Dynamic Management of Heterogenous Resources

In this paper we develop a new method for solving Dynamic Resource Allocation Problems (DRAP) that occur in the operation of freight transportation systems. Such problems involve the allocation of resources to perform tasks over a discrete-time, dynamic network. Our particular interest is in ultra-large scale problems, that involve managing thousands of resources (such as drivers or vehicles). We focus on problems with dynamic attributes, where the characteristics of the resource may change as it handles each task. We provide a general and very exible formulation, and provide a solution based on the principle of dynamic programming. A newly proposed linearization approximation is shown to provide high quality solutions with reasonable execution times. The technique is illustrated in the context of the driver management problem for a large motor carrier. We consider the problem of optimizing, in a dynamic setting, the management of thousands of discrete resources characterized by a number of attributes. Our application is motivated by a driver scheduling problem arising in freight transportation, where we were faced with the challenge of routing and scheduling over 5,000 drivers to serve 30,000 loads over a four day horizon. Similar problems arise in other resource management problems where there is a relatively high level of uncertainty. Examples include both crew scheduling and asset management (locomotives and aircraft) for railroads and the Air Mobility Command. Complex equipment such as locomotives and aircraft generally need to be described by a rich set of attributes. Our problem is di erent in a signi cant way from two closely related problem classes. The rst is crew scheduling, which is generally done in the context of a deterministic environment (all information is known) and where the attributes of a resource (crew) can be very complex, consisting possibly of dozens of dimensions. Our problem class is characterized by a relatively high level of uncertainty; partly as a result of this uncertainty, it makes sense to use a moderate level of aggregation and characterize resources with fewer attributes. The second problem class is the dynamic vehicle allocation problem, where uncertainty in customer demands is often modeled explicitly, but where the vehicles are either homogeneous (the so-called \single commodity" problem) or with a single attribute giving the type of vehicle (where the number of vehicle types might range between one and three dozen). The focus of the project was to develop a system that would run in real time, but which would provide tactical information to a group of centralized planners. As a result, we were not interested in assigning a particular driver to a particular load \here and now" but rather to provide forecasts of available drivers and loads waiting to be moved over a four day horizon. For this reason, we did not need to model each driver individually, but we did need to capture the attributes of a driver with su cient accuracy to model basic ows. An optimization model was needed since we needed to project decisions (assigning drivers to loads, moving empty, holding freight) in the future. We approach the problem as a dynamic resource allocation problem (DRAP) which involves the management of two types of multiattribute resources (drivers and loads) over time. A driver may move a load, or move alone (an empty move). Loads, of course, cannot move without a driver, but may sit idle if no driver is assigned to move a load. Loads incur a service penalty for each shipment that arrives at its destination after its delivery date. Dynamic resource allocation problems of the type we consider arise in a number of settings in