Measuring and managing the learning requirements of route reoptimization of delivery vehicle drivers

Journal of Business Logistics, 2002 by Haughton, Michael A

Uncertainty in day-to-day demands by customers complicates the tasks of dispatching and routing road delivery vehicles to cost-effectively satisfy these customers' demands. This paper considers situations where the demand uncertainty follows a Bernoulli process. Specifically, each customer, i, has probability p^sub i^ of ordering q^sub i^ units (which, without, loss of generality can be treated as a multiple of 1 unit; e.g., an order of 150 pounds is equivalent to 0.5 of a unit for an item that might be packaged in quantities of 300 pounds). This would apply in any situation where each customer follows a reorder point policy of ordering a fixed quantity at randomly fluctuating intervals between orders. A specific example is where a supermarket issues a fixed order quantity of a grocery item when the available inventory reaches the reorder point.

The complication of stochastic demand can be understood from the perspective that the depot's dispatcher/router has to assess the advantages and disadvantages of either maintaining stable routes in the face of demand uncertainty or constantly adjusting the dispatch and routing plans in response to the fluctuations. Stable delivery routes, which involve constant daily deliveries of each customer's expected daily demand (p^sub i^q^sub i^), provide the advantage of not imposing any requirement on drivers to learn new routes each day, thus enabling them to perform their delivery duties efficiently. Its downside stems from the fact that it allows no opportunity to effect efficient route adjustments in response to fluctuating customer demands. So, in the face of fluctuating demands, fixed delivery routes, and concomitantly, fixed delivery quantities, will lead to risks of delivery shortages during periods of demand surges, and hence reduced customer service performance in terms of order-fill rate.

Amore demand-responsive strategy of reoptimizing the delivery routes each day overcomes this problem and is designed to minimize the average daily transportation cost (see, for example, Bertsimas 1992). A concern with this strategy is that the optimum routes will sometimes require a driver to visit customer locations beyond those he would have to visit if each customer's demand remained constant at its mean of p^sub i^q^sub i^. Referring to a driver's route for constant demand as his subregion/territory or standard route, this means that the driver must be sufficiently knowledgeable of the customer locations outside of his standard route in order to perform his delivery assignments efficiently each day. The per day extra distance that a driver must travel (measured as a percentage of the distance for the standard route and averaged across all drivers) is this paper's core metric for depicting route reoptimization's learning requirements on drivers. The practical importance of being able to gauge the learning requirements stems from the paper's premise that the larger the requirements are, the harder it will be for drivers to perform their jobs in routing/dispatch operations that use route reoptimization.

It is worth noting that the system of fixed/stable delivery routes described earlier is not being presented as a tactic that is known to exist in actual dispatch/routing operations. Instead, it is being presented as a baseline system to assist in quantifying route reoptimization's learning burden on drivers. It is an appropriate baseline because, as explained previously, the constancy of each day's routes makes its learning burden on drivers zero. Viewed another way, using it as a baseline facilitates possible answers to the following question: "If, perhaps because of the inherent benefits of operational stability, a firm were to sacrifice demand-responsiveness by running fixed routes, what would be the increased learning burden of switching to the demand-responsive system of route reoptimization?" A question that might arise from this is whether there is some intermediate tactic that eliminates each driver's burden of learning routes outside of his territory yet provides some measure of demand responsiveness.

Using as an example, grocery deliveries from a central depot to supermarkets (the depot's customers), one way that this can be accomplished is by partially reoptimizing each day's routes so that each driver stays within his sub-region. While this would not assure complete day-to-day stability of the routes, each driver would still be able to focus only on the pre-specified sub-region within which his standard customers are located. An illustration of how the tactic might work is that a driver would complete a route to supermarkets requiring deliveries in his sub-region on a particular day then hand-off the vehicle at a border point between his territory and the territory of another driver. Like the first driver, the second driver would then proceed to make the day's required deliveries within his territory. A conspicuous drawback of this tactic is that since the routes are reoptimized only for deliveries to customers within each driver's territory, the overall routing solution will be suboptimal, thus involving a longer travel distance than is attainable with global route reoptimization across all customers served by the depot. This paper will analyze the extent of the suboptimality in order to yield some insights into the tactic's potential cost of limiting the learning burden on drivers.