by Leendert Kok and Joaquim Gromicho, ORTEC
“German CIT truck robbed with Bazooka” 12-12-2015, “Attack on CIT in Amsterdam” 4-06-2015, “Failed robbery on the Italian highways” 15-05-2015. These are three examples of the motivation of one part of a joint research project of ORTEC, Geldservice Nederland (GSN), and the Vrije Universiteit (VU) Amsterdam called ‘Optimizing cash supply chain networks’.
One of the goals in cash supply chains is to manage the inventory of ATMs. GSN, a cooperation of banks, manages the inventory of the majority of ATMs in the Netherlands. To this end, they generate money pickup and delivery orders which they outsource to Cash in Transit (CIT) companies to deliver the money to and from the ATMs. Since trucks carrying money are attractive to robbers, an important goal in planning the delivery routes (besides being efficient to lower transport costs), is to make the routes unpredictable.
In 2015, three PhD students at the VU started working on this problem. The problem can be seen as a special case of the inventory routing problem, see [1], where the goal is to manage the inventory of fuel for a set of customers, for example, by making sure that they do not run out of stock. The long term goal is to minimize transport costs. The problem is a generalization of the well-known vehicle routing problem (VRP), by adding two extra decisions to the problem: when to deliver and how much.
Within the cash replenishment business, an extra requirement appears for these delivery routes: they should be unpredictable. In a sense, the problem is the opposite of the consistent VRP [2], where the goal is to deliver to the same customer at the same time of the day and the same day of the week. There are different measures for the unpredictability of vehicle routes: the time of replenishment, the sequence of replenishments, and the routes driven between two replenishments (K-shortest paths).
The PhD students developed a model for varying the time of delivery by generating multiple non-overlapping time windows with the last delivery for each specific ATM. The VRP with multiple time windows has received little attention in the literature. A special modelling characteristic in cash supply is that waiting time at customers (ATMs in this case) is not allowed. Especially when time windows are tight, this extra constraint has a major impact on solution methods for this vehicle routing problem.
As mentioned above, a key decision within inventory routing is the moment of delivery and the amount to deliver. To minimize the long run transport costs, an objective was introduced by [3] which minimizes transport costs by delivered volume. Figure 1 illustrates how a larger transport cost still leads to a better plan with respect to the long term transport costs.
![Figure 1: Example of improving the long term transport costs per delivered volume ([3]).](/images/stories/EN105/kok.png "Figure 1: Example of improving the long term transport costs per delivered volume ([3]).")
Figure 1: Example of improving the long term transport costs per delivered volume ([3]).
ORTEC, one of the world’s largest suppliers of advanced planning software, has extensive experience in solving Inventory Routing Problems and, with the involvement of many master’s students, is continuously updating its innovative solutions. One of the current master’s students is looking at ways to improve the inventory routing solutions by making a clever preselection in which customers are selected for delivery. The student developed a mechanism that decides which so-called may-go orders (orders that may be postponed until the next day) should be included in the batch for the planning day. The results are very promising and indicate that with minimal computational effort, the long term transportation costs can be reduced by more than 5%.
The final part of the research project focuses on contract design. Currently, GSN decides on the orders, and third parties are responsible for delivering the money. This leads to suboptimal solutions (the preferred amount to deliver may depend on the driven vehicle routes). Moreover, service level agreements are done between GSN and the banks, but the logistics companies are crucial for fulfilling them. This research aims to develop incentives to better deal with all these challenges.
References:
[1] L. Bertazzi, S. Bertazzi, M. Grazia: “Inventory routing problems: an introduction”, EURO Journal on Transportation and Logistics, Vol. 1, No. 4, pp. 307-326; 2012
[2] C. Groër, B. Golden, E. Wasil: “The Consistent Vehicle Routing Problem”, Manufacturing & Service Operations Management, Vol. 11, No. 4, pp. 630–643, 2009.
[3] W. J. Bell, et al.: “Improving the distribution of industrial gases with an online computerized routing and scheduling optimizer”, Interfaces, 13, pp. 4–23, 1983.
Please contact:
Leendert Kok
ORTEC, The Netherlands
