A Review of Production Scheduling

Production scheduling can be defined as the allocation of available production resources over time to best satisfy some set of criteria. Typically, the scheduling problem involves a set of tasks to be performed, and the criteria may involve both tradeoffs between early and late completion of a task, and between holding inventory for the task and frequent production changeovers. The intent of this paper is to present a broad classification for various scheduling problems, to review important theoretical developments for these problem classes, and to contrast the currently available theory with the practice of production scheduling. This paper will highlight problem areas for which there is both a significant discrepancy between practice and theory, and for which the practice corresponds closely to the theory.

[1]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[2]  F. Hohn,et al.  Production Planning Over Time and the Nature of the Expectation and Planning Horizon , 1955 .

[3]  J. R. Jackson SCHEDULING A PRODUCTION LINE TO MINIMIZE MAXIMUM TARDINESS , 1955 .

[4]  Wayne E. Smith Various optimizers for single‐stage production , 1956 .

[5]  Alan S. Manne,et al.  Programming of Economic Lot Sizes , 1958 .

[6]  Robert McNaughton,et al.  Scheduling with Deadlines and Loss Functions , 1959 .

[7]  G. Thompson,et al.  Algorithms for Solving Production-Scheduling Problems , 1960 .

[8]  C. C. Holt,et al.  Planning Production, Inventories, and Work Force. , 1962 .

[9]  Jack Heller,et al.  Some Numerical Experiments for an M × J Flow Shop and its Decision-Theoretical Aspects , 1960 .

[10]  T. C. Hu Parallel Sequencing and Assembly Line Problems , 1961 .

[11]  Shimon Even,et al.  Bounds for the Optimal Scheduling of n Jobs on m Processors , 1964 .

[12]  E. Zabel Some Generalizations of an Inventory Planning Horizon Theorem , 1964 .

[13]  Eugene L. Lawler On Scheduling Problems with Deferral Costs , 1964 .

[14]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[15]  E. Ignall,et al.  Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems , 1965 .

[16]  James G. Root Scheduling with Deadlines and Loss Functions on k Parallel Machines , 1965 .

[17]  Z. A. Lomnicki A “Branch-and-Bound” Algorithm for the Exact Solution of the Three-Machine Scheduling Problem , 1965 .

[18]  Michael H. Rothkopf,et al.  Scheduling Independent Tasks on Parallel Processors , 1966 .

[19]  William S. Gere Heuristics in Job Shop Scheduling , 1966 .

[20]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[21]  G. B. McMahon,et al.  Flow-Shop Scheduling with the Branch-and-Bound Method , 1967, Oper. Res..

[22]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[23]  Samuel Eilon,et al.  Industrial Scheduling Abstracts (1950‐1966) , 1968 .

[24]  Salah E. Elmaghraby The machine sequencing problem – review and extensions , 1968 .

[25]  J. M. Moore An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs , 1968 .

[26]  F. J. Gould,et al.  A Lagrangian Application to Production Models , 1968, Oper. Res..

[27]  Linus Schrage,et al.  Letter to the Editor - A Proof of the Optimality of the Shortest Remaining Processing Time Discipline , 1968, Oper. Res..

[28]  J. G. Madigan,et al.  Scheduling a Multi-Product Single Machine System for an Infinite Planning Period , 1968 .

[29]  Harold H. Greenberg A Branch-Bound Solution to the General Scheduling Problem , 1968, Oper. Res..

[30]  Egon Balas,et al.  Machine Sequencing Via Disjunctive Graphs: An Implicit Enumeration Algorithm , 1969, Oper. Res..

[31]  Sant Arora,et al.  The Sequencing Problem , 1969 .

[32]  W. Zangwill A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System---A Network Approach , 1969 .

[33]  Arthur F. Veinott,et al.  Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems , 1969, Oper. Res..

[34]  Hamilton Emmons,et al.  One-Machine Sequencing to Minimize Certain Functions of Job Tardiness , 1969, Oper. Res..

[35]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[36]  Ashour Said A Branch-and-Bound Algorithm for Flow Shop Scheduling Problems , 1970 .

[37]  R. A. Dudek,et al.  A Heuristic Algorithm for the n Job, m Machine Sequencing Problem , 1970 .

[38]  Linus Schrage,et al.  Solving Resource-Constrained Network Problems by Implicit Enumeration - Nonpreemptive Case , 1970, Oper. Res..

[39]  James E. Day,et al.  Review of sequencing research , 1970 .

[40]  John M. Charlton,et al.  A Generalized Machine-Scheduling Algorithm , 1970 .

[41]  V. Srinivasan A hybrid algorithm for the one machine sequencing problem to minimize total tardiness , 1971 .

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

[43]  W. Szwarc Elimination methods in the m × n sequencing problem , 1971 .

[44]  Frank T. Shu Economic Ordering Frequency for two Items Jointly Replenished , 1971 .

[45]  Michael Florian,et al.  An Implicit Enumeration Algorithm for the Machine Sequencing Problem , 1971 .

[46]  Salah E. Elmaghraby,et al.  On the Scheduling of Jobs on a Number of Identical Machines. , 1972 .

[47]  M. H. Wagner,et al.  Dynamic Lot Size Models for Multi-Stage Assembly Systems , 1973 .

[48]  Kenneth R. Baker,et al.  Scheduling with parallel processors and linear delay costs , 1973 .

[49]  Z. Lieber An Extension to Modigliani and Hohn's Planning Horizons Results , 1973 .

[50]  Arnoldo C. Hax,et al.  Hierarchical integration of production planning and scheduling , 1973 .

[51]  Thom J. Hodgson,et al.  An N-Product, Multi-Machine, Lotsize Scheduling Model , 1973 .

[52]  S. K. Goyal Scheduling a Multi-Product Single Machine System , 1973 .

[53]  Marshall L. Fisher,et al.  Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I , 1973, Oper. Res..

[54]  Eugene L. Lawler,et al.  Optimal Sequencing of a Single Machine Subject to Precedence Constraints , 1973 .

[55]  Leroy B. Schwarz,et al.  A Simple Continuous Review Deterministic One-Warehouse N-Retailer Inventory Problem , 1973 .

[56]  M. Rao,et al.  A Class of Deterministic Production Planning Problems , 1973 .

[57]  D. Nocturne Note--Economic Ordering Frequency for Several Items Jointly Replenished , 1973 .

[58]  C L Doll,et al.  AN ITERATIVE PROCEDURE FOR THE SINGLE-MACHINE, MULTI-PRODUCT LOT SCHEDULING PROBLEM : A WORKING PAPER , 1973 .

[59]  Jeffrey D. Ullman,et al.  Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms , 1974, SIAM J. Comput..

[60]  S. Goyal Determination of Optimum Packaging Frequency of Items Jointly Replenished , 1974 .

[61]  A. J. Clewett,et al.  Introduction to sequencing and scheduling , 1974 .

[62]  L. Gelders,et al.  Coordinating Aggregate and Detailed Scheduling Decisions in the One-Machine Job Shop: Part I. Theory , 2015, Oper. Res..

[63]  T. E. Moore,et al.  An Implicit Enumeration Algorithm for the Nonpreemptive Shop Scheduling Problem , 1974 .

[64]  R. Jaikumar An operational optimization procedure for production scheduling , 1974 .

[65]  John L. Burbidge,et al.  The introduction of group technology , 1975 .

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

[67]  P. S. Eisenhut A Dynamic Lot Sizing Algorithm with Capacity Constraints , 1975 .

[68]  Ludo Gelders,et al.  Coordinating Aggregate and Detailed Scheduling in the One-Machine Job Shop: II - Computation and Structure , 1975, Oper. Res..

[69]  B. J. Lageweg,et al.  Minimizing Total Costs in One-Machine Scheduling , 1975, Oper. Res..

[70]  Rolf A. Lundin,et al.  Planning Horizons for the Dynamic Lot Size Model: Zabel vs. Protective Procedures and Computational Results , 1975, Oper. Res..

[71]  C. Swoveland A Deterministic Multi-Period Production Planning Model with Piecewise Concave Production and Holding-Backorder Costs , 1975 .

[72]  Leroy B. Schwarz,et al.  Optimal and System Myopic Policies for Multi-Echelon Production/Inventory Assembly Systems , 1975 .

[73]  H. D. Ratliff,et al.  A Network Approach to a Multi-Facility, Multi-Product Production Scheduling Problem Without Backordering , 1975 .

[74]  Kenneth R. Baker,et al.  A Comparative Study of Flow-Shop Algorithms , 1975, Oper. Res..

[75]  William L. Berry,et al.  Critical Ratio Scheduling: An Experimental Analysis , 1975 .

[76]  Edward G. Coffman,et al.  Computer and job-shop scheduling theory , 1976 .

[77]  Arthur M. Geoffrion,et al.  Scheduling Parallel Production Lines with Changeover Costs: Practical Application of a Quadratic Assignment/LP Approach , 1976, Oper. Res..

[78]  A. Kan Machine Scheduling Problems: Classification, Complexity and Computations , 1976 .

[79]  J Jaap Wessels,et al.  Multi item lot size determination and scheduling under capacity constraints , 1976 .

[80]  Marshall L. Fisher,et al.  A dual algorithm for the one-machine scheduling problem , 1976, Math. Program..

[81]  E. Silver A Simple Method of Determining Order Quantities in Joint Replenishments Under Deterministic Demand , 1976 .

[82]  J. J. Brennan,et al.  An Improved Algorithm for Scheduling Jobs on Identical Machines , 1977 .

[83]  Thom J. Hodgson,et al.  Note---A Note on Single Machine Sequencing with Random Processing Times , 1977 .

[84]  Leroy B. Schwarz,et al.  Single Cycle Continuous Review Policies for Arborescent Production/Inventory Systems , 1977 .

[85]  S. S. Panwalkar,et al.  A Survey of Scheduling Rules , 1977, Oper. Res..

[86]  J. Lenstra,et al.  Job-Shop Scheduling by Implicit Enumeration , 1977 .

[87]  Kenneth R. Baker,et al.  AN EXPERIMENTAL STUDY OF THE EFFECTIVENESS OF ROLLING SCHEDULES IN PRODUCTION PLANNING , 1977 .

[88]  David G. Dannenbring,et al.  An Evaluation of Flow Shop Sequencing Heuristics , 1977 .

[89]  H. Emmons,et al.  Scheduling on Parallel Machines to Minimize Two Criteria Related to Job Tardiness , 1977 .

[90]  R. A. Holmes,et al.  On the Use of A Vehicle Routing Algorithm for the Parallel Processor Problem with Sequence Dependent Changeover Costs , 1977 .

[91]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[92]  Linus Schrage,et al.  Finding an Optimal Sequence by Dynamic Programming: An Extension to Precedence-Related Tasks , 1978, Oper. Res..

[93]  H. Donald Ratliff Network Models for Production Scheduling Problems with Convex Cost and Batch Processing , 1978 .

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

[95]  Robert R. Love,et al.  The Single-Plant Mold Allocation Problem with Capacity and Changeover Restrictions , 1978, Oper. Res..

[96]  S. Elmaghraby The Economic Lot Scheduling Problem (ELSP): Review and Extensions , 1978 .

[97]  Thomas E. Morton,et al.  Universal Planning Horizons for Generalized Convex Production Scheduling , 1978, Oper. Res..

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

[99]  Victor B. Godin,et al.  Interactive Scheduling: Historical Survey and State of the Art , 1978 .

[100]  Ronald L. Graham,et al.  Performance Guarantees for Scheduling Algorithms , 1978, Oper. Res..

[101]  Maurice Queyranne,et al.  The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling , 1978, Oper. Res..

[102]  Kenneth L. Stott,et al.  Practice of Management Science---Orderbook Balancing Using a Combination of Linear Programming and Heuristic Techniques , 1978 .

[103]  B. J. Lageweg,et al.  A General Bounding Scheme for the Permutation Flow-Shop Problem , 1978, Oper. Res..

[104]  Linus Schrage,et al.  Dynamic Programming Solution of Sequencing Problems with Precedence Constraints , 1978, Oper. Res..

[105]  K. R. Baker,et al.  An Algorithm for the Dynamic Lot-Size Problem with Time-Varying Production Capacity Constraints , 1978 .

[106]  W L Maxwell,et al.  Coordination of Production Schedules with Shipping Schedules. , 1979 .

[107]  Stephen C. Graves Multistage Lot-Sizing: An Iterative Procedure. , 1979 .

[108]  R. C. Carlson,et al.  Less Nervous MRP Systems: A Dynamic Economic Lot-Sizing Approach , 1979 .

[109]  S. Graves Note---On the Deterministic Demand Multi-Product Single-Machine Lot Scheduling Problem , 1979 .

[110]  Moshe M. Barash,et al.  Operational control of item flow in versatile manufacturing systems , 1979 .

[111]  K. R. Baker,et al.  An Analytic Framework for Evaluating Rolling Schedules , 1979 .

[112]  Arnoldo C. Hax,et al.  Diagnostic Analysis of a Production and Distribution System , 1980 .

[113]  Harvey M. Wagner,et al.  Feature Article - Research Portfolio for Inventory Management and Production Planning Systems , 1980, Oper. Res..

[114]  Edward A. Silver,et al.  Operations Research in Inventory Management: A Review and Critique , 1981, Oper. Res..