Heuristical Solution for Scheduling Single Stage Parallel Machines Production of Calcium Silicate Masonry Units with Sequence-Dependent Changeover Times to Improve Energy Efficiency

Determination of optimal production schedules is a complex combinatorial task and may be dependent on various objectives. Hence, many mathematical problem formulations and solving strategies have already been proposed each considering individually constrained applications in order to minimize non-value-adding times or other cost driving factors. Nevertheless, obtaining optimal solutions is still related to extensive computational resources and time efforts.As a result, heuristical approaches or combinations of heuristics and exact algorithms are of major importance when it comes to automatically creating optimal production schedules. Considering the manufacturing of calcium silicate masonry units (CS), this paper describes an advancement for the General Lot-Sizing Problem (GLSP) in order to allow sequence-dependent changeovers as well as multiple different machines and backlogging (GLSPPLB). For solving the GLSPPLB, a heuristical algorithm consisting of neighborhood search and threshold accepting techniques was implemented. To validate the results of the heuristic and compare required computational resources to accurate mathematical solvers, a test set of a realistic scenario has been used.The developed heuristic is able to create nearly optimal production schedules and thereby minimizing the trade off between energy demand regarding idle times of production machinery and stocks. It is transferable to every discrete single stage production with similar constraints and can be used as an input for further simulations to improve energy consumption.

[1]  Herbert Meyr.  Simultane Losgrößen- und Reihenfolgeplanung für kontinuierliche Produk-tionslinien – Modelle und Methoden im Rahmen des Supply Chain Management , 1999 .

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

[3]  Daniel Quadt,et al.  Capacitated lot‐sizing and scheduling with parallel machines, back‐orders, and setup carry‐over , 2009 .

[4]  John J. DeMatteis.  An Economic Lot-Sizing Technique I: The Part-Period Algorithm , 1968, IBM Syst. J..

[5]  Kurt Andler.  Rationalisierung der Fabrikation und optimale Losgröße , 1929 .

[6]  C. R. Glassey,et al.  Minimum Change-Over Scheduling of Several Products on One Machine , 1968, Oper. Res..

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

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

[9]  Ford W. Harris,et al.  How Many Parts to Make at Once , 1990, Oper. Res..

[10]  A. Clark,et al.  Rolling-horizon lot-sizing when set-up times are sequence-dependent , 2000 .

[11]  Jörg Franke,et al.  Simulation-Based Optimization of the Energy Consumption in the Hardening Process for Calcium Silicate Masonry Units , 2015 .

[12]  Jörg Franke,et al.  Valid Methodology for Using Discrete Event Simulation to Improve the Resource Consumption for the Manufacturing of Masonry Units , 2016 .

[13]  Melvin E. Salveson,et al.  ON A QUANTITATIVE METHOD IN PRODUCTION PLANNING AND SCHEDULING , 1952 .

[14]  C. C. Holt,et al.  A Linear Decision Rule for Production and Employment Scheduling , 1955 .

[15]  Herbert Meyr,et al.  Simultaneous lotsizing and scheduling on parallel machines , 2002, Eur. J. Oper. Res..

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

[17]  A. Drexl,et al.  Proportional lotsizing and scheduling , 1995 .

[18]  J. DeMatteisJ..  An economic lot-sizing technique , 1968 .

[19]  M. W. B. Townsend.  Decision Rules for Inventory Management , 1968 .

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

[21]  Laureano F. Escudero,et al.  On Solving a Large-Scale Resource Allocation Problem in Production Planning , 1993 .

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

[23]  Uday S. Karmarkar,et al.  The Deterministic Dynamic Product Cycling Problem , 1985, Oper. Res..

[24]  Herbert Meyr.  Simultane Losgrößen- und Reihenfolgeplanung für kontinuierliche Produktionslinien , 1999 .