Problem and Methodology to Solve Lot Sizing Problems

This article aims to explore articles related to lot sizing problems by focusing to explain different types of problems and methodology to solve them. Lot sizing problems can be distinguished into three main types which are single item, multiple items and multi levels lot sizing problems. These three main types can have both capacitated and uncapacitated resources constraints which make three main types become 6 types of lot sizing problems. Exact methods, Heuristics and Meta heuristic have been used to solve lot sizing problems. An Exact method is mostly used to solve a small size of lot sizing problems whereas Heuristics and Meta-heuristics are used to solve a larger size of problems. Recently, Meta-heuristics are widely used in many articles when compared to other methods because Metaheuristics are easy to implement and obtain good solution quality in shorter time.

[1]  Laurence A. Wolsey,et al.  Polyhedra for lot-sizing with Wagner—Whitin costs , 1994, Math. Program..

[2]  Yi-Feng Hung,et al.  Solving mixed integer programming production planning problems with setups by shadow price information , 1998, Comput. Oper. Res..

[3]  Nicolas Jonard,et al.  A genetic algorithm to solve the general multi-level lot-sizing problem with time-varying costs , 2000 .

[4]  William W. Trigeiro,et al.  Capacitated lot sizing with setup times , 1989 .

[5]  Ikou Kaku,et al.  Solving uncapacitated multilevel lot-sizing problems using a particle swarm optimization with flexible inertial weight , 2009, Comput. Math. Appl..

[6]  Richard F. Hartl,et al.  Combining population-based and exact methods for multi-level capacitated lot-sizing problems , 2006 .

[7]  Marc Salomon,et al.  LINEAR PROGRAMMING, SIMULATED ANNEALING AND TABU SEARCH HEURISTICS FOR LOTSIZING IN BOTTLENECK ASSEMBLY SYSTEMS , 1993 .

[8]  J. K. Lenstra,et al.  Deterministic Production Planning: Algorithms and Complexity , 1980 .

[9]  R. Kuik,et al.  Multi-level lot-sizing problem: Evaluation of a simulated-annealing heuristic , 1990 .

[10]  Dirk Cattrysse,et al.  A dual ascent and column generation heuristic for the discrete lotsizing and scheduling problem with setup times , 1993 .

[11]  Hoesel van Cpm,et al.  A linear description of the discrete lot-sizing and scheduling problem , 1994 .

[12]  Ömer Kirca,et al.  A new heuristic approach for the multi-item dynamic lot sizing problem , 1994 .

[13]  G. Bitran,et al.  Computational Complexity of the Capacitated Lot Size Problem , 1982 .

[14]  H. O. Gu¨nther.  Planning lot sizes and capacity requirements in a single stage production system , 1987 .

[15]  Jully Jeunet,et al.  Solving large unconstrained multilevel lot-sizing problems using a hybrid genetic algorithm , 2000 .

[16]  Marc Lambrecht,et al.  A facilities in series capacity constrained dynamic lot-size model , 1978 .

[17]  Ömer Kirca.  An efficient algorithm for the capacitated single item dynamic lot size problem , 1990 .

[18]  Albert P. M. Wagelmans,et al.  Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems , 2001, Math. Oper. Res..

[19]  Luk N. Van Wassenhove,et al.  A simple heuristic for the multi item single level capacitated lotsizing problem , 1986 .

[20]  Luk N. Van Wassenhove,et al.  Multi Item Single Level Capacitated Dynamic Lotsizing Heuristics: A Computational Comparison (Part II: Rolling Horizon) , 1986 .

[21]  Hartmut Stadtler,et al.  Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows , 2003, Oper. Res..

[22]  Albert P. M. Wagelmans,et al.  An $O(T^3)$ algorithm for the economic lot-sizing problem with constant capacities , 1993 .

[23]  Luk N. Van Wassenhove,et al.  Multi Item Single Level Capacitated Dynamic Lotsizing Heuristics: A Computational Comparison (Part I: Static Case) , 1986 .

[24]  Nicolas Jonard,et al.  Single-point stochastic search algorithms for the multi-level lot-sizing problem , 2005, Comput. Oper. Res..

[25]  E. Silver,et al.  A heuristic solution procedure for the multi-item, single-level, limited capacity, lot-sizing problem , 1981 .

[26]  Horst Tempelmeier,et al.  Mehrstufige Mehrprodukt-Losgrößenplanung bei beschränkten Ressourcen und genereller Erzeugnisstruktur , 1993 .

[27]  Edward A. Silver,et al.  A heuristic algorithm for determining lot sizes of an item subject to regular and overtime production capacities , 1983 .

[28]  Regina Berretta,et al.  A memetic algorithm for a multistage capacitated lot-sizing problem , 2004 .

[29]  Horst Tempelmeier,et al.  A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures , 1994 .

[30]  Laurence A. Wolsey,et al.  bc -- prod: A Specialized Branch-and-Cut System for Lot-Sizing Problems , 2000 .

[31]  Luk N. Van Wassenhove,et al.  Multi-Item Single-Level Capacitated Dynamic Lot-Sizing Heuristics: A General Review , 1988 .

[32]  M. Lambrecht,et al.  A capacity constrained single-facility dynamic lot-size model , 1978 .

[33]  Marc Salomon,et al.  Batching decisions: structure and models , 1994 .

[34]  Terry P. Harrison,et al.  Lot Sizing in Serial Assembly Systems with Multiple Constrained Resources , 1996 .

[35]  S. Lippman.  Optimal inventory policy with multiple set-up costs , 1968 .

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

[37]  E. Newson.  Multi-Item Lot Size Scheduling by Heuristic Part II: With Variable Resources , 1975 .

[38]  M. Florian,et al.  DETERMINISTIC PRODUCTION PLANNING WITH CONCAVE COSTS AND CAPACITY CONSTRAINTS. , 1971 .

[39]  Jinxing Xie,et al.  Heuristic genetic algorithms for general capacitated lot-sizing problems☆ , 2002 .

[40]  H. Tempelmeier,et al.  A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times , 1996 .

[41]  James H. Bookbinder,et al.  Production planning for mixed assembly/arborescent systems , 1990 .

[42]  Laurence A. Wolsey,et al.  Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs , 2001, Manag. Sci..

[43]  N. Adam,et al.  The Dynamic Lot-Sizing Problem for Multiple Items Under Limited Capacity , 1981 .

[44]  Terry P. Harrison,et al.  Lot Sizing in General Assembly Systems with Setup Costs, Setup Times, and Multiple Constrained Resources , 1998 .

[45]  Alok Aggarwal,et al.  Improved Algorithms for Economic Lot Size Problems , 1993, Oper. Res..

[46]  L. V. Wassenhove,et al.  Some extensions of the discrete lotsizing and scheduling problem , 1991 .

[47]  A. Federgruen,et al.  A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0n log n or 0n Time , 1991 .

[48]  Terry P. Harrison,et al.  Lot-Sizing with Start-Up Times , 1998 .

[49]  Christian Almeder,et al.  A hybrid optimization approach for multi-level capacitated lot-sizing problems , 2010, Eur. J. Oper. Res..

[50]  Jatinder N. D. Gupta,et al.  Determining lot sizes and resource requirements: A review , 1987 .

[51]  Jully Jeunet,et al.  Randomized multi-level lot-sizing heuristics for general product structures , 2003, Eur. J. Oper. Res..

[52]  E. Newson.  Multi-Item Lot Size Scheduling by Heuristic Part I: With Fixed Resources , 1975 .

[53]  Richard F. Hartl,et al.  A MAX-MIN ant system for unconstrained multi-level lot-sizing problems , 2007, Comput. Oper. Res..

[54]  Dong X. Shaw,et al.  An Algorithm for Single-Item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs , 1998 .

[55]  Albert P. M. Wagelmans,et al.  Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case , 1992, Oper. Res..