A master production scheduling procedure for stochastic demand and rolling planning horizons

The problem of interest is a one product, uncapacitated master production schedule (MPS) in which decisions are made under rolling planning horizons. Demand is stochastic and time varying, and effectiveness is measured by inventory holding, production setup, and backorder costs. Typically, in both the research literature and the business practice the stochastic nature of the problem is modeled in an ad hoc fashion. The stochastic MPS problem is usually solved by adding safety stock to production quantities obtained from a deterministic lot-sizing algorithm. Here, the stochastic nature of the problem is explicitly considered, as an optimal algorithm for solving the static probabilistic dynamic lot-sizing problem is adapted to rolling planning horizons. The resulting algorithm is found to dominate traditional approaches over a wide variety of experimental factors, reducing total costs by an average of 16% over traditional methods.

[1]  Zeger Degraeve,et al.  Modeling industrial lot sizing problems: a review , 2008 .

[2]  R. Ehrhardt.  The Power Approximation for Computing (s, S) Inventory Policies , 1979 .

[3]  J. Rezaei,et al.  Multi-objective models for lot-sizing with supplier selection , 2011 .

[4]  Urban Wemmerlöv,et al.  Lot-sizing under uncertainty in a rolling schedule environment , 1984 .

[5]  D. Clay Whybark,et al.  MATERIAL REQUIREMENTS PLANNING UNDER UNCERTAINTY , 1976 .

[6]  M. Cardós,et al.  Exact and approximate calculation of the cycle service level in periodic review inventory policies , 2011 .

[7]  Urban Wemmerlöv,et al.  The behavior of lot-sizing procedures in the presence of forecast errors , 1989 .

[8]  Richard Metters,et al.  Adapting lot-sizing techniques to stochastic demand through production scheduling policy , 1996 .

[9]  Lawrence R LaForge,et al.  MRP practices in a random sample of manufacturing firms , 1986 .

[10]  Vicente Vargas,et al.  Production , Manufacturing and Logistics An optimal solution for the stochastic version of the Wagner – Whitin dynamic lot-size model , 2009 .

[11]  James H. Bookbinder,et al.  Strategies for the Probabilistic Lot-Sizing Problem with Service-Level Constraints , 1988 .

[12]  V. Sridharan,et al.  Freezing the Master Production Schedule: Implications for Fill Rate* , 1994 .

[13]  Thomas E. Callarman,et al.  A Comparison of Dynamic Lot Sizing Rules for Use in a Single Stage MRP System with Demand Uncertainty , 1984 .

[14]  V. Sridharan,et al.  The impact of safety stock on schedule instability, cost and service , 1989 .

[15]  S. Karlin.  Dynamic Inventory Policy with Varying Stochastic Demands , 1960 .

[16]  L. V. Wassenhove,et al.  COST INCREASES DUE TO DEMAND UNCERTAINTY IN MRP LOT SIZING , 1983 .

[17]  Milind Dawande,et al.  Discrete Forecast Horizons for Two-Product Variants of the Dynamic Lot-Size Problem , 2008 .

[18]  Manoj K. Malhotra,et al.  Operations Management: Processes and Value Chains , 2004 .

[19]  E. Silver.  Inventory control under a probabilistic time-varying, demand pattern , 1978 .

[20]  Gerard M. Campbell.  Master Production Scheduling Under Rolling Planning Horizons with Fixed Order Intervals , 1992 .

[21]  Shey-Huei Sheu,et al.  Economic production quantity model for randomly failing production process with minimal repair and imperfect maintenance , 2011 .

[22]  Graham K. Rand,et al.  Decision Systems for Inventory Management and Production Planning , 1979 .

[23]  R. C. Carlson,et al.  An analysis of scheduling policies in multiechelon production systems , 1985 .

[24]  Urban Wemmerlüv.  COMMENTS ON “COST INCREASES DUE TO DEMAND UNCERTAINTY IN MRP LOT SIZING”: A VERIFICATION OF ORDERING PROBABILITIES , 1985 .

[25]  Xiande Zhao,et al.  Freezing the master production schedule for material requirements planning systems under demand uncertainty , 1993 .

[26]  Xiande Zhao,et al.  Lot-sizing rules and freezing the master production schedule in material requirements planning systems under demand uncertainty , 1995 .

[27]  Jr. Arthur F. Veinott.  On the Opimality of $( {s,S} )$ Inventory Policies: New Conditions and a New Proof , 1966 .

[28]  David F. Pyke,et al.  Inventory management and production planning and scheduling , 1998 .

[29]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[30]  V. Sridharan,et al.  Freezing the Master Production Schedule Under Rolling Planning Horizons , 1987 .

[31]  W. C. Benton.  Safety Stock and Service Levels in Periodic Review Inventory Systems , 1991 .

[32]  Ronald G. Askin.  A Procedure for Production Lot Sizing with Probabilistic Dynamic Demand , 1981 .

[33]  Moncer Hariga,et al.  A single-item continuous review inventory problem with space restriction , 2010 .

[34]  V. Sridharan,et al.  Freezing the Master Production Schedule Under Demand Uncertainty , 1990 .

[35]  Stephen A. Smith,et al.  Estimating negative binomial demand for retail inventory management with unobservable lost sales , 1996 .