Multi-Product Inventory-Routing Problem in the Supermarket Distribution Industry
-
Demetrio Laganà
und
Francesco Santoro
Abstract
The Inventory Routing Problem (IRP) is an integrated logistic problem arising in several industries (e.g. petrochemical, grocery, soft drink and automotive). A vendor decides the optimal delivery strategy for a set of customers, taking into account their inventory policies and avoiding product stock-out in a finite and discrete time horizon. Delivery strategy includes the time and size of deliveries in order to minimize the total delivery cost. Most commonly studied are IRP real cases where a single homogeneous product with deterministic but time-varying demand is delivered over a finite time horizon. This paper is focused on an efficient methodology for industrial problems where a vendor resupplies a set of customers of heterogeneous products (as in the supermarket distribution industry). In this context, the paper reports on an effort facing the inventory routing problem for multi-category products per customer in conjunction with different inventory policies per category. The paper is motivated by real applications arising in the food engineering field. For instance, industries dealing with food’s distribution to stores located in a given geographic area. The planning strategy is formulated as a linear model. The core of the decision problem consists in determining both the delivery route and the corresponding day of activation along the time horizon. A decomposition of the problem into two phases has been proposed. A suitable penalty cost modeled by simulating the possibility of having an early or delayed product delivery on the delivery day returned from the inventory model (e.g. Economic Order Quantity) is the key feature of the first phase. In the second phase, deliveries are scheduled on a daily basis by taking into account the time windows associated to each customer. This is accomplished by using a constructive heuristic algorithm for the vehicle routing problem with time windows. Computational results on some realistic instances are presented and discussed.
References
1. Beltrami L., Bodin F. Networks and vehicle routing for municipal waste collection. Networks 1974;40:65–9410.1002/net.3230040106Suche in Google Scholar
2. Assad A, Dahl R, Golden B. Analysis of a large scale vehicle routing problem with an inventory component. Large Scale Syst 1984;70:181–190.Suche in Google Scholar
3. Federgruen A, and Zipkin P. A combined vehicle routing and inventory allocation problem. Oper Res 1984;320:1019–1037.10.1287/opre.32.5.1019Suche in Google Scholar
4. Dror M, Ball M, Golden B. Computational comparison of algorithms for the inventory routing problem. Ann Oper Res 1985;40:1–23.10.1007/BF02022035Suche in Google Scholar
5. Dror M, Ball M. Inventory/routing: Reduction from an annual to a short period problem. Nav Res Logist Q 1987;340:891–905.10.1002/1520-6750(198712)34:6<891::AID-NAV3220340613>3.0.CO;2-JSuche in Google Scholar
6. Bard J, Dror M, Huang L, Jaillet P. Delivery cost approximations for inventory routing problems in a rolling horizon framework. Transp Sci 2002;360:292–300.10.1287/trsc.36.3.292.7829Suche in Google Scholar
7. Bard J, Huang L, Dror M, Jaillet P. A branch and cut algorithm for the VRP with satellite facilities. IIE Trans Oper Eng 1998a;30:821–834.10.1080/07408179808966528Suche in Google Scholar
8. Bard J, Huang L, Dror M, Jaillet P. A decomposition approach to the inventory routing problem with satellite facilities. Transp Sci 1998b;330:189–203.10.1287/trsc.32.2.189Suche in Google Scholar
9. Anily S, Federgruen A. One warehouse multiple retailer systems with vehicle routing costs. Manag Sci 1990;360:92–114.10.1287/mnsc.36.1.92Suche in Google Scholar
10. Anily S, Federgruen A. Rejoinder to “comments on one-warehouse multiple retailer systems with vehicle routing costs”. Manag Sci 1991;370:1497–1499.10.1287/mnsc.37.11.1497Suche in Google Scholar
11. Gallego G, Simchi-Levi D. On the effectiveness of direct shipping strategy for the one-warehouse multi-retailer r-systems. Manag Sci 1990;360:240–243.10.1287/mnsc.36.2.240Suche in Google Scholar
12. Bramel J, Simchi-Levi D. A location based heuristic for general routing problems. Oper Res 1995;430:649–660.10.1287/opre.43.4.649Suche in Google Scholar
13. Chan LM, Federgruen A, Simchi-Levi D. Probabilistic analyses and practical algorithms for inventory-routing models. Oper Res 1998;460:96–106.10.1287/opre.46.1.96Suche in Google Scholar
14. Bertazzi L, Paletta G, Speranza MG. Deterministic order-up-to level policies in an inventory routing problem. Transp Sci 2002;360:119–132.10.1287/trsc.36.1.119.573Suche in Google Scholar
15. Archetti C, Bertazzi L, Laporte G, Speranza MG. A branch-and-cut algorithm for a vendor-managed inventory-routing problem. Transp Sci 2007;410:382–391.10.1287/trsc.1060.0188Suche in Google Scholar
16. Bertazzi L, Paletta G, Speranza MG. Minimizing the total cost in an integrated vendor-managed inventory system. J Heuristics 2005;11:393–419.10.1007/s10732-005-0616-6Suche in Google Scholar
17. Campbell A, Savelsbergh M. A decomposition approach for the inventory-routing problem. Transp Sci 2004c;380:488–502.10.1287/trsc.1030.0054Suche in Google Scholar
18. Savelsbergh M., Song J-H. Performance measurement for inventory routing. Transp Sci 2004;410:44–54.Suche in Google Scholar
19. Gaur V, Fisher ML. A periodic inventory routing problem at a supermarket chain. Oper Res 2004;520:813–822.10.1287/opre.1040.0150Suche in Google Scholar
20. Savelsbergh M. and Song J-H. Inventory routing with continuous moves. Comput Oper Res 2007;340:1744–1763.10.1016/j.cor.2005.05.036Suche in Google Scholar
21. Savelsbergh M and Song J-H. An optimization algorithm for the inventory routing problem with continuous moves. Comput Oper Res 2008;350:2266–2282.10.1016/j.cor.2006.10.020Suche in Google Scholar
22. Cordeau JF, Laganà D, Musmanno R, Vocaturo F. A decomposition-based heuristic for the multiple-product inventory-routing problem. Comput Oper Res 2014. doi: http://dx.doi.org/10.1016/j.cor.2014.06.007.http://dx.doi.org/10.1016/j.cor.2014.06.007Suche in Google Scholar
23. Minkoff A. A Markov decision model and decomposition heuristic for dynamic vehicle dispatching. Oper Res 1993;410:77–90.10.1287/opre.41.1.77Suche in Google Scholar
24. Kleywegt A, Nori V, Savelsbergh M. The stochastic inventory routing problem with direct deliveries. Transp Sci 2002;36:94–118.10.1287/trsc.36.1.94.574Suche in Google Scholar
25. Kleywegt A, Nori V, Savelsbergh M. Dynamic programming approximations for a stochastic inventory routing problem. Transp Sci 2004;38:42–70.10.1287/trsc.1030.0041Suche in Google Scholar
26. Adelman D. Price-directed replenishment of subsets: methodology and its application to inventory routing. Manuf Serv Oper Manag 2003;50:348–371.10.1287/msom.5.4.348.24884Suche in Google Scholar
27. Adelman D. A price-directed approach to stochastic inventory/routing. Oper Res 2004;520:499–514.10.1287/opre.1040.0114Suche in Google Scholar
28. Lejeune MA and Ruszczynski A. An efficient trajectory method for probabilistic production-inventory-distribution problems. Oper Res 2007;550:378–394.10.1287/opre.1060.0356Suche in Google Scholar
29. Hvattum LM, Laporte G, Lokketangen A. Scenario tree-based heuristics for stochastic inventory-routing problems. INFORMS J Comput 2009;210:268–285.10.1287/ijoc.1080.0291Suche in Google Scholar
30. Vonolfen S, Affenzeller M, Beham A, Lengauer E, Wagner S. Simulation-based evolution of resupply and routing policies in rich vendor-managed inventory scenarios, Central European Journal of Operations Research 2013;21:379–400.10.1007/s10100-011-0232-5Suche in Google Scholar
31. Chen H, Chu F, Yu Y. A new model and hybrid approach for large scale inventory routing problems. Eur J Oper Res 2008;189:1022–1040.10.1016/j.ejor.2007.02.061Suche in Google Scholar
32. Chen H, Chu F, Yu Y. A Stackelberg game and its improvement in a VMI system with a manufacturing vendor. Eur J Oper Res 2009;1920:929–948.10.1016/j.ejor.2007.10.016Suche in Google Scholar
33. Huang GQ, Liang L, Yu. Y. Stackelberg game theory model for optimizing advertising, pricing and inventory policies in vendor managed inventory (VMI) supply chains. Comput Ind Eng 2009;570:368–382.10.1016/j.cie.2008.12.003Suche in Google Scholar
34. Bertazzi L, Bosco A, Guerriero F, Laganà D. A stochastic inventory routing problem with stock-out. Transp Res Part C: Emerg Technol 2013;270:89–107.10.1016/j.trc.2011.06.003Suche in Google Scholar
35. Bertazzi L, Bosco A, Laganà D. Managing stochastic demand in an inventory routing problem with transportation procurement. Omega 2014b. doi: http://dx.doi.org/10.1016/j.omega.2014.09.010.http://dx.doi.org/10.1016/j.omega.2014.09.010Suche in Google Scholar
36. Bertazzi L, Bosco A, Laganà D. Min-max policies in the robust inventory routing problem with outsourced transportation. Technical report, Working Papers, Department of Economics and Management, University of Brescia, Italy, 2014a.Suche in Google Scholar
37. Federgruen A, Simchi–Levi D. Analysis of vehicle routing and inventory–routing problems. In Ball MO, Magnanti TL, Monma CL, Nemhauser GL, editor. Handbooks in operations research and management science, vol 8. North Holland, 1995:297–373.10.1016/S0927-0507(05)80108-2Suche in Google Scholar
38. Campbell A, Clarke L, Kleywegt A, Savelsbergh M. Fleet management and logistics. Chapter Inventory routing. Kluwer Academic Publishers, Boston, MA. 1998.10.1007/978-1-4615-5755-5_4Suche in Google Scholar
39. Cordeau JF, Laporte G, Savelsbergh M, Vigo D. Short-haul routing. In Laporte G, Barnhart C, editors. Handbooks in operations research and management science: transportation, vol 14. 2007:367–428.10.1016/S0927-0507(06)14006-2Suche in Google Scholar
40. Moin NH, Salhi S. Inventory routing problems: a logistical overview. J Oper Res Soc 2007;58:1185–1194.10.1057/palgrave.jors.2602264Suche in Google Scholar
41. Bertazzi L, Savelsbergh M, Speranza MG. Inventory routing. In Golden B, Raghavan S, Wasil E, editors. The vehicle routing problem, latest advances and new challenges. Springer, 2008:49–72.10.1007/978-0-387-77778-8_3Suche in Google Scholar
42. Andersson H, Hoff A, Christiansen M, Hasle G, Løkketangen A. Industrial aspects and literature survey: combined inventory management and routing. Comput Oper Res 2010;37:1515–1536.10.1016/j.cor.2009.11.009Suche in Google Scholar
43. Bertazzi L, Speranza MG. Matheuristics for inventory routing problems in hybrid algorithms for service, computing and manufacturing systems: routing, scheduling and availability solutions. In: Montoya-Torres JR, Juan AA, Huatuco LH, Faulin J, Rodriguez-Verjan GL, editors. Igi Global, 2011.Suche in Google Scholar
44. Coelho LC, Cordeau JF, Laporte G. Thirty years of inventory-routing. Transp Sci 2014;480:1–19.10.1287/trsc.2013.0472Suche in Google Scholar
©2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Selected Papers from MAS2014 Workshop
- Special Section “Selected papers from the workshop on Modeling and Simulation of Food Processing and Operations of the MAS 2014 conference (Bordeaux, September 10–12, 2014)”
- Three-Dimensional CFD Simulation of a “Steam Water Spray” Retort Process for Food Vegetable Products
- Temperature Analysis of the Water Supply System of a Dairy Company by Means of a Simulation Model
- Multi-Product Inventory-Routing Problem in the Supermarket Distribution Industry
- Decision Support System, Based on the Paradigm of the Petri Nets, for the Design and Operation of a Dairy Plant
- Critical Reviews
- Rice: Parboiling and Milling Properties
- A Review of Drying Processes in the Production of Pumpkin Powder
- Original Research Articles
- Modelling of Changes in Postharvest Quality Parameters of Stored Carrots Subjected to Pre- and Postharvest Treatments
- Evaluation of Viscosity of Non-Newtonian Liquid Foods with a Flow Tube Instrument
- Characterization of Pyrolysis Products Obtained from Desmodesmus sp. Cultivated in Anaerobic Digested Effluents (DADE)
- The Effects of Nano-SiO2 on Mechanical, Barrier, and Moisture Sorption Isotherm Models of Novel Soluble Soybean Polysaccharide Films
- Adsorption and Desorption Studies of Anthocyanins from Black Peanut Skins on Macroporous Resins
- Convective Air Drying Characteristics and Qualities of Non-fried Instant Noodles
- Microwave-Assisted Extraction of Trigona Propolis: The Effects of Processing Parameters
Artikel in diesem Heft
- Frontmatter
- Selected Papers from MAS2014 Workshop
- Special Section “Selected papers from the workshop on Modeling and Simulation of Food Processing and Operations of the MAS 2014 conference (Bordeaux, September 10–12, 2014)”
- Three-Dimensional CFD Simulation of a “Steam Water Spray” Retort Process for Food Vegetable Products
- Temperature Analysis of the Water Supply System of a Dairy Company by Means of a Simulation Model
- Multi-Product Inventory-Routing Problem in the Supermarket Distribution Industry
- Decision Support System, Based on the Paradigm of the Petri Nets, for the Design and Operation of a Dairy Plant
- Critical Reviews
- Rice: Parboiling and Milling Properties
- A Review of Drying Processes in the Production of Pumpkin Powder
- Original Research Articles
- Modelling of Changes in Postharvest Quality Parameters of Stored Carrots Subjected to Pre- and Postharvest Treatments
- Evaluation of Viscosity of Non-Newtonian Liquid Foods with a Flow Tube Instrument
- Characterization of Pyrolysis Products Obtained from Desmodesmus sp. Cultivated in Anaerobic Digested Effluents (DADE)
- The Effects of Nano-SiO2 on Mechanical, Barrier, and Moisture Sorption Isotherm Models of Novel Soluble Soybean Polysaccharide Films
- Adsorption and Desorption Studies of Anthocyanins from Black Peanut Skins on Macroporous Resins
- Convective Air Drying Characteristics and Qualities of Non-fried Instant Noodles
- Microwave-Assisted Extraction of Trigona Propolis: The Effects of Processing Parameters
