Routing; Transshipment; Substitution; Spare parts management; Sample average approximation
Résumé :
[en] We study a two-level spare parts supply chain in which a manufacturer supplies a central warehouse (CW) with original equipment manufacturer (OEM) and replacement or pattern parts (PP). The CW, distantly located from the manufacturer, distributes both OEM parts and PP to a given number of depots facing stochastic demands. The demand for spare parts is intermittent, exhibiting an infrequent rate and extreme dispersal over time periods. Along with lateral transshipment, PP can be used as substitutes for the OEM parts to sidestep shortage at depots. Assuming that emergency shipments are significantly longer and more expensive, we aim at underlining the relative effectiveness of such a new spare parts inventory management policy. A mixed-integer linear programming model is proposed to solve the inventory routing problem with transshipment and substitution under stochastic demands. The objective is to minimise costs of holding inventory, transportation which includes regular shipment and transshipment, substitution and lost sales. To solve the problem, Sample Average Approximation method is used. Based on empirical goodness-of-fit tests, three demand patterns are studied: Poisson distribution, stuttering Poisson distribution and negative binomial distribution. The model is tested on well-known benchmark instances generated for multi-product multi-vehicle IRP. Computational experiments highlight the benefits of promoting transshipment and substitution on the overall supply chain performance. Results also suggest insights, which are of interest to professionals who are willing to develop new decision support models for the most efficient management of such items.
Beiderbeck, D., Deradjat, D., Minshall, T., The Impact of Additive Manufacturing Technologies on Industrial Spare Parts Strategies. 2018.
Lacerda, A.P., Xambre, A.R., Alvelos, H.M., Applying value stream mapping to eliminate waste: a case study of an original equipment manufacturer for the automotive industry. Int. J. Prod. Res. 54:6 (2016), 1708–1720, 10.1080/00207543.2015.1055349.
Ronzoni, C., Ferrara, A., Grassi, A., A stochastic methodology for the optimal management of infrequent demand spare parts in the automotive industry. IFAC-PapersOnLine 48:3 (2015), 1405–1410.
Johnston, F.R., Boylan, J.E., Shale, E.A., An examination of the size of orders from customers, their characterisation and the implications for inventory control of slow moving items. Journal of the Operational Research Society 54:8 (2003), 833–837, 10.1057/palgrave.jors.2601586.
Turrini, L., Meissner, J., Spare parts inventory management: new evidence from distribution fitting. Eur J Oper Res 273:1 (2019), 118–130.
Syntetos, A.A., Babai, M.Z., Altay, N., On the demand distributions of spare parts. Int. J. Prod. Res. 50:8 (2012), 2101–2117.
Van Jaarsveld, W., Dekker, R., Spare parts stock control for redundant systems using reliability centered maintenance data. Reliability Engineering & System Safety 96:11 (2011), 1576–1586.
Paterson, C., Kiesmüller, G., Teunter, R., Glazebrook, K., Inventory models with lateral transshipments: areview. Eur J Oper Res 210:2 (2011), 125–136.
Coelho, L.C., Cordeau, J.-F., Laporte, G., Consistency in multi-vehicle inventory-routing. Transportation Research Part C: Emerging Technologies 24 (2012), 270–287.
Lefever, W., Aghezzaf, E.-H., Hadj-Hamou, K., Penz, B., Analysis of an improved branch-and-cut formulation for the inventory-routing problem with transshipment. Computers & Operations Research 98 (2018), 137–148, 10.1016/j.cor.2018.05.023 https://www.sciencedirect.com/science/article/pii/S0305054818301527.
Minner, S., Multiple-supplier inventory models in supply chain management: a review. Int. J. Prod. Econ. 81–82 (2003), 265–279, 10.1016/S0925-5273(02)00288-8 Proceedings of the Eleventh International Symposium on Inventories.
Sgarbossa, F., Peron, M., Lolli, F., Balugani, E., Conventional or additive manufacturing for spare parts management: an extensive comparison for poisson demand. Int. J. Prod. Econ., 233, 2021, 107993, 10.1016/j.ijpe.2020.107993 https://www.sciencedirect.com/science/article/pii/S092552732030342X.
Achetoui, Z., Mabrouki, C., Mousrij, A., A review of spare parts supply chain management. Jurnal Sistem dan Manajemen Industri, 3, 2019, 67, 10.30656/jsmi.v3i2.1524.
Achetoui, Z., Mabrouki, C., Mousrij, A., Performance measurement system for automotive spare parts supply chain: a categorization. Journal of Transportation and Logistics, 2019, 31–50, 10.26650/JTL.2018.04.01.03.
Van der Auweraer, S., Boute, R., Forecasting spare part demand using service maintenance information. Int. J. Prod. Econ. 213 (2019), 138–149.
Lengu, D., Syntetos, A.A., Babai, M.Z., Spare parts management: linking distributional assumptions to demand classification. Eur J Oper Res 235:3 (2014), 624–635.
Boylan, J.E., Syntetos, A.A., Karakostas, G.C., Classification for forecasting and stock control: a case study. Journal of the operational research society 59:4 (2008), 473–481.
Coelho, L.C., Cordeau, J.-F., Laporte, G., Thirty years of inventory routing. Transportation Science 48:1 (2014), 1–19.
Archetti, C., Bertazzi, L., Laporte, G., Speranza, M.G., A branch-and-cut algorithm for a vendor-managed inventory-routing problem. Transportation Science 41:3 (2007), 382–391.
Geiger, M.J., Sevaux, M., Practical inventory routing: a problem definition and an optimization method. arXiv preprint arXiv:1102.5635, 2011.
Coelho, L.C., Laporte, G., A branch-and-cut algorithm for the multi-product multi-vehicle inventory-routing problem. Int. J. Prod. Res. 51:23–24 (2013), 7156–7169.
Christiansen, M., Fagerholt, K., Flatberg, T., Haugen, Ø., Kloster, O., Lund, E.H., Maritime inventory routing with multiple products: acase study from the cement industry. Eur J Oper Res 208:1 (2011), 86–94.
Zhao, Q.-H., Chen, S., Zang, C.-X., Model and algorithm for inventory/routing decision in a three-echelon logistics system. Eur J Oper Res 191:3 (2008), 623–635.
Bertazzi, L., Bosco, A., Guerriero, F., Laganá, D., A stochastic inventory routing problem with stock-out. Transportation Research Part C: Emerging Technologies 27 (2013), 89–107, 10.1016/j.trc.2011.06.003 Selected papers from the Seventh Triennial Symposium on Transportation Analysis (TRISTAN VII).
Soysal, M., Bloemhof-Ruwaard, J.M., Haijema, R., van der Vorst, J.G., Modeling an inventory routing problem for perishable products with environmental considerations and demand uncertainty. Int. J. Prod. Econ. 164 (2015), 118–133, 10.1016/j.ijpe.2015.03.008 https://www.sciencedirect.com/science/article/pii/S0925527315000766.
Huang, S.-H., Lin, P.-C., A modified ant colony optimization algorithm for multi-item inventory routing problems with demand uncertainty. Transportation Research Part E: Logistics and Transportation Review 46:5 (2010), 598–611, 10.1016/j.tre.2010.01.006 https://www.sciencedirect.com/science/article/pii/S1366554510000177.
Li, M., Wang, Z., Chan, F.T., A robust inventory routing policy under inventory inaccuracy and replenishment lead-time. Transportation Research Part E: Logistics and Transportation Review 91 (2016), 290–305, 10.1016/j.tre.2016.05.001 https://www.sciencedirect.com/science/article/pii/S1366554515303252.
Coelho, L.C., Cordeau, J.-F., Laporte, G., Heuristics for dynamic and stochastic inventory-routing. Computers & Operations Research 52 (2014), 55–67, 10.1016/j.cor.2014.07.001 https://www.sciencedirect.com/science/article/pii/S0305054814001828.
Roldán, R.F., Basagoiti, R., Coelho, L.C., Robustness of inventory replenishment and customer selection policies for the dynamic and stochastic inventory-routing problem. Computers & Operations Research 74 (2016), 14–20, 10.1016/j.cor.2016.04.004 https://www.sciencedirect.com/science/article/pii/S0305054816300740.
Yu, Y., Chu, C., Chen, H., Chu, F., Large scale stochastic inventory routing problems with split delivery and service level constraints. Ann Oper Res 197:1 (2012), 135–158 https://EconPapers.repec.org/RePEc:spr:annopr:v:197:y:2012:i:1:p:135-158:10.1007/s10479-010-0772-4.
Rahim, M.K.I.A., Zhong, Y., Aghezzaf, E.-H., Aouam, T., Modelling and solving the multiperiod inventory-routing problem with stochastic stationary demand rates. Int. J. Prod. Res. 52:14 (2014), 4351–4363, 10.1080/00207543.2014.883470.
Gruler, A., Panadero, J., de Armas, J., Moreno Pérez, J.A., Juan, A.A., Combining variable neighborhood search with simulation for the inventory routing problem with stochastic demands and stock-outs. Computers & Industrial Engineering 123 (2018), 278–288, 10.1016/j.cie.2018.06.036 https://www.sciencedirect.com/science/article/pii/S0360835218303140.
Coelho, L.C., Cordeau, J.-F., Laporte, G., The inventory-routing problem with transshipment. Computers & Operations Research 39:11 (2012), 2537–2548.
Peres, I.T., Repolho, H.M., Martinelli, R., Monteiro, N.J., Optimization in inventory-routing problem with planned transshipment: a case study in the retail industry. Int. J. Prod. Econ. 193 (2017), 748–756.
Tarhini, H., Karam, M., Jaber, M.Y., An integrated single-vendor multi-buyer production inventory model with transshipments between buyers. Int. J. Prod. Econ., 2019, 107568.
Dehghani, M., Abbasi, B., Oliveira, F., et al. Proactive Transshipment in the Blood Supply Chain. 2019.
Fattahi, P., Tanhatalab, M., Stochastic inventory-routing problem with lateral transshipment for perishable product. Journal of Modelling in Management, 2021.
Coelho, L.C., Laporte, G., A branch-and-cut algorithm for the multi-product multi-vehicle inventory-routing problem. Int. J. Prod. Res. 51:23–24 (2013), 7156–7169, 10.1080/00207543.2012.757668.
Kleywegt, A.J., Shapiro, A., Homem-de Mello, T., The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12:2 (2002), 479–502.
Shastri, Y., Diwekar, U., An efficient algorithm for large scale stochastic nonlinear programming problems. Computers & chemical engineering 30:5 (2006), 864–877.
Banholzer, D., Fliege, J., Werner, R., On rates of convergence for sample average approximations in the almost sure sense and in mean. Math Program, 2019, 1–39.
Jiang, J., Sun, H., Zhou, B., Convergence analysis of sample average approximation for a class of stochastic nonlinear complementarity problems: from two-stage to multistage. Numer Algorithms, 2021, 1–28.
Dupacová, J., Wets, R., Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. The annals of statistics 16:4 (1988), 1517–1549.
Shapiro, A., Dentcheva, D., Ruszczyński, A., Lectures on stochastic programming: Modeling and theory. 2014, SIAM.
Verweij, B., Ahmed, S., Kleywegt, A.J., Nemhauser, G., Shapiro, A., The sample average approximation method applied to stochastic routing problems: a computational study. Comput Optim Appl 24:2 (2003), 289–333.
Santoso, T., Ahmed, S., Goetschalckx, M., Shapiro, A., A stochastic programming approach for supply chain network design under uncertainty. Eur J Oper Res 167:1 (2005), 96–115.
Royset, J., Polak, E., Reliability-based optimal design using sample average approximations. Probab. Eng. Mech. 19:4 (2004), 331–343.
Homem-de Mello, T., Bayraksan, G., Monte carlo sampling-based methods for stochastic optimization. Surveys in Operations Research and Management Science 19:1 (2014), 56–85.
Royset, J.O., Szechtman, R., Optimal budget allocation for sample average approximation. Oper Res 61:3 (2013), 762–776.
Shapiro, A., Philpott, A., A tutorial on stochastic programming. Manuscript. Available at www2. isye. gatech. edu/ashapiro/publications. html, 17, 2007.
Conceição, S.V., da Silva, G.L.C., Lu, D., Nunes, N.T.R., Pedrosa, G.C., A demand classification scheme for spare part inventory model subject to stochastic demand and lead time. Production Planning & Control 26:16 (2015), 1318–1331.
