Featured Story July 2018 - September 2018
Vendor Managed Inventory Policy and Inventory Routing Problem

By Lefteris Manousakis, PhD Candidate

Worldwide, the distribution of goods and services is a core daily activity for the vast majority of companies and organizations. Undoubtedly, the effective and efficient supply chain management is a determining success factor and it is important for gaining competitive advantage. At the heart of the distribution management lies the classic Vehicle Routing Problem (VRP) that formally appeared as a challenging optimization problem in 1959 [1]. Since then, it has been extensively studied in combination with other supply chain management processes and from several aspects such as inventory management, production scheduling, resources utilization, multiple echelons of distribution network, transshipments, crossdocking, loading and batching, etc.

Vendor Managed Inventory. A large part of the net operating assets for big companies is the inventory holding. More specifically, it has been calculated that inventory is responsible for 30% of net operating assets in manufacturing, 62% in distribution and 56% in retail [2] . Consequently, one of the most interesting and important processes that was incorporated in the VRP and studied jointly is the inventory control. The complex optimization problem that aroused [3] is named Inventory Routing Problem (IRP) and the fundamental concept behind it, is the Vendor Managed Inventory policy (VMI) in contrast to the "traditional" Retailer Managed Inventory (RMI). According to RMI, the customers are responsible for monitoring their inventories and placing orders to the supplier, who is responsible for serving the demands on a daily basis. On the contrary, according to VMI policy the supplier is responsible for monitoring the customers' inventory levels maintaining an agreed inventory of the material in the customers location. The supplier decides the quantities and the times to replenish to the customers with the only restriction that no customer stock-outs occur at any time. Consequently, the supplier operating costs are reduced due to the fact the there is a planning horizon that allows to schedule and balance routes, replenishment days and quantities which results in lower inventory needs and smaller vehicle fleet. VMI creates a win-win situation and better customer experience, as the retailer does not use resources to monitor the inventories and to place orders. Studies show that VMI policies can achieve remarkable savings both in terms of inventory and transportation costs (9.49%) and number of vehicles used (9.06%) [4].

Optimization Problem. IRP is a complex optimization problem in which a supplier is responsible for supplying the geographically dispersed retailers with a certain product across a period of time with a vehicle fleet. In order to minimize the transportation and inventory costs of the distribution, the decision maker must specify:
1.        the time to serve each customer,
2.        the quantities to deliver in each visit and
3.        the order in which retailers are visited
Consequently, IRP is exponentially harder than VRP which is already established as NP-hard optimization problem and therefore finding a good quality solution is more than challenging. Researchers have presented numerous approaches for the diverse IRP variants [5]. Methods range from exact mathematical programming ([6], [7], [8]) to heuristics ([9]) and even metaheuristics ([10]).

Industrial Applications. As mentioned before, IRP has many different variants related to time horizon, structure, routing, inventory decisions, fleet composition and size. The complex problem is capable modeling real process with relatively small abstractions. Consequently, there is a large number of interesting industrial applications that have been presented [11]. Application can be categorized to road-based and maritime featuring the transportation and inventory control of heating oil, beer, soft drinks, industrial gases, groceries, ammonia, fuel, liquefied gas, cement etc.  IRP contributes even in the healthcare sector by providing solutions to the demanding blood transportation problem [12], [13].

Conclusions & Insight. Concluding, IRP offers a variety of options for structuring, modelling and solving real-life supply chain management problems. It has been proven to provide noticeable benefits to both partners and it has been constantly attracting researchers' attention. Undoubtedly, due to rapid technological advancements, the computing power and the data availability have exponential increased in comparison with some years before. This creates a broad spectrum of opportunities for any researcher in two major directions. Firstly, industry has shown a vivid interest to enhance the current models by incorporating more features, operational constraints and processes in order to create solutions that are immediately applicable to reality without assumptions. Secondly, as the models become more and more challenging, there is a realized requirement for solution methods that will render them intractable. All in all, inventory routing problems are a challenging, promising and most importantly impactful field of academic and industrial research.


References

[1]        G. B. Dantzig and J. H. Ramser, "The Truck Dispatching Problem," Manage. Sci., vol. 6, no. 1, pp. 80-91, 1959.

[2]        S. G. Timme and C. Williams-Timme, "The real cost of holding inventory," Supply Chain Manag. Rev., vol. 7, no. 4, pp. 30-37, 2003.

[3]        W. J. Bell et al., "Improving the Distribution of Industrial Gases with an On-Line Computerized Routing and Scheduling Optimizer," Interfaces (Providence)., vol. 13, no. 6, pp. 4-23, 1983.

[4]        C. Archetti and M. G. Speranza, "The inventory routing problem: The value of integration," Int. Trans. Oper. Res., vol. 23, no. 3, 2016.

[5]        L. C. Coelho, J.-F. Cordeau, and G. Laporte, "Thirty Years of Inventory Routing," Transp. Sci., vol. 48, no. 1, pp. 1-19, 2014.

[6]        C. Archetti, L. Bertazzi, G. Laporte, and M. G. Speranza, "A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem," Transp. Sci., vol. 41, no. 3, pp. 382-391, 2007.

[7]        L. C. L. C. Coelho and G. Laporte, "The exact solution of several classes of inventory-routing problems," Comput. Oper. Res., vol. 40, no. 2, pp. 558-565, 2013.

[8]        G. Desaulniers, "Routing Problem A Branch-Price-and-Cut Algorithm for the Inventory-Routing Problem," Transp. Sci., 2016.

[9]        C. Archetti et al., "A hybrid heuristic for an inventory routing problem," INFORMS J. Comput., vol. 24, no. 1, 2012.

[10]        C. Archetti, N. Boland, and M. G. Speranza, "A matheuristic for the multivehicle inventory routing problem," INFORMS J. Comput., vol. 29, no. 3, 2017.

[11]        H. Andersson, A. Hoff, M. Christiansen, G. Hasle, and A. L?kketangen, "Industrial aspects and literature survey: Combined inventory management and routing," Comput. Oper. Res., vol. 37, no. 9, pp. 1515-1536, 2010.

[12]        V. Hemmelmayr, K. F. Doerner, R. F. Hartl, and M. W. P. Savelsbergh, "Delivery strategies for blood products supplies," OR Spectr., vol. 31, no. 4, pp. 707-725, 2009.

[13]        V. Hemmelmayr, K. F. Doerner, R. F. Hartl, and M. W. P. Savelsbergh, "Vendor managed inventory for environments with stochastic product usage," Eur. J. Oper. Res., vol. 202, no. 3, 2010.


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