Skip to main content

Advertisement

SpringerLink
Log in

Two metaheuristics to solve a multi-item multiperiod inventory control problem under storage constraint and discounts

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

In this paper, a multi-item multiperiod inventory control problem with all-unit and/or incremental quantity discount policies under limited storage capacity is presented. The independent random demand rates of the items in the periods are known and the items are supplied in distinct batch sizes. The cost consists of ordering, holding, and purchasing. The objective is to find the optimal order quantities of all items in different periods such that the total inventory cost is minimized and the constraint is satisfied. A mixed binary integer programming model is first developed to model the problem. Then, a parameter-tuned genetic algorithm (GA) is employed to solve it. Since there is no benchmark available in the literature, a memetic algorithm (MA) is utilized as well to validate and verify the results obtained. The model implementation is next presented using some numerical examples and finally the performances of the proposed GA and MA are compared using two statistical tests and a simple additive weighting method. The results show that GA has better performance than MA in terms of average objective function value and average run time using the two comparison procedures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Roach B (2005) Origin of the economic order quantity formula; transcription or transformation? Manag Decis 43:1262–1268

    Article  Google Scholar 

  2. Lee AHI, Kang H-Y (2008) A mixed 0-1 integer programming for inventory model: a case study of TFT-LCD manufacturing company in Taiwan. Kybernetes 37:66–82

    Article  MathSciNet  MATH  Google Scholar 

  3. Das K, Roy TK, Maiti M (2000) Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: a geometric programming approach. Prod Plan Control 11:781–788

    Article  Google Scholar 

  4. Silver EA, Moon I (2001) Multi-item economic order quantity model with an initial stock of convertible units. Eng Econ 46:129–138

    Article  Google Scholar 

  5. Panda S, Banerjee K, Basu M (2005) Determination of EOQ of multi-item inventory problems through nonlinear goal programming with penalty function. Asia Pac J Oper Res 22:539–553

    Article  MATH  Google Scholar 

  6. Kim JU, Kim YD (2000) A Lagrangian relaxation approach to multi-period inventory/distribution planning. J Oper Res Soc 51:264–370

    Google Scholar 

  7. Luciano E, Peccati L, Cifarelli DM (2002) VaR as a risk measure for multiperiod static inventory models. Int J Prod Econ 81:375–384

    Google Scholar 

  8. Matsuyama K (2006) The multi-period newsboy problem. Eur J Oper Res 171:170–88

    Article  MathSciNet  MATH  Google Scholar 

  9. Maiti AK, Maiti M (2008) Discounted multi-item inventory model via genetic algorithm with roulette wheel selection, arithmetic crossover and uniform mutation in constraints bounded domains. Int J Comput Math 85:1341–1353

    Article  MathSciNet  MATH  Google Scholar 

  10. Sana SS, Chaudhuri KS (2008) A deterministic EOQ model with delays in payments and price-discount offers. Eur J Oper Res 184:509–533

    Article  MathSciNet  MATH  Google Scholar 

  11. Dellaert N, Jeunet J, Jonard N (2000) A genetic algorithm to solve the general multi-level lot-sizing problem with time-varying costs. Int J Prod Econ 68:241–257

    Article  Google Scholar 

  12. Rezaei J, Davoodi M (2008) A deterministic, multi-item inventory model with supplier selection and imperfect quality. Appl Math Model 32:2106–2116

    Article  MathSciNet  MATH  Google Scholar 

  13. Guner Goren H, Tunali S, Jans R (2010) A review of applications of genetic algorithms in lot sizing. J Intell Manuf 21:575–590

    Article  Google Scholar 

  14. Rezaei J, Davoodi M (2011) Multi-objective models for lot-sizing with supplier selection. Int J Prod Econ 130:77–86

    Article  Google Scholar 

  15. Schemeleva K, Delorme X, Dolgui A, Grimaud F (2012) Multi-product sequencing and lot-sizing under uncertainties: a memetic algorithm. Eng Appl Artif Intel 25:1598–1610

    Article  Google Scholar 

  16. Hillier FS, Lieberman GJ (2001) Introduction to operations research. McGraw-Hill, New York

    Google Scholar 

  17. Fugenschuh A, Martin A (2005) Computational integer programming and cutting planes. Discrete Opt 25:69–121

    Article  Google Scholar 

  18. Ziaee M, Sadjadi SJ (2007) Mixed binary integer programming formulations for the flow shop scheduling problems. A case study: ISD projects scheduling. Appl Math Comput 185:218–228

    Article  MathSciNet  MATH  Google Scholar 

  19. Pan JC-H, Chen J-S (2005) Mixed binary integer programming formulations for the reentrant job shop scheduling problem. Comput Oper Res 32:1197–1212

    Article  MathSciNet  MATH  Google Scholar 

  20. Kozanidis G, Melachrinoudis E (2004) A branch & bound algorithm for the 0-1 mixed integer knapsack problem with linear multiple choice constraints. Comput Oper Res 31:695–711

    Article  MathSciNet  MATH  Google Scholar 

  21. Michalewicz Z, Janikow CZ (1991) Genetic algorithms for numerical optimization. Stat Comput 1:75–91

    Article  Google Scholar 

  22. Guvenir HA (1995) In: Pearson DW, Steele NC, Albrecht RF (eds) A genetic algorithm for multicriteria inventory classification in artificial neural nets and genetic algorithms. Proceedings of the International Conference, Ales, France. Springer, Wien

    Google Scholar 

  23. Davis L (ed) (1991) Handbook of genetic algorithms. Reinhold, NewYork

    Google Scholar 

  24. Pal SK, De S, Ghosh A (1997) Designing Hopfield type networks using genetic algorithms and its caparisons with simulated annealing. Int J Patterns Recog Artif Intell 11:447–461

    Article  Google Scholar 

  25. Mondal S, Maiti M (2002) Multi-item fuzzy EOQ models using genetic algorithm. Comput Ind Eng 44:105–117

    Article  Google Scholar 

  26. Maiti MK, Maiti M (2005) Production policy for damageable items with variable cost function in an imperfect production process via genetic algorithm. Math Comput Model 42:977–990

    Article  MathSciNet  MATH  Google Scholar 

  27. Maiti MK, Maiti M (2006) Fuzzy inventory model with two-warehouse under possibility constraints. Fuzzy Set Syst 157:52–73

    Article  MathSciNet  MATH  Google Scholar 

  28. Maiti MK, Maiti M (2013) Two-storage inventory model with lot size dependent fuzzy lead-time under possibility constraints via genetic algorithm. Eur J Oper Res 207(179):352–371

    MathSciNet  Google Scholar 

  29. Pasandideh SHR, Niaki STA, Mirhosseyni SS (2010) A parameter-tuned genetic algorithm to solve multi-product economic production quantity model with defective items, rework, and constrained space. Int J Adv Manuf Technol 49:827–837

    Article  Google Scholar 

  30. Pasandideh SHR, Niaki STA, Aryan Yeganeh J (2010) A parameter-tuned genetic algorithm for multi-product economic production quantity model with space constraint, discrete delivery orders and shortages. Adv Eng Softw 41:306–314

    Article  MATH  Google Scholar 

  31. Pasandideh SHR, Niaki STA, Roozbeh-Nia A (2011) A genetic algorithm for vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Syst Appl 38:2708–2716

    Article  Google Scholar 

  32. Pasandideh SHR, Niaki STA (2008) A genetic algorithm approach to optimize a multi-products EPQ model with discrete delivery orders and constrained space. Appl Math Comput 195:506–514

    Article  MathSciNet  MATH  Google Scholar 

  33. Taleizadeh AA, Niaki STA, Aryanezhad MB, Fallah Tafti A (2010) A genetic algorithm to optimize multi-product multi-constraint inventory control system with stochastic replenishment and discount. Int J Adv Manuf Technol 51:311–323

    Article  Google Scholar 

  34. Taleizadeh AA, Niaki STA, Hoseini V (2009) Optimizing the multi-product, multi-constraint, bi-objective newsboy problem with discount by a hybrid method of goal programming and genetic algorithm. Eng Optim 41:437–457

    Article  MathSciNet  Google Scholar 

  35. Taleizadeh AA, Niaki STA, Aryanezhad MB (2009) A hybrid method of Pareto, TOPSIS, and genetic algorithm to optimize multi-product, multi-constraint inventory systems with random fuzzy replenishments. Math Comput Model 49:1044–1057

    Article  MathSciNet  MATH  Google Scholar 

  36. Taleizadeh AA, Niaki STA, Aryanezhad MB (2009) Multi-product multi-constraint inventory control systems with stochastic replenishment and discount under fuzzy purchasing price and holding costs. Am J Appl Sci 6:1–12

    Google Scholar 

  37. Taleizadeh AA, Niaki STA, Hosseini SV (2008) The multi-product multi-constraint newsboy problem with incremental discount and batch order. Asian J Appl Sci 1:110–122

    Article  Google Scholar 

  38. Taleizadeh AA, Aryanezhad MB, Niaki STA (2008) Optimizing multi-product multi-constraint inventory control systems with stochastic replenishments. J Appl Sci 8:1228–1234

    Article  Google Scholar 

  39. Moscato P (1989) On evolution, search, optimization, genetic algorithms and martial arts: towards memetic algorithms. Technical Report, Caltech Concurrent Computation Program, Report 826. California Institute of Technology, Pasadena

    Google Scholar 

  40. Reeves C (1996) Hybrid genetic algorithms for bin-packing and related problems. Ann Oper Res 63:371–396

    Article  MATH  Google Scholar 

  41. Burke E, Newall J, Weare R (1996) A memetic algorithm for university exam timetabling. In: Burke E, Ross P (eds) The practice and theory of automated timetabling. Lecture notes in Computer Science 1153. Springer, New York, pp 241–250

    Google Scholar 

  42. Fleurent C, Ferland J (1997) Genetic and hybrid algorithms for graph coloring. Ann Oper Res 63:437–461

    Article  Google Scholar 

  43. He L, Mort N (2000) Hybrid genetic algorithms for telecommunications network back-up routing. BT Technol J 18:42–50

    Article  Google Scholar 

  44. Cheng R, Gen M (1997) Parallel machine scheduling problems using memetic algorithms. Comput Ind Eng 33:761–764

    Article  Google Scholar 

  45. Hart, WE (1994) Adaptive global optimization with local search. Ph.D. Thesis, University of California, San Diego

  46. Morris GM, Goodsell DS, Halliday RS, Huey R, Hart WE, Belew RK, Olson AJ (1998) Automated docking using a Lamarkian genetic algorithm and an empirical binding free energy function. J Comp Chem 14:1639–1662

    Article  Google Scholar 

  47. Niesse J, Mayne H (1996) Global geometry optimization of atomic clusters using a modified genetic algorithm in space-fixed coordinates. J Chem Phys 105:4700–4706

    Article  Google Scholar 

  48. Wang H, Wang D, Yang S (2008) A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems. Soft Comput 13:763–780

    Article  Google Scholar 

  49. Caponio A, Cascella G, Neri F, Salvatore N, Sumner M (2007) A fast adaptive memetic algorithm for on-line and off-line control design of PMSM drives. IEEE Trans Syst Man Cybern B 37:28–41

    Article  Google Scholar 

  50. Ishibuchi H, Kaige S (2004) Implementation of simple multiobjective memetic algorithms and its application to knapsack problems. Int J Hybrid Intell Syst 1:22–35

    Google Scholar 

  51. Jaszkiewicz A (2002) Genetic local search for multi-objective combinatorial optimization. Eur J Oper Res 137:50–71

    Article  MathSciNet  MATH  Google Scholar 

  52. Liu D, Tan KC, Goh CK, Ho WK (2007) A multiobjective memetic algorithm based on particle swarm optimization. IEEE Trans Syst Man Cybern B 37:42–50

    Article  Google Scholar 

  53. Moscato P (1999) Memetic algorithms: a short introduction. In: Corne D, Glover F, Dorigo M (eds) New ideas in optimization. McGraw-Hill, Maidenhead

    Google Scholar 

  54. Franca PM, Mendes AS, Moscato P (2001) A memetic algorithm for the total tardiness single machine scheduling problem. Eur J Oper Res 132:224–242

    Article  MathSciNet  MATH  Google Scholar 

  55. Mendes AS, Muller FM, Franca PM, Moscato P (2002) Comparing meta-heuristic approaches for parallel machine scheduling problems. Prod Plan Control 13:143–154

    Article  Google Scholar 

  56. Moscato P, Cotta C (2003) A gentle introduction to memetic algorithms. In: Glover F, Kochenberger G (eds) Handbook of metaheuristics. Kluwer, Boston

    Google Scholar 

  57. Ng EYK, Ng EWK (2006) Parametric study of the biopotential equation for breast tumors identification using ANOVA and Taguchi method. Med Biol Eng Comput 44:131–139

    Article  Google Scholar 

  58. Phadke MS (1989) Quality engineering using robust design. Prentice-Hall, Upper Saddle River

    Google Scholar 

  59. Ross RJ (1989) Taguchi techniques for quality engineering. McGraw-Hill, New York

    Google Scholar 

  60. Holland JH (1975) Adaptive in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  61. Goldberg D.E. (1989) Genetic algorithms in search, optimization and machine learning. 1st ed. Boston: Addison-Wesley

  62. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Kharazmi University, Tehran, Iran

    Seyed Hamid Reza Pasandideh

  2. Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

    Seyed Taghi Akhavan Niaki

  3. Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia

    Seyed Mohsen Mousavi

Authors
  1. Seyed Hamid Reza Pasandideh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seyed Taghi Akhavan Niaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seyed Mohsen Mousavi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seyed Taghi Akhavan Niaki.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pasandideh, S.H.R., Niaki, S.T.A. & Mousavi, S.M. Two metaheuristics to solve a multi-item multiperiod inventory control problem under storage constraint and discounts. Int J Adv Manuf Technol 69, 1671–1684 (2013). https://doi.org/10.1007/s00170-013-5130-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-013-5130-7

Keywords

Search

Navigation