Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8Page 9Page 10Page 11Page 12Page 132004-06 Spring 2004 Optimal Group Assignment andScheduling Model Mark Turner Optimal Group Assignmentand Scheduling Model ForDr. James Smith Engineering Management, Information, and Systems Department Southern Methodist University School of Engineering Dallas, Texas 75275Optimal Group Assignmentand Scheduling Model ForDr. James Smith By:Mark Turner EMIS 4395 - Mark TurnerPage 1 of 12Executive Summary The need for this model rose when the United States Military decided to implement a new system involving the assignment of troops to different bases scattered around the globe. In order to test the new system, the Military decided to use students at various college campuses nationwide. The Military needed an efficient way to schedule hundreds of students to participate in these two hour sessions over the course of two weeks. The sessions, totaling sixty (60), were to be guided by two servicemen trained in the use of the system and required six (6) students at minimum and eight (8) at maximum. To solve the problem, a network model was constructed using the AMPL programminglanguage and applied to the data given by students. A corresponding front-end wasdesigned and implemented in Microsoft Excel, allowing less computer-savvy people touse an otherwise unfriendly interface. After the output of AMPL is formatted into a user-friendly format, the consequent schedules can be formatted and displayed. All of this isachieved with minimal input and action from the user. EMIS 4395 - Mark TurnerIPage 2 of 12Table of Contents Background of Project ................................................................... 4 Analysisof Situation.......................................................................6 BasicFlow of Network ................................................................... 8 Analysis and Managerial Interpretation....................................10 Conclusions....................................................................................10 Appendices AppendixA....................................................................................11 AppendixB....................................................................................12 EMIS 4395 - Mark TurnerPage 3 of 12Background of Project The United States Military has been developing a system to aid them in deploying troops to different bases scattered around the globe. The central idea behind the system is to allow troops to have more of a say in where they are stationed. The Military, realizing that some destinations would be more popular than others, decided to implement a type of bidding system to aid the selection process. For example, a soldier willing to be stationed in Siberia may get a pay raise, whereas a soldier wanting to be stationed in Hawaii may have to take a pay cut. Rank is also a deciding factor in this new system. When the time came to test the system, the military had another problem - scheduling people to test it. For this reason, the scheduling model used in this particular project was developed. The Military wanted to test the system at various college campuses and have students participate in the trials. Several concerns were raised when discussing the potential model: 1.Effectiveness of model 2.Ease of use 3.Portability 4.Cost The effectiveness of the model was a task easily explained. The efficiency offered by a networking model is easily noticed after more than ten students need to be scheduled. The costs of doing the project by hand are astronomical and extremely tedious work. On the other hand, the problem is extremely simple for a computer to solve. Another issue with the scheduling model was ease of use. The interface had to be as user-friendly as possible, as not all of the users would be as technically proficient as one would like. The answer to this problem lies in Microsoft Excel. Incorporating basic worksheet templates EMIS 4395 - Mark TurnerPage 4 of 12and macros allow users to accomplish sophisticated tasks by merely clicking a button. Through Excel, users are able to build new schedules, output raw data, and input optimal results; all by pressing a single button. Because the Military would like to use the system around various college campuses nationwide, portability is a pertinent issue. Unfortunately, because of the sheer size of the problem, only commercial software is able to solve it. AMPL, the language used for this model, is typically available at universities with engineering departments. Other than purchasing a license for commercial software, the cost of the project is negligible to the Military. The project was completed salary and cost free to the Military. EMIS 4395 - Mark TurnerPage 5 of 12Analysis of Situation The problems involved in the scheduling process are fairly clear - What is the optimal number of sessions that can be held with the amount of students available? These students need to be scheduled in two hour sessions from 9 AM —9 PM, Monday through Friday for two weeks, totaling sixty (60) sessions. The solution to this issue is found in the form of a maximum flow networking problem. The basic issues of the network are fairly easy to navigate. The largest problem in the project is the inclusion of a binary variable that effectively opens or closes the sessions for use. This means that a session is either used, or it is not. After it is determined that a session is to be used, the session must meet the bound requirements set by the user (in this model the minimum number of people is six, maximum is eight). After a thorough search of the internet, the AMPL programming language was picked to write the model in because of its reputation and documentation. The model consists of several sets of nodes and arcs that connect those nodes to allow the maximum flow from the source to sink nodes (i.e. - the most sessions scheduled). The source and sink nodes are artificial nodes placed on the beginning and end of the network flow model. Arcs connect the source node with other nodes that correspond to individual students. From there, another set of arcs connects a particular student with a session offering node (i.e. - the student is available for that session). Arcs that originate from the individual session nodes connect to the sink node. These arcs have the weight of the binary variable on them. If the sessions are in use, they