On production planning and scheduling in food processing industry: Modelling non-triangular setups andproduct decay

Production planning and scheduling in food processing industry (FPI) requires taking specific characteristics into account. First of all, setups are usually sequence-dependent and may include the so-called non-triangular setup conditions. Secondly, planning problems in FPI must take product decay into consideration. We present an MILP model that handles these characteristics. We study its behaviour and complexity and show that optimal production schedules become significantly different when non-triangular setups and product decay are taken into account. Numerical results are provided for medium size instances, including a comparison with a standard MP-based heuristic. The study focusses on simultaneous lot-sizing and scheduling for food processing industry.Surprisingly little research has been devoted to include issues of perishability.A trend exists in which (hybrid) Big Bucket (BB) models are preferred to Small Bucket (SB) models.Non-triangular setups are hardly considered, particularly not in SB models.Using BB models and its (hybrid) variants can easily disrupt the main principle of optimality in lot-sizing.

[1]  G. D. Eppen,et al.  Solving Multi-Item Capacitated Lot-Sizing Problems Using Variable Redefinition , 1987, Oper. Res..

[2]  Fred Raafat,et al.  Survey of Literature on Continuously Deteriorating Inventory Models , 1991 .

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

[4]  Itir Z. Karaesmen,et al.  Managing Perishable and Aging Inventories: Review and Future Research Directions , 2011 .

[5]  Mei-Shiang Chang,et al.  Production scheduling and vehicle routing with time windows for perishable food products , 2009, Comput. Oper. Res..

[6]  M. Lütke entrup,et al.  Mixed-Integer Linear Programming approaches to shelf-life-integrated planning and scheduling in yoghurt production , 2005 .

[7]  Herbert Meyr,et al.  Simultaneous lotsizing and scheduling by combining local search with dual reoptimization , 2000, Eur. J. Oper. Res..

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

[9]  Bernardo Almada-Lobo,et al.  A decision support system for the operational production planning and scheduling of an integrated pulp and paper mill , 2015, Comput. Chem. Eng..

[10]  Alf Kimms,et al.  Lot sizing and scheduling -- Survey and extensions , 1997 .

[11]  Alistair Clark,et al.  Single-stage formulations for synchronised two-stage lot sizing and scheduling in soft drink production , 2012 .

[12]  Ik Sun Lee,et al.  Coordinated scheduling of production and delivery stages with stage-dependent inventory holding costs , 2010 .

[13]  Diwakar Gupta,et al.  The capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times , 2005, Comput. Oper. Res..

[14]  Martin Grunow,et al.  Realizing block planning concepts in make-and-pack production using MILP modelling and SAP APO © , 2006 .

[15]  Heinrich Kuhn,et al.  Capacitated lot-sizing with extensions: a review , 2008, 4OR.

[16]  G.D.H. Claassen,et al.  Planning and scheduling packaging lines in food industry , 1993 .

[17]  Ruud H. Teunter,et al.  Review of inventory systems with deterioration since 2001 , 2012, Eur. J. Oper. Res..

[18]  C. R. Sox,et al.  The capacitated lot sizing problem with setup carry-over , 1999 .

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

[20]  Wu Zhang,et al.  On practical resource allocation for production planning and scheduling with period overlapping setups , 1994 .

[21]  van Zyl,et al.  Inventory control for perishable commodities , 1963 .

[22]  Markku Kuula,et al.  Multiperiod production planning carrying over set-up time , 2003 .

[23]  Gerard Gaalman,et al.  A basic period approach to the economic lot scheduling problem with shelf life considerations , 2004 .

[24]  D. P. Donk,et al.  Combined make-to-order and make-to-stock in a food production system , 2004 .

[25]  Stefan Minner,et al.  A hybrid general lot-sizing and scheduling formulation for a production process with a two-stage product structure August 24 , 2009 , 2009 .

[26]  Diego Klabjan,et al.  Modeling lotsizing and scheduling problems with sequence dependent setups , 2014, Eur. J. Oper. Res..

[27]  Steven Nahmias,et al.  Optimal Ordering Policies for Perishable Inventory - II , 1975, Oper. Res..

[28]  Laurence A. Wolsey,et al.  MIP modelling of changeovers in production planning and scheduling problems , 1997 .

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

[30]  Awi Federgruen,et al.  Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems , 2007, Oper. Res..

[31]  Reinaldo Morabito,et al.  An optimization approach for the lot sizing and scheduling problem in the brewery industry , 2014, Comput. Ind. Eng..

[32]  Mohan Gopalakrishnan,et al.  A modified framework for modelling set-up carryover in the capacitated lotsizing problem , 2000 .

[33]  Hartmut Stadtler,et al.  The Capacitated Lot-Sizing Problem with Linked Lot Sizes , 2003, Manag. Sci..

[34]  Hermann Jahnke,et al.  The discrete lot-sizing and scheduling problem: Complexity and modification for batch availability , 2000, Eur. J. Oper. Res..

[35]  John M. Wilson,et al.  The capacitated lot sizing problem: a review of models and algorithms , 2003 .

[36]  Hans-Otto Günther,et al.  Multi-objective integrated production and distribution planning of perishable products , 2012 .

[37]  Ross J. W. James,et al.  Single and parallel machine capacitated lotsizing and scheduling: New iterative MIP-based neighborhood search heuristics , 2011, Comput. Oper. Res..

[38]  Laureano F. Escudero,et al.  On a Fix-and-Relax Framework for a Class of Project Scheduling Problems , 2005, Ann. Oper. Res..

[39]  B. Fleischmann.  The discrete lot-sizing and scheduling problem with sequence-dependent setup costs , 1994 .

[40]  Alistair R. Clark,et al.  Capacitated lot-sizing and scheduling with sequence-dependent, period-overlapping and non-triangular setups , 2011, J. Sched..

[41]  P. Amorim,et al.  Managing perishability in production-distribution planning: a discussion and review , 2013 .

[42]  Alf Kimms,et al.  Lot Sizing and Scheduling with Sequence Dependent Setup Costs and Times and Efficient Rescheduling O , 2000 .

[43]  Maria Antónia Carravilla,et al.  A note on "the capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times , 2008, Comput. Oper. Res..

[44]  Chetan Soman,et al.  Capacitated planning and scheduling for combined make-to-order and make-to-stock production in the food industry: An illustrative case study , 2007 .

[45]  Reinaldo Morabito,et al.  Solution approaches for the soft drink integrated production lot sizing and scheduling problem , 2009, Eur. J. Oper. Res..

[46]  Stéphane Dauzère-Pérès,et al.  Solving the discrete lotsizing and scheduling problem with sequence dependent set-up costs and set-up times using the Travelling Salesman Problem with time windows , 1997, Eur. J. Oper. Res..

[47]  Miguel Constantino,et al.  A cutting plane approach to capacitated lot-sizing with start-up costs , 1996, Math. Program..

[48]  Diego Klabjan,et al.  Pricing, relaxing and fixing under lot sizing and scheduling , 2013, Eur. J. Oper. Res..

[49]  Herbert Meyr,et al.  The general lotsizing and scheduling problem , 1997 .

[50]  Eligius M. T. Hendrix,et al.  On Modelling Approaches for Planning and Scheduling in Food Processing Industry , 2014, ICCSA.

[51]  A. Drexl,et al.  Discrete Lotsizing and Scheduling by Batch Sequencing , 1998 .

[52]  D. Klabjan,et al.  Single machine multi-product capacitated lot sizing with sequence-dependent setups , 2007 .

[53]  Laurence A. Wolsey,et al.  Production Planning by Mixed Integer Programming , 2010 .

[54]  Socorro Rangel,et al.  Production lot sizing and scheduling with non-triangular sequence-dependent setup times , 2014 .

[55]  Michael Pinedo,et al.  Planning and Scheduling in Supply Chains: An Overview of Issues in Practice , 2004 .

[56]  B. Fleischmann.  The discrete lot-sizing and scheduling problem , 1990 .

[57]  Bernardo Almada-Lobo,et al.  Lot sizing and scheduling: industrial extensions and research opportunities , 2011 .

[58]  Laurence A. Wolsey,et al.  Production Planning by Mixed Integer Programming (Springer Series in Operations Research and Financial Engineering) , 2006 .

[59]  Franklina Maria Bragion Toledo,et al.  HOPS - Hamming-Oriented Partition Search for production planning in the spinning industry , 2014, Eur. J. Oper. Res..

[60]  David M. Miller,et al.  A framework for modelling setup carryover in the capacitated lot sizing problem , 1995 .

[61]  Beatriz Brito Oliveira,et al.  A relax-and-fix-based algorithm for the vehicle-reservation assignment problem in a car rental company , 2014, Eur. J. Oper. Res..

[62]  Carlos Henggeler Antunes,et al.  Multi-Objective Lot-Sizing and Scheduling Dealing with Perishability Issues , 2011 .