The inventory routing problem (IRP) involves the integration and coordination of two components of the logistics value chain: inventory management and vehicle routing.
The IRP is concerned with the distribution of single product from a single facility to a set of n customers over a given planning horizon of length T, possibly infinity. Customers consume the product at a rate u_i and can maintain an inventory of the product up to a level C_i. Local inventory is assumed to be Ii at time 0. A fleet of m homogeneous vehicles of capacity Q are available for the distribution of the product. The objective is to minimize the distribution costs during the planning period without causing stockouts at any of the customers.
Vendor managed resupply is an emerging trend in logistics that is an example of value creating logistics. Vendor managed resupply refers to a policy in which a supplier manages the inventory of his customers. The application of vendor managed resupply principles creates advantages for both supplier and customer. The vendor saves on distribution costs by being able to better coordinate deliveries to different customers. Customers may receive incentives and all save time and effort on inventory management.
The inventory routing problem captures the essential characteristics of a vendor managed inventory policy, and methodologies developed for this problem form the building blocks for logistics planning systems.
One reason that vendor managed resupply has been receiving a lot of attention is the recent low cost availability of technology that allows monitoring customers' inventory. For example, Praxair uses the Tracker™ system which is an advanced microprocessor installed on a customer's industrial gas supply tank to access to current inventory readings. To be able to solve these problems in practice, it is important that the vendor have access to accurate and timely information about the inventory status of customers.
Though first introduced into the literature through applications with liquid air products, many different industries are currently involved with vendor managed inventory systems or are exploring their use.
Examples
- Aerospace
- Aircraft
- Apparel
- Automotive
- Chemicals
- Electronics Assembly
- Electronics/Semiconductor
- Food & Beverage
- Fuel Cells
- Glass
- Healthcare / Medical
- Home Healthcare
- Metal Fabrication
- Metal Production
- Petroleum
- Printing
- Pulp & Paper
- Retail
- Utilities
- Water & Waste
From my involvement with Praxair, we created a sample case study to demonstrate the difficult issues in solving the IRP.
I also found there were no common datasets like those that exist for the TSP. At Georgia Tech, we created a library of test sets which are now publicly available.
We even created a game to illustrate the difficulty of the IRP.
I have written several articles involving the inventory routing problem. These include:
Campbell, A. and M. Savelsbergh, 2004, "A Decomposition Approach for the Inventory Routing Problem'' Transportation Science, Volume 38, Number 4, Pages 488-502.
Campbell, A. and M. Savelsbergh , 2004, "Delivery Volume Optimization'' Transportation Science, Volume 38, Number 2, 210-223.
Campbell, A. and M. Savelsbergh , 2004, "Efficient Insertion Heuristics for Vehicle Routing and Scheduling Problems" Transportation Science, Volume 38, Number 3, 369-378.
Campbell, A. and M. Savelsbergh, 2002, "Inventory Routing in Practice", The Vehicle Routing Problem, edited by P. Toth and D. Vigo, SIAM Monographs on Discrete Mathematics and Applications.
Campbell, A. , M. Savelsbergh , L. Clarke and A. Kleywegt, 1998, "The Inventory Routing Problem'', Fleet Management and Logistics, edited by T. G. Crainic and G. Laporte, Kluwer Academic Publishers, 95-112.
There are a growing number of references to inventory routing and related problems in the literature. Here are some examples:
Anupindi, R. and Akella, R. (1993) "Diversification Under Supply Uncertainty", Management Sciences, 39(8), p.944-963.
Anupindi, R. and Bassok Y. (1998) "Supply Contracts with Quantity Commitments and Stochastic Demand", in Tayur, S., Ganeshan, R. and Magazine M. (Eds.), Quantitative Models for Supply Chain Management. Boston: Kluwer Academic Publishers, p.197-232.
Anily, S. and Federgruen, A. (1990) "One Warehouse Multiple Retailer Systems with Vehicle Routing Costs", Management Science, 36, p.92-114.
Anily, S. and Federgruen, A. (1993) "Two-Echelon Distribution Systems with Vehicle Routing Costs and Central Inventories", Operations Research, 41, p.37-47.
Benerjee, A. (1986) "A Joint Economic Lot Size Model for Purchaser and Vendor", Decision Sciences, 17, p.292-311.
Bramel, J. and Simchi-Levi, D. (1995) "A Location Based Heuristic for General Routing Problems", Operations Research, 43, p.649-660.
Burns, L. D., Hall, R. W., Blumenfeld, D. E. and Daganzo, C. F. (1985) "Distribution Strategies That Minimize Transportation and Inventory Costs", Operations Research, 33(3), p.469-490.
Chen, F., Drezner, Z., Ryan, J. K. and Simchi-Levi, D. (2000) "Quantifying the Bullwhip Effect in a Simple Supply Chain: the Impact of Forecasting, Lead Times and Information", Management Sciences, 46(3), p.436-443.
Chan, L. M. A., Federgruen, A. and Simchi-Levi, D. (1998) "Probabilistic Analyses and Practical Algorithms for Inventory-Routing Models", Operations Research, 46, p.96-106.
Chien, T.W., Balakrishnan, A. and Wong, R. T. (1989) "An Integrated Inventory Allocation and Vehicle Routing Problem", Transportation Science, 23, p.67-76.
Closs, D. J. and Cook, R. L. (1987) "Multi-stage Transportation Consolidation Analysis Using Dynamic Simulation", Internat. J. Phys. Distribution Materials Management, 17(3), p.28-45.
Cousineau-Ouimet, K. (2002) "A Tabu Search Heuristic for theInventory Routing Problem", Proceedings of 37th Annual ORSNZ Conference.
Federgruen, A. and Zipkin, P. (1984) "A Combined Vehicle Routing and Inventory Allocation Problem", Operations Research, 32, p.109-1037.
Gallego, G. and Simchi-Levi, D. (1990) "On the Effectiveness of Direct Shipping Strategy for the One-warehouse Multi-retailer R-systems", Management Science, 36, p.240-243.
Golden, B. L., Assad, A. A. and Dahl, R. (1984) "Analysis of a Large Scale Vehicle Routing Problem with an Inventory Component", Large Scale Systems, 7, p.181-190.
Gupta, Y. P. and Bagchi, P. K. (1987) "Inbound Freight Consolidation Under Just-in-time Procurement: Application of Clearing Models", J. Bus. Logist, 8(2), p.74-94.
Higginson, J. K. and Bookbinder, J. H. (1994) "Policy Recommendations for a Shipment Consolidation Program", J. Bus. Logist, 15(1), p.87-112.
Higginson, J. K. and Bookbinder, J. H. (1995) "Markovian Decision Processes in Shipment Consolidation", Transportation Sci., 29(3), p.242-255. 22.
Kleywegt, A, Nori, V. and Savelsbergh, M (2002), "The Stochastic Inventory Routing Problem with Direct Deliveries", Transportation Science, Vol. 36, No. 1
Kohli, R. and Park, H. (1994) "Coordinating Buyer-Seller Transactions Across Multiple Products", Management Science, 40(9), p.45-50.
Lariviere, Martin (1998) "Supply Chain Contracting and Coordination with Stochastic Demand", in Tayur, S., Ganeshan, R. and Magazine, M. (Eds.), Quantitative Models for Supply Chain Management. Boston: Kluwer Academic Publishers, p.233-268.
Lau, H.C., Liu, Q. and H. Ono (2002) "Integrating Local Search and Network Flow to Solve the Inventory Routing Problem", American Association for Artificial Intelligence, 02, p. 9-14.
Reiman, M., Rubio, R., and L.M. Wein (1999) "Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem", Transportation Science, 33(4), p.361-372.
Russell, R. M.and Krajewski, L. (1991) "Optimal Purchase and Transportation Cost Lot Sizing or a Single Item", Decision Sci., 22, p.940-952.
Trudeau, P. and Dror, M. (1992) "Stochastic Inventory Routing: Route Design with Stockouts and Route Failures", Transportation Science, 26, p.17-184.
Waller, M., Johnson, M. E. and Davis, T. (1999) "Vendor-Managed Inventory in the Retail Supply Chain", Journal of Business Logistics, 20(1), p.183-203.
Zhao Q, Wang S Y, Lai, K K & G P Xia, “ Dynamic Multi-Period Transportation Model for Vehicle Composition with Transshipment Points”, Journal of Advanced Modeling and Optimization, Vol. 3, No. 1,2001
www.vendormanagedinventory.com - discusses the factors involved in setting up a full scale VMI program
www.cpfr.org/Vendor-Managed.html - discusses the data needed to set up a VMI program
Have you been working with inventory routing? If so, and you have papers, data or websites to post, please email me (ann-campbell@uiowa.edu).