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OBRUN algorithm for the capacity-constrained joint replenishment and delivery problem with trade credits

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Abstract

This study investigates the joint replenishment and delivery problem taking trade credits the delay in payment permitted by suppliers and capacity-constrained into consideration (CJRD-TC). The CJRD-TC aims to minimize the total system costs by finding a reasonable replenishment and delivery schedule policy. In this paper, an opposite-based RUNge Kutta optimization algorithm (OBRUN) is proposed to compare with other intelligent algorithms, including the differential evolution (DE), RUNge Kutta optimization algorithm (RUN), sine cosine algorithm (SCA), and adaptive differential evolution with optimal external archive (JADE). The proposed algorithm is tested on 14 optimization functions. The values of average, standard deviation, and the best are the lowest for 12 functions, which demonstrates OBRUN is superior to other algorithms. We also provide graphs of search history, 2D views of functions, trajectory curve, average fitness history, and convergence curve of OBRUN, the balance between exploration and exploitation over the course of iterations can be observed. The convergence curves of five algorithms are also depicted, which show OBRUN has a fast convergence rate and accuracy than other algorithms. We conduct numerical experiments, parameter tuning, and sensitivity analysis for each of the small-scale, medium-scale, and large-scale number of items. The OBRUN can always find better solutions with the lowest mean values and the best-found total cost results than other algorithms. Indicators of the average optimality gap and the optimality gap dominate by the value of zero. These computational results have demonstrated OBRUN is a suitable and effective candidate for managers to solve the practical CJRD-TC problems.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Goyal SK (1974) Determination of optimum packaging frequency of items jointly replenished. Manage Sci 21(4):436–443

    Article  Google Scholar 

  2. Liu R, Zhou ZH, Qin QD, Fan B (2022) Centralized drug procurement operation scheduling with a capacitated joint replenishment and delivery strategy: Evidence from China. Comput Ind Eng 172:108584

  3. Arkin E, Joneja D, Roundy R (1989) Computational complexity of uncapacitated multi-echelon production planning problems. Oper Res Lett 8(2):61–66

    Article  MathSciNet  Google Scholar 

  4. Cohen-Hillel T, Yedidsion L (2018) The periodic joint replenishment problem is strongly NP-hard. Math Oper Res 43(4):1269–1289

    Article  MathSciNet  Google Scholar 

  5. Cha BC, Moon IK, Park JH (2008) The joint replenishment and delivery scheduling of the one-warehouse, n-retailer system. Transp Res E: Log Transp Rev 44(5):720–730

    Article  Google Scholar 

  6. Chen Y, Yang L, Jiang Y, Wahab MIM, Yang J (2019) Joint replenishment decision considering shortages, partial demand substitution, and defective items. Comput Ind Eng 127:420–435

    Article  Google Scholar 

  7. Cui L, Wang L, Deng J, Zhang J (2015) Intelligent algorithms for a new joint replenishment and synthetical delivery problem in a warehouse centralized supply chain. Knowl-Based Syst 90:185–198

    Article  Google Scholar 

  8. Qu H, Wang L, Zeng YR (2013) Modeling and optimization for the joint replenishment and delivery problem with heterogeneous items. Knowl-Based Syst 54:207–215

    Article  Google Scholar 

  9. Wang L, Liu R, Liu S (2016) An effective and efficient fruit fly optimization algorithm with level probability policy and its applications. Knowl-Based Syst 97:158–174

    Article  Google Scholar 

  10. Kang HY, Lee AHI, Wu CW, Lee CH (2017) An efficient method for dynamic-demand joint replenishment problem with multiple suppliers and multiple vehicles. Int J Prod Res 55(4):1065–1084

    Article  Google Scholar 

  11. Wang L, Peng L, Wang SR, Liu S (2020) Advanced backtracking search optimization algorithm for a new joint replenishment problem under trade credit with grouping constraint. Appl Soft Comput 86:105953

    Article  Google Scholar 

  12. Cui L, Deng J, Zhang Y, Tang G, Xu M (2020) Hybrid differential artificial bee colony algorithm for multi-item replenishment-distribution problem with stochastic lead-time and demands. J Clean Prod 254:119873

    Article  Google Scholar 

  13. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  14. Yılmaz BG, Yılmaz ÖF (2022) Lot streaming in hybrid flowshop scheduling problem by considering equal and consistent sublots under machine capability and limited waiting time constraint. Comput Ind Eng 173:108745

  15. Ahmadianfar I, Heidari AA, Gandomi AH, Chu XF, Chen HL (2021) RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method. Expert Syst Applic 181:115079

  16. Abd El-Sattar H, Kamel S, Hassan MH, Jurado F (2022) Optimal sizing of an off-grid hybrid photovoltaic/biomass gasifier/battery system using a quantum model of Runge Kutta algorithm. Energy Convers Manag 258:115539

    Article  Google Scholar 

  17. Manjula DR, Premkumar M, Jangir P, Mohamed AE, Rajvikram ME, Nisar KS (2022) IRKO: An improved runge-kutta optimization algorithm for global optimization problems. Comput Mater Continua 70(3):4803–4827

    Article  Google Scholar 

  18. Chen HL, Ahmadianfar I, Liang GX, Bakhsizadeh H, Azad B, Chu XF (2022) A successful candidate strategy with Runge-Kutta optimization for multi-hydropower reservoir optimization. Expert Syst Applic 209:118383

  19. Mahdavi S, Rahnamayan S, Deb K (2018) Opposition based learning: A literature review. Swarm Evol Comput 39:1–23

    Article  Google Scholar 

  20. Abd Elaziz M, Oliva D, Xiong S (2017) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500

    Article  Google Scholar 

  21. Dhargupta S, Ghosh M, Mirjalili S, Sarkar R (2020) Selective opposition based grey wolf optimization. Expert Syst Appl 151:113389

    Article  Google Scholar 

  22. Abed-alguni BH, Alawad NA, Al-Betar MA, Paul D (2023) Opposition-based sine cosine optimizer utilizing refraction learning and variable neighborhood search for feature selection. Appl Intell 53:13224–13260

    Article  Google Scholar 

  23. Oliva D, Esquivel-Torres S, Hinojosa S, Pérez-Cisneros M, Osuna-Enciso V, Ortega-Sánchez N, Dhiman G, Heidari AA (2021) Opposition-based moth swarm algorithm. Expert Syst Appl 184:115481

    Article  Google Scholar 

  24. Musikawan P, Kongsorot Y, Muneesawang P, So-In C (2022) An enhanced obstacle-aware deployment scheme with an opposition-based competitive swarm optimizer for mobile WSNs. Expert Syst Appl 189:116035

    Article  Google Scholar 

  25. Khouja M, Goyal S (2008) A review of the joint replenishment problem literature: 1989–2005. Eur J Oper Res 186(1):1–16

  26. Ai XY, Zhang JL, Wang L (2017) Optimal joint replenishment policy for multiple non-instantaneous deteriorating items. Int J Prod Res 55(16):4625–4642

    Article  Google Scholar 

  27. Liu R, Zeng YR, Qu H, Wang L (2018) Optimizing the new coordinated replenishment and delivery model considering quantity discount and resource constraints. Comput Ind Eng 116:82–96

    Article  Google Scholar 

  28. Carvajal J, Castano F, Sarache W, Costa Y (2020) Heuristic approaches for a two echelon constrained joint replenishment and delivery problem. Int J Prod Econ 220:107420

    Article  Google Scholar 

  29. Khoukhi S, Bojji C, Bensouda Y (2021) Joint optimisation of replenishment policies on a downstream multi-echelon, multi-product pharmaceutical supply chain with lost sales, stochastic demands and storage capacity constraints: Centralised vs. decentralised structure. Int J Logist Syst Manag 39(1):1–21

  30. Liu R, Wang SR, Pi YY, Qin QD (2021) An effective heuristic with evolutionary algorithm for the coordinated capacitated dynamic lot-size and delivery problem. Comput Ind Eng 153:107051

    Article  Google Scholar 

  31. Wang S, Wang L (2022) Efficient methods for stochastic joint replenishment and delivery problem. Int Trans Oper Res 29(4):2288–2315

    Article  MathSciNet  Google Scholar 

  32. Goyal SK (1985) Economic order quantity under conditions of permissible delay in payments. J Oper Res Soc 36(4):335–338

  33. Abad PL, Jaggi CK (2003) A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive. Int J Prod Econ 83:115–122

  34. Mohan S, Gopalakrishnan M (2007) Analytical framework for the multi-item, economic order quantity model with permissible delay in payments and a budget constraint. A note. Prod Plann Control 18(4):361–363

    Article  Google Scholar 

  35. Chang CT, Teng JT, Goyal SK (2008) Inventory lot-size models under trade credits:a review. Asia-Pac J Oper Res 25:89–112

    Article  MathSciNet  Google Scholar 

  36. Tsao YC, Teng WG (2013) Heuristics for the joint multi-item replenishment problem under trade credits. IMA J Manag Math 24(1):63–77

    MathSciNet  Google Scholar 

  37. Zeng YR, Peng L, Zhang J, Wang L (2016) An effective hybrid differential evolution algorithm incorporating simulated annealing for joint replenishment and delivery problem with trade credit. Int J Comput Intell Syst 9(6):1001–1015

    Article  Google Scholar 

  38. Peng L, Wang L, Wang S (2023) Hybrid arithmetic optimization algorithm for a new multi-warehouse joint replenishment and delivery problem under trade credit. Neural Comput Appl 35:7561–7580

    Article  Google Scholar 

  39. Lee FC, Yao MJ (2003) A global optimum search algorithm for the joint replenishment problem under power-of-two policy. Comput Oper Res 30:1319–1333

  40. Wang L, Wang S, Gong Y, Peng L (2023) Optimizing a multi-echelon location inventory problem with joint replenishment: A Lipschitz ϵ-optimal approach using Lagrangian relaxation. Comput Oper Res 151:106128

    Article  MathSciNet  Google Scholar 

  41. Tizhoosh H (2005) Opposition-based learning: A new scheme for machine intelligence. International Conference on Computational Intelligence For Modelling, Control And Automation And International Conference On Intelligent Agents, Web Technologies and Internet Commerce, 695–701

  42. Zhang J, Sanderson AC (2009) JADE: Adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958

    Article  Google Scholar 

  43. Mirjalili S (2016) SCA: A sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Article  Google Scholar 

  44. Wang L, Dun CX, Bi WJ, Zeng YR (2012) An effective and efficient differential evolution algorithm for the integrated stochastic joint replenishment and delivery model. Knowl-Based Syst 36:104–114

    Article  Google Scholar 

  45. Yılmaz ÖF, Yazıcı B (2022) Tactical level strategies for multi-objective disassembly line balancing problem with multi-manned stations: an optimization model and solution approaches. Ann Oper Res 319:1793–1843

    Article  Google Scholar 

  46. Yilmaz ÖF, Ozcelik G, Yeni FB (2020) Lean holistic fuzzy methodologyemploying cross-functional worker teams for new product development projects: Areal case study from high-tech industry. Eur J Oper Res 282:989–1010

    Article  Google Scholar 

  47. Tirkolaee EB, Mahdavi I, Esfahani MMS, Weber GW (2020a) A robust green location-allocation-inventory problem to design an urban waste management system under uncertainty. Waste Manag 102:340–350

  48. Tirkolaee EB, Goli A, Faridnia A, Soltani M, Weber GW (2020) Multi-objective optimization for the reliable pollution-routing problem with cross-dock selection using Pareto-based algorithms. J Clean Prod 276:122927

    Article  Google Scholar 

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Acknowledgements

This research is partially supported by National Social Science Foundation of China (No. 20&ZD126).

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Authors and Affiliations

  1. School of Management, Huazhong University of Science and Technology, Wuhan, 430074, China

    Lin Wang, Yingying Pi, Sirui Wang & Ziqing Zhang

  2. School of Management, Wuhan University of Technology, Wuhan, 430074, China

    Lu Peng

  3. Department of Management Science, College of Management, Shenzhen University, Shenzhen, 518060, China

    Rui Liu

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  1. Lin Wang
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Correspondence to Ziqing Zhang.

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Wang, L., Pi, Y., Peng, L. et al. OBRUN algorithm for the capacity-constrained joint replenishment and delivery problem with trade credits. Appl Intell 53, 30266–30299 (2023). https://doi.org/10.1007/s10489-023-05055-9

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