59.32478 |
| [20] | Rydzak, F., & Chlebus, E. (2007). Application of resilience analysis in production systems? Bombardier Transportation case study, In Proceedings of the 25th International Conference of the System Dynamics Society. Boston: USA. · Zbl 0286.90023 |
| [21] | Rydzak, F., Magnuszewski, P., Sendzimir, J., & Chlebus, E. (2006). A concept of resilience in production systems, In Proceedings of the 24th International Conference of the System Dynamics Society. The Netherlands: Nijmegen. |
| [22] | Saleh, M., Oliva, R., Davidsen, P., & Kampmann, C. (2010). A comprehensive analytical approach for policy analysis of system dynamics models. European Journal of Operational Research, 203, 673-683. · Zbl 1177.90222 |
| [23] | Sarimveisa, H., Patrinosa, P., Tarantilisb, C., & Kiranoudisa, C. (2008). Dynamic modeling and control of supply chain systems: A review. Computers & Operations Research, 35, 3530-3561. · Zbl 1146.90353 · doi:10.1016/j.cor.2007.01.017 |
| [24] | Simon, H. (1952). On the application of servomechanism theory in the study of production control. Econometrica, 20(2), 247-268. · Zbl 0046.37804 · doi:10.2307/1907849 |
| [25] | Soyster, A. L. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 21(5), 1154-1157. · Zbl 0266.90046 · doi:10.1287/opre.21.5.1154 |
| [26] | Sterman, J. (1989). Modeling managerial behavior: Misperceptions of feedback in a dynamic decision making experiment. Management Science, 35(3), 321-339. · doi:10.1287/mnsc.35.3.321 |
| [27] | Towill, D. (1982). Dynamic analysis of an inventory and order based production control system. International Journal of Production Research, 20, 671-687. · doi:10.1080/00207548208947797 |
| [28] | Vassian, J. (1955). Application of discrete variable servo theory to inventory control. Operations Research, 3, 272-282. · Zbl 1414.90054 |
| [29] | Vidyasagar, M., & Blondel, V. (2001). Probabilistic solutions to some NP-hard matrix problems. Automatica, 37, 1397-1405. · Zbl 1031.93165 · doi:10.1016/S0005-1098(01)00089-9 |
| [30] | Yourdon, E. (2004). Wojny na bity: wplyw wydarzeń z 11 września na technike informacyjna. Warszawa: Wydawnictwo Naukowo-Techniczne. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
