RI12008 07 March 2012 Computer Science IBM Research Report An Efficient Method to Formulate, Solve and Reuse Resource Allocation Problems Using Semantic Models Pranav Gupta and Biplav Srivastava IBM Research Division IBM India Research Lab 4, Block C, I.S.I.D. Campus, Vasant Kunj New Delhi 110070, India. IBM Research Division Almaden - Austin - Beijing - Delhi - Haifa - T.J. Watson - Tokyo - Zurich LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will proba- bly be copyrighted is accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). Copies may be requested from IBM T.J. Watson Re- search Center, Publications, P.O. Box 218, Yorktown Heights, NY 10598 USA (email: [email protected]). Some reports are available on the internet at http://domino.watson.ibm.com/library/CyberDig.nsf/home An Efficient Method to Formulate, Solve and Reuse Resource Allocation Problems Using Semantic Models Pranav Gupta and Biplav Srivastava IBM Research - India, New Delhi & Bangalore, India fprguptan,[email protected] Abstract 2009; Wang et al. 2008) and excavating earth during road construction(Ji et al. 2010). Resource allocation is a common problem in industry Some of the major issues in solving allocation prob- and real world wherein the demand for resources is matched to supply while optionally optimizing some lems are the following: (1) Setting up such problems objectives. However, setting up such problems for ef- for efficient solving is time-consuming and error-prone. ficient solving is time-consuming and error-prone be- This is because there is a diverse set of techniques cause there is a diverse set of techniques that could be that could be applicable depending on subtle problem applicable depending on subtle problem variations. In variations. (2) There is little or no reuse of infor- this paper, we seek to tackle this by creating a seman- mation sub-models which occur frequently. (3) Prob- tic model of demand, supply and allocation aspects of lem solving is highly dependent on availability of ex- the problem. Then using code-generation utilities for perts, although the solvers, that automatically solve on standard solvers and semantic queries, we show that the models, are easily available. Example: LP(AMPL one can create new allocation problems rapidly, reuse 2011), ILP(ILOG 2011), SAT(Moskewicz et al. 2001). results for known allocation instances while setting up new problems, discover problem characteristics quickly In this paper, we aim to capture common patterns and understand deep similarity among problems. The from allocation problems, create a reusable semantic breadth of allocation problems we consider are job-shop model to represent these patterns and reuse them while scheduling, tackling forest fires, assigning people to IT solving current and new problems types. The fact tasks in a service delivery center and evacuating peo- that semantic modeling can enable information shar- ple and goods. Thus, using semantic technologies, we ing, especially on the web, has long been articulated are able to extend the reach of allocation techniques to (Berners-Lee et al. 2001). However, surprisingly, this more real world applications. approach has not been used for resource allocation. Us- ing the models and and analysis techniques like seman- Introduction tic queries and model comparison, we can reuse and create problem instances faster. Furthermore, we have Much of the effort in solving a scheduling (and plan- developed utilities to automatically create solver inputs ning) problem is the time needed to set up such prob- from semantic models. Thus, we address the above is- lems. In order to reduce it as well as make the sues and employ semantic technologies to extend the whole process less error-prone, knowledge engineering reach of allocation techniques to more real world appli- for planning and scheduling has taken off in recent years cations. with there now being even a competition(ICAPS-KE Our contributions are that we: 2011) to compare such tools. We are especially inter- ested in efficiently solving the resource allocation prob- • identify common information requirements in alloca- lem(Riley 1996; Beck and Fox 1998) which is a common tion problem class of problems seen in industry and real world. • develop an ontology called Resource Allocation In these problems, the demand for resources is Model (RAM) to capture the demand, supply and matched to their availability or supply in order to allocation models achieve the most effective allocation. There exists a comprehensive summary of the past thirty years of re- • demonstrate the generality and benefits of the cre- search on algorithmic aspects of the allocation problem ated semantic models and its variant (Ibaraki and Katoh 1998). The breadth • address issues of formulating and solving allocation of allocation problems span job-shop scheduling(Gra- problems using the created ontology with a decision ham 1966), tackling forest fires(Bratten 1970), assign- support tool and methodology, respectively ing people to IT tasks in a service delivery center(Dixit et al. 2009), evacuating people(Inampudi and Ganz In what follows, we first define the terminology used, motivate a sample of allocation problems: job-shop Copyright c 2012, Association for the Advancement of Ar- scheduling, assigning people to IT tasks in a service tificial Intelligence (www.aaai.org). All rights reserved. delivery center and tackling forest fires, and demon- # Term Description Examples Job Shop: The job shop (scheduling) problem(Gra- 1 Problem The analytical problem Resource allocation solved ham 1966) is that of efficiently allocating resources to 2 Problem Real-world Work force matching, domain situation for problem Fire-fighting a demand of a set of N jobs (J = fj1; j2; ::jN g) to the 3 Problem Type of problem Maximal matching, available supply of M machines (M = fm1; m2; ::mN g). class objective demand satisfiability, maximum utility An allocation is an assignment x of J to M. If C(x) rep- 4 Scenario Set of parameterized demand supply feasibility resents the cost of an assignment, the allocation prob- problem instances constraints, demand attributes 5 Problem Exact set of demand, lem is to find x with minimum C(x). We will refer to instance supply, constraints the problem as Job-Shop. Variants of the problem dif- and objective fer in the requirements of the job for processing, the capability of the machines and how the cost of assign- Table 1: Terminology used in the paper. ment is calculated. Although the simplest of the allo- cation problems considered, it is NP-Hard to solve by directly mapping the known NP-Hard Traveling Sales- strate how they may be reused during evacuation of person Problem(Applegate et al. 2006) to it (let m=1; people and non-living goods (earth). Then we present salesman is the machine and the cities are the jobs). the RAM semantic model capturing the common in- Workforce Matching: An IT organization is re- formation requirements. Next, we use the case-study sponsible for providing delivery services to its customers of work-force matching to show how the ontology may across the globe. Here demand is a steady stream of op- be used. We discuss how the ontology can be consumed portunities/projects which can be described with some and demonstrate its benefits in new situations. We con- structured fields such as skills required, duration of clude with related work and contributions. To the best the project, cost description, geo-spatial attributes and of our knowledge, this is the first work on knowledge business restrictions and some unstructured attributes engineering in resource allocation problems. such as good communication skills, development expe- rience should be more than 5 years, etc.(Dixit et al. Preliminaries 2009). To meet this demand, they carry workforce vary- ing in their skills, aspirations, preferences, cost and ex- In this section, we clarify the terminology used, illus- perience levels which evolves continuously as resources trate resource allocation problems and motivate the aim move in and out, acquire new skills and experience over of the paper. time. By allocation, we refer to the matching of certain Terminology Used skilled resources meeting all or some requirements spec- ified in a demand description for a specified duration. Since resource allocation problems appear in a variety Forest Firefighting: On average, more than of areas, we clarify the terminology used in the paper 100,000 wildfires, also called wild land fires or forest in Table 1. Among the terms, scenario is peculiar to fires, clear 4 million to 5 million acres (1.6 million to industry since a collection of problem instances, slightly 2 million hectares) of land in the U.S. every year. Un- varying in inputs, are solved together to arrive at a controlled blazes fueled by weather, wind, and dry un- decision for a business situation. derbrush, wildfires can burn acres of land-and consume everything in their paths-in mere minutes. These fires Sample of Allocation Problems need to be contained and a tactical plan is created in We look at allocation problems in 4 different domains. wake of such a demand. Demand for firefighting re- We use three to build the semantic model and the fourth sources and equipments can be assessed by forest agen- to test it. cies depending of the various field factors and sent to dispatch locations(Bratten 1970). These dispatch lo- cations are spread across the state and some actor is E1 responsible for allocating type of resources, how many E2 E3 and from where they should be dispatched.