Production planning with resources subject to congestion. (English) Zbl 1158.90337
Summary: A fundamental difficulty in developing effective production planning models has been accurately reflecting the nonlinear dependency between workload and lead times. We develop a mathematical programming model for production planning in multiproduct, single stage systems that captures the nonlinear dependency between workload and lead times. We then use outer linearization of this nonlinear model to obtain a linear programming formulation and extend it to multistage systems. Extensive computational experiments validate the approach and compare its results to conventional models that assume workload-independent planning lead times.
MSC:
| 90B30 | Production models |
References:
| [1] | Agnew, Dynamic modeling and control of some congestion prone systems, Oper Res 24 pp 400– (1976) · Zbl 0336.90011 |
| [2] | Anli, Tractable supply chain production planning modeling nonlinear lead time and quality of service constraints, J Manufact Syst · Zbl 1153.90389 |
| [3] | Asmundsson, Tractable nonlinear production planning models for semiconductor wafer fabrication facilities, IEEE Trans Semiconductor Manufact 19 pp 95– (2006) |
| [4] | Buzacott, Stochastic models of manufacturing systems (1993) · Zbl 1094.90518 |
| [5] | Byrne, Production planning using a hybrid simulation-analytical approach, Int J Prod Econ 59 pp 305– (1999) |
| [6] | Byrne, Production planning: An improved hybrid approach, Int J Prod Econ 93-94 pp 225– (2005) |
| [7] | Dauzere-Peres, An integrated approach in production planning and scheduling (1994) · Zbl 0842.90053 · doi:10.1007/978-3-642-46804-9 |
| [8] | Ettl, A supply chain network model with base-stock control and service requirements, Oper Res 48 pp 216– (2000) |
| [9] | Graves, A tactical planning model for a job shop, Oper Res 34 pp 552– (1986) · Zbl 0609.90061 |
| [10] | Hackman, A general framework for modeling production, Management Sci 35 pp 478– (1989) |
| [11] | Holt, Planning production, inventories and work force (1960) |
| [12] | Hopp, Factory physics : foundations of manufacturing management (2001) |
| [13] | Hung, A production planning approach based on iterations of linear programming optimization and flow time prediction, J Chin Inst Indus Eng 18 pp 55– (2001) |
| [14] | Hung, A production planning methodology for semiconductor manufacturing based on iterative simulation and linear programming calculations, IEEE Trans Semiconductor Manufact 9 pp 257– (1996) |
| [15] | S. Hwang, and R. Uzsoy, A single stage multi-product dynamic lot sizing model with work in process and congestion, Research Report, Laboratory for Extended Enterprises at Purdue, School of Industrial Engineering, Purdue University, West Lafayette, IN, 2005. |
| [16] | D. F. Irdem, N. B. Kacar, and R. Uzsoy, ”An experimental study of an iterative simulation-optimization algorithm for production planning,” Winter Simulation Conference, S.J. Mason, R. Hill, L. Moench, and O. Rose, Miami, FL, 2008. |
| [17] | Johnson, Operations research in production planning, scheduling and inventory control (1974) |
| [18] | Karmarkar, Capacity loading and release planning with work-in-progress (WIP) and lead-times, J Manufact Oper Management 2 pp 105– (1989) |
| [19] | Karmarkar, Logistics of production and inventory 4 (1993) · doi:10.1016/S0927-0507(05)80186-0 |
| [20] | Karmarkar, Lotsizing in multimachine job shops, IIE Trans 13 pp 290– (1985) |
| [21] | Kekre, Some issues in job shop design, Simon Graduate School of Business Administration (1984) |
| [22] | Kim, Extended model for a hybrid production planning approach, Int J Prod Econ 73 pp 165– (2001) |
| [23] | M. Lautenschlager, and H. Stadtler, Modelling lead times depending on capacity utilization, Research Report, Technische Universitat Darmstadt, 1998. |
| [24] | Medhi, Stochastic models in queuing theory (1991) · Zbl 0743.60100 |
| [25] | Missbauer, Aggregate order release planning for time-varying demand, Int J Prod Res 40 pp 688– (2002) · Zbl 1060.90508 |
| [26] | H. Missbauer, Order release planning with clearing functions: A queueing-theoretical analysis of the clearing function concept, 15th Inter Working Seminar Prod Econ, Innsbruck, Austria, 2008, pp. 301-313. |
| [27] | Orlicky, Material requirements planning: the new way of life in production and inventory management (1975) |
| [28] | Pahl, Production planning with load dependent lead times, 4OR: Quart J Oper Res 3 pp 257– (2005) · Zbl 1134.90375 |
| [29] | A. A. B. Pritsker, and K. Snyder, ”Production scheduling using FACTOR,” The planning and scheduling of production systems, A. Artiba and S.E. Elmaghraby, Chapman and Hall, 1997. |
| [30] | G. Riaño, Transient behavior of stochastic networks: Application to production planning with load-dependent lead times, School of industrial and systems engineering, Georgia Institute of Technology, Atlanta, GA, 2003. |
| [31] | G. Riaño, R. Serfozo, S. Hackman, S. H. Ng, L. P. Chan, P. Lendermann, Benchmarking of a stochastic production planning model in a simulation testbed, Winter Simulation Conference, 2003. |
| [32] | Spearman, An analytic congestion model for closed production systems with IFR processing times, Management Sci 37 pp 1015– (1991) · Zbl 0737.90033 |
| [33] | Srinivasan, Resource pricing and aggregate scheduling in manufacturing systems, Graduate School of Industrial Administration (1988) |
| [34] | Turkseven, Computational evaluation of production planning formulations using clearing functions, School of Industrial Engineering (2005) |
| [35] | Vollmann, Manufacturing planning and control for supply chain management (2005) |
| [36] | Voss, Introduction to computational optimization models for production planning in a supply chain (2003) · doi:10.1007/978-3-540-24764-7 |
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