Discrete Optimization Dynamic resource allocation: A flexible and tractable modeling framework Dimitris Bertsimas a,⇑ , Shubham Gupta b , Guglielmo Lulli c a Operations Research Center, Massachusetts Institute of Technology, E40-147, Cambridge, MA 02139-4307, United States b Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, United States c Dept. of Informatics, Systems and Communication, University of Milano-Bicocca, 20126 Milano, Italy article info Article history: Received 7 December 2012 Accepted 27 October 2013 Available online 14 November 2013 Keywords: Applications of integer optimization Resource allocation Scheduling Fairness abstract This paper presents a binary optimization framework for modeling dynamic resource allocation prob- lems. The framework (a) allows modeling flexibility by incorporating different objective functions, alter- native sets of resources and fairness controls; (b) is widely applicable in a variety of problems in transportation, services and engineering; and (c) is tractable, i.e., provides near optimal solutions fast for large-scale instances. To justify these assertions, we model and report encouraging computational results on three widely studied problems – the Air Traffic Flow Management, the Aircraft Maintenance Problems and Job Shop Scheduling. Finally, we provide several polyhedral results that offer insights on its effectiveness. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction Allocation of resources over time is a problem of significant importance that many organizations in industry, government and education face. Correspondingly, resource allocation problems have received considerable attention in the Operations Research literature. In real world applications of resource allocation prob- lems, specific issues arise: assignment of requests to resources over time, allowing the flexibility of utilizing alternative resources to complete the requests, fairness issues among different requests, among others. There has been extensive work on specific examples of resource allocation problems (for example, the extensive litera- ture on Job Shop Scheduling). Still, to the best of our knowledge, we are not aware of a unified approach that can be easily modified to accommodate variations, while simultaneously being computa- tionally tractable for large scale instances. On the contrary, it is widely believed that optimization might not be the right approach for certain classes of resource allocation problems such as schedul- ing for example. In fact, commercial solvers like ILOG for schedul- ing problems are typically not optimization based, but rather rule based. Our aspiration in this paper is to develop a widely applicable, flexible and tractable modeling framework based on binary optimi- zation that is capable of modeling and solving large scale instances for a variety of resource allocation problems over time. The paper has its intellectual origins with the work of Bertsimas and Stock (1998) on air traffic flow management, which is a resource alloca- tion problem over time. In this problem, the resources are airports and sectors of the airspace, the requests are flights and the objec- tive is to minimize delays in the system. To this date, within the scope of air traffic flow management, this modeling approach has proven successful, as it continues to be used extensively by several researchers and practitioners around the world. Two significant generalizations of the model in the context of air traffic flow man- agement that suggest flexibility include: (a) the work of Bertsimas and Gupta (submitted for publication) that shows how fairness is- sues among airlines can be modeled in a computationally effective way, and (b) the work of Bertsimas, Lulli, and Odoni (2011) that al- lows the use of alternative routing of flights, when the current re- sources decrease possibly because of bad weather. Given the success of this modeling approach to air traffic flow management, it is natural to ask: (a) Can we develop a modeling approach to general dynamic resource allocation problems that is flexible, tractable and widely applicable? (b) Can we give some insights (both theoretical and empirical) on the reasons of the approach effectiveness in the context of resource allocation? The broad framework we have in mind for Dynamic Resource Allocation Problem (DRAP) is as follows. The primitive quantities are: a set of resources R and a set of requests I belonging to a set of owners O that need to be processed by these resources over 0377-2217/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ejor.2013.10.063 ⇑ Corresponding author. E-mail addresses: dbertsim@mit.edu (D. Bertsimas), shubhamg@mit.edu (S. Gupta), lulli@disco.unimib.it (G. Lulli). European Journal of Operational Research 236 (2014) 14–26 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor