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Formulation of a multi-period multi-echelon location-inventory-routing problem comparing different nature-inspired algorithms

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Abstract

The efficacy of an integrated approach to supply chain decision-making has demonstrated cost-effectiveness in contrast to the traditional sequential decision-making strategy. This has inspired researchers to challenge conventional practices and emphasize the importance of integrated decision-making in the realm of supply chains. This article addresses a multi-period multi-echelon location-inventory-routing problem consisting of a single factory, multiple distribution centres, and multiple retailers where important managerial decisions such as the location of distribution centres, vehicle routing schedule, delivery quantity to the various retailers, and replenishment schedule of the distribution centres are determined in different time periods so as to minimize the total cost of the supply chain which is one of the significant contributions of this research work. To solve the mathematical model, a novel chromosome representation is designed, specifically tailored for genetic algorithm, adding an innovative dimension to this research. To ascertain the results, different selection mechanisms of the genetic algorithm have been employed. The determined results are also compared with particle swarm optimization. The study reveals that genetic algorithm with tournament selection criteria gives the best optimal solution compared to the other algorithms for the proposed mathematical model in all the numerical instances. Further, a sensitivity analysis is also carried out to highlight the impact of various input parameters and provide relevant managerial insights.

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All the associated data are included in the manuscript.

References

  1. Madankumar S and Rajendran C 2019 A mixed integer linear programming model for the vehicle routing problem with simultaneous delivery and pickup by heterogeneous vehicles, and constrained by time windows. Sadhan a 39: 44–39

    Google Scholar 

  2. Nagy G and Salhi S 2007 Location-routing: Issues, models and methods. Eur. J. Oper. Res. 177(2): 649–672

    Article  MathSciNet  MATH  Google Scholar 

  3. Baita F, Ukovich W, Pesenti R and Favaretto D 1998 Dynamic routing-and-inventory problems: a review. Transp. Res. Part A Policy Practice 32(8): 585–598

    Article  MATH  Google Scholar 

  4. Wu T H, Low C and Bai J W 2002 Heuristic solutions to multi-depot location-routing problems. Comput. Oper. Res. 29(10): 1393–1415

    Article  MATH  Google Scholar 

  5. Moin N H and Salhi S 2007 Inventory routing problems: a logistical overview. J. Oper. Res. Soc. 58: 1185–1194

    Article  MATH  Google Scholar 

  6. Shen Z J M, Coullard C and Daskin M S 2003 A joint location-inventory model. Transp. Sci. 37(1): 40–55

    Article  Google Scholar 

  7. Daskin M S, Coullard C R and Shen Z J M 2002 An inventory-location model: Formulation, solution algorithm and computational results. Ann. Oper. Res. 110(1–4): 83–106

    Article  MathSciNet  MATH  Google Scholar 

  8. Diabat A, Richard J P and Codrington C W 2013 A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design. Ann. Oper. Res. 203: 55–80

    Article  MathSciNet  MATH  Google Scholar 

  9. Federgruen A and Zipkin P 1984 A combined vehicle routing and inventory allocation problem. Oper. Res. 32(5): 1019–1037

    Article  MathSciNet  MATH  Google Scholar 

  10. Saragih N I, Bahagia S N and Syabri I 2017 Integration model of location, vehicle route, and inventory control decisions on a three-echelon supply chain system. J. Teknik Industri. https://doi.org/10.9744/jti.19.1.1-10(inIndonesian)

    Article  Google Scholar 

  11. Liu S C and Lee S B 2003 A two-phase heuristic method for the multi-depot location routing problem taking inventory control decisions into consideration. Int. J. Adv. Manuf. Technol. 22: 941–950

    Article  Google Scholar 

  12. Dai Z, Aqlan F, Gao K and Zhou Y 2018 A two-phase method for multi-echelon location-routing problems in supply chains. Exp. Syst. Appl. 115: 618–634

    Article  Google Scholar 

  13. Yu X, Zhou Y and Liu X F 2019 A novel hybrid genetic algorithm for the location routing problem with tight capacity constraints. Appl. Soft Comput. J. 85: 105760

    Article  Google Scholar 

  14. Yaghoubi A and Akrami F 2019 Proposing a new model for location-routing problem of perishable raw material suppliers with using meta-heuristic algorithms. Heliyon 5(12): e03020

    Article  Google Scholar 

  15. Ferreira K M and de Queiroz T A 2022 A simulated annealing based heuristic for a location-routing problem with two-dimensional loading constraints. Appl. Soft Comput. 118: 108443

    Article  Google Scholar 

  16. Diabat A, Dehghani E and Jabbarzadeh A 2017 Incorporating location and inventory decisions into a supply chain design problem with uncertain demands and lead times. J. Manuf. Syst. 43: 139–149

    Article  Google Scholar 

  17. Wang M, Wu J, Kafa N and Klibi W 2020 Carbon emission-compliance green location-inventory problem with demand and carbon price uncertainties. Transp. Res. Part E 142: 102038

    Article  Google Scholar 

  18. Bell W J, Dalberto L M, Fisher M L, Greenfield A J, Jaikumar R, Kedia P, Mack R G and Prutzman P J 1983 Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer. Interfaces 13(6): 4–23

    Article  Google Scholar 

  19. Mirzaei S and Seifi A 2015 Considering lost sale in inventory routing problems for perishable goods. Comput. Ind. Eng. 87: 213–227

    Article  Google Scholar 

  20. Park Y B, Yoo J S and Park H S 2016 A genetic algorithm for the vendor-managed inventory routing problem with lost sales. Expert Syst. Appl. 53: 149–159

    Article  Google Scholar 

  21. Chitsaz M, Divsalar A and Vansteenwegen P 2016 A two-phase algorithm for the cyclic inventory routing problem. Eur. J. Oper. Res. 254(2): 410–426

    Article  MathSciNet  MATH  Google Scholar 

  22. Bertazzi L, Coelho L C, Maio A D and Lagana D 2019 A matheuristic algorithm for the multi-depot inventory routing problem. Transp. Res. Part E 122: 524–544

    Article  Google Scholar 

  23. Golsefidi A H and Jokar M R A 2020 A robust optimization approach for the production-inventory-routing problem with simultaneous pickup and delivery. Comput. Ind. Eng. 143: 106388

    Article  Google Scholar 

  24. Uggen K T, Fodstad M and Nørstebø V S 2013 Using and extending fix-and-relax to solve maritime inventory routing problems. TOP 21(2): 355–377

    Article  MathSciNet  MATH  Google Scholar 

  25. Alinaghian M, Tirkolaee E B, Dezaki Z K, Hejazi S R and Ding W 2021 An augmented Tabu search algorithm for the green inventory-routing problem with time windows. Swarm Evol. Comput. 60: 100802

    Article  Google Scholar 

  26. Coelho L C, Maio A D and Laganà D 2021 A variable MIP neighborhood descent for the multi-attribute inventory routing problem. Transp. Res. Part E 144: 102137

    Article  Google Scholar 

  27. Guemri O, Bekrar A, Beldjilali B and Trentesaux D 2016 GRASP-based heuristic algorithm for the multi-product multi-vehicle inventory routing problem. 4OR-Q. J. Oper. Res. 14: 377–404

    Article  MATH  Google Scholar 

  28. Ji Y, Du J, Han X, Wu X, Huang R, Wang S and Liu Z 2020 A mixed integer robust programming model for two-echelon inventory routing problem of perishable products. Physica A 548: 124481

    Article  Google Scholar 

  29. Le T, Diabat A, Richard J-P and Yih Y 2013 A column generation-based heuristic algorithm for an inventory routing problem with perishable goods. Optim. Lett. 7: 1481–1502

    Article  MathSciNet  MATH  Google Scholar 

  30. Sindhuchao S, Romeijn H E, Akcali E and Boondiskulchok R 2005 An integrated inventory routing system for multi-item joint replenishment with limited vehicle capacity. J. Glob. Optim. 32: 93–118

    Article  MathSciNet  MATH  Google Scholar 

  31. Vadseth S T, Andersson H and Stålhane M 2021 An iterative matheuristic for the inventory routing problem. Comput. Oper. Res. 131: 105262

    Article  MathSciNet  MATH  Google Scholar 

  32. Guerrero W J, Prodhon C, Velasco N and Amaya C A 2013 Hybrid heuristic for the inventory location-routing problem with deterministic demand. Int. J. Prod. Econ. 146(1): 359–370

    Article  Google Scholar 

  33. Zhang Y, Qi M, Miao L and Liu E 2014 Hybrid metaheuristic solutions to inventory location routing problem. Transp. Res. Part E 70: 305–323

    Article  Google Scholar 

  34. Ghorbani A and Akbari Jokar M R 2016 A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem. Comput. Ind. Eng. 101: 116–127

    Article  Google Scholar 

  35. Hiassat A, Diabat A and Rahwan I 2017 A genetic algorithm approach for location-inventory-routing problem with perishable products. J. Manuf. Syst. 42: 93–103

    Article  Google Scholar 

  36. Wu W, Zhou W, Lin Y, Xie Y and Jin W 2021 A hybrid metaheuristic algorithm for location inventory routing problem with time windows and fuel consumption. Expert Syst. Appl. 166: 114034

    Article  Google Scholar 

  37. Ahmadi-Javed A and Seddighi A H 2012 A location-routing-inventory model for designing multisource distribution networks. Eng. Optim. 44(6): 637–656

    Article  MathSciNet  Google Scholar 

  38. Karakostas P, Sifaleras A and Georgiadis M C 2022 Variable neighborhood search-based solution methods for the pollution location-inventory-routing problem. Optim. Lett. 16(1): 211–235

    Article  MathSciNet  MATH  Google Scholar 

  39. Li Y, Guo H, Wang L and Fu J 2013 A hybrid genetic-simulated annealing algorithm for the location-inventory-routing problem considering returns under e-supply chain environment. Sci. World J. 125893

  40. Yavari M, Enjavi H and Geraeli M 2020 Demand management to cope with routes disruptions in location-inventory-routing problem for perishable products. Res. Transp. Bus. Manag. 37: 100552

    Google Scholar 

  41. Tharwat A and Schenck W 2021 A conceptual and practical comparison of PSO-style optimization algorithms. Expert Syst. Appl. 167: 114430

    Article  Google Scholar 

  42. Duggirala A, Jana R K, Shesu R V and Bhattacharjee P 2018 Design optimization of deep groove ball bearings using crowding distance particle swarm optimization. Sādhanā 43: 1–8

    Article  MathSciNet  MATH  Google Scholar 

  43. Dye C-Y 2012 A finite horizon deteriorating inventory model with two-phase pricing and time-varying demand and cost under trade credit financing using particle swarm optimization. Swarm Evol. Comput. 5: 37–53

    Article  Google Scholar 

  44. Kunhare N, Tiwari R and Dhar J 2020 Particle swarm optimization and feature selection for intrusion detection system. Sādhanā 45: 1–14

    Article  Google Scholar 

  45. Pitchai K M 2022 Maximizing energy efficiency using Dinklebach’s and particle swarm optimization methods for energy harvesting wireless sensor networks. Sādhanā 47(2): 60

    Article  Google Scholar 

  46. Pratap P, Bhatia R S and Kumar B 2016 Design and simulation of equilateral triangular microstrip antenna using particle swarm optimization (PSO) and advanced particle swarm optimization (APSO). Sādhanā 41: 721–725

    Article  MATH  Google Scholar 

  47. Rau H, Budiman S D and Widyadana G A 2018 Optimization of the multi-objective green cyclical inventory routing problem using discrete multi-swarm PSO method. Transp. Res. Part E 120: 51–75

    Article  Google Scholar 

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Acknowledgements

The authors are thankful to the anonymous reviewers and the editors for their constructive comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, 788010, India

    Mamta Kumari & Pijus Kanti De

  2. Statistical Quality Control and Operation Research Unit, Indian Statistical Institute, Kolkata, West Bengal, 700108, India

    Ashis Kumar Chakraborty

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  1. Mamta Kumari
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  2. Pijus Kanti De
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  3. Ashis Kumar Chakraborty
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Correspondence to Mamta Kumari.

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Kumari, M., De, P.K. & Chakraborty, A.K. Formulation of a multi-period multi-echelon location-inventory-routing problem comparing different nature-inspired algorithms. Sādhanā 48, 280 (2023). https://doi.org/10.1007/s12046-023-02288-9

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