Capacity acquisition for the single-item lot sizing problem under energy constraints

We study a single-item lot sizing problem integrated with some energy constraints, called energy-LSP in the rest of the paper. We consider a production system composed of identical and capacitated machines in parallel. One has to decide how many machines to start and how much to produce to serve the demand and/or to replenish the inventory. In addition to the production capacity limit in each period, induced by the machines on, we have a limit on the energy that can be consumed by the start-ups of the machines and the production of units. We first provide a mixed integer programming formulation for the problem in the general case. We then develop efficient polynomial time algorithms running in O(Tlog T), with T the length of the planning horizon, for several subproblems: (i) energy-LSP where all energy parameters are set to 0, (ii) energy-LSP where only the machine start-ups consume energy, (iii) energy-LSP where only the production of units consumes energy. We show that, in all these special cases, energy-LSP can be seen as an extension of the integrated capacity acquisition and lot sizing problem. This allows us, as by-product of our approach, to significantly improve the existing result proposed for the capacity acquisition problem without energy constraint nor subcontracting.

[1]  Frieder Borggrefe,et al.  The potential of demand-side management in energy-intensive industries for electricity markets in Germany , 2011 .

[2]  Ignacio E. Grossmann,et al.  Optimal production planning under time-sensitive electricity prices for continuous power-intensive processes , 2012, Comput. Chem. Eng..

[3]  Iiro Harjunkoski,et al.  Resource–Task Network Formulations for Industrial Demand Side Management of a Steel Plant , 2013 .

[4]  Markus Heck,et al.  Lot-Size Planning with Non-Linear Cost Functions Supporting Environmental Sustainability , 2010, Int. J. Green Comput..

[5]  Monique Guignard-Spielberg,et al.  Dynamic Production Scheduling for a Process Industry , 1994, Oper. Res..

[6]  Helene Lidestam,et al.  Including energy in supply chain planning at a pulp company , 2013 .

[7]  Tadeusz Sawik,et al.  Coordinated supply chain scheduling , 2009 .

[8]  Raf Jans,et al.  An industrial extension of the discrete lot-sizing and scheduling problem , 2004 .

[9]  Lixin Tang,et al.  A stochastic production planning problem with nonlinear cost , 2012, Comput. Oper. Res..

[10]  Hongyan Li,et al.  Capacitated dynamic lot sizing with capacity acquisition , 2011 .

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

[12]  Pierluigi Siano,et al.  A survey of industrial applications of Demand Response , 2016 .

[13]  Linet Özdamar,et al.  A hierarchical planning system for energy intensive production environments , 1999 .

[14]  A. Yalaoui,et al.  Lot-sizing in a multi-stage flow line production system with energy consideration , 2017, Int. J. Prod. Res..

[15]  Axel Tuma,et al.  Energy-efficient scheduling in manufacturing companies: A review and research framework , 2016, Eur. J. Oper. Res..

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

[17]  Konstantinos Salonitis,et al.  Forty Sixth CIRP Conference on Manufacturing Systems 2013 Energy efficient manufacturing from machine tools to manufacturing systems , 2013 .

[18]  Pierre Lopez,et al.  The energy scheduling problem: Industrial case-study and constraint propagation techniques , 2013 .

[19]  Rakesh Nagi,et al.  Scheduling injection molding operations with multiple resource constraints and sequence dependent setup times and costs , 2005, Comput. Oper. Res..

[20]  Alper Atamtürk,et al.  Capacity Acquisition, Subcontracting, and Lot Sizing , 2001, Manag. Sci..

[21]  Waldemar Kaczmarczyk.  Proportional lot-sizing and scheduling problem with identical parallel machines , 2011 .

[22]  Fabrizio Marinelli,et al.  Capacitated lot sizing and scheduling with parallel machines and shared buffers: A case study in a packaging company , 2007, Ann. Oper. Res..

[23]  Gunther Reinhart,et al.  An Approach for Energy-oriented Production Control Using Energy Flexibility , 2015 .

[24]  Albert Corominas,et al.  A review of mathematical programming models for strategic capacity planning in manufacturing , 2014 .

[25]  Gang Rong,et al.  Production planning optimization of an ethylene plant considering process operation and energy utilization , 2016, Comput. Chem. Eng..

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

[27]  Stéphane Dauzère-Pérès,et al.  Single item lot sizing problems , 2006, Eur. J. Oper. Res..

[28]  Bernardo Almada-Lobo,et al.  Integrated pulp and paper mill planning and scheduling , 2012, Comput. Ind. Eng..

[29]  Leon S. Lasdon,et al.  An Efficient Algorithm for Multi-Item Scheduling , 1971, Oper. Res..

[30]  Konstantin Biel,et al.  Systematic literature review of decision support models for energy-efficient production planning , 2016, Comput. Ind. Eng..

[31]  Massimo Paolucci,et al.  Energy-aware scheduling for improving manufacturing process sustainability: A mathematical model for flexible flow shops , 2012 .

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

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

[34]  Anand Sivasubramaniam,et al.  Managing server energy and operational costs in hosting centers , 2005, SIGMETRICS '05.

[35]  Diego Klabjan,et al.  Multiple machine continuous setup lotsizing with sequence-dependent setups , 2010, Comput. Optim. Appl..

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

[37]  Isi Mitrani.  Managing performance and power consumption in a server farm , 2013, Ann. Oper. Res..