APPLYING DECISION UTILITY TO SOLVE PROBLEMS WITH LIMITED RESOURCES Authors: Ceyhun Ozgur, Valparaiso University J. Randall Brown, Kent State University

Decision Utility to Solve Problems with Limited Resources  Abstract  For application of decision utility involving variables that can be traded off, their wider use in actual business applications has been retarded by a variety of obstacles. This paper will first list a number of these obstacles and then suggest ways to overcome them.

Decision Utility to Solve Problems with Limited Resources  Let’s look at a situation situation encountered in 1970’s by one of the authors in devising a computerized quantitative production scheduling system for a tire production plant.  The schedule produced by the system was constrained by the machines available, the sequencing of the machines for each type of job, the flow of materials, the demand of make to order jobs, the demand of make to stock jobs, the job due dates, and the personnel available.

Decision Utility to Solve Problems with Limited Resources  After much thought, there were many reasons for the non-implementation  Job control  Efficient schedule  Short-term physical changes  Short-term priority changes  Trade-offs  Preference and knowledge input  Using the computer schedule as a tool  Incomplete information

Priority Class Scheduling  Priority class scheduling is used to reduce due date conflicts between marketing and the production schedulers by replacing due dates with production periods and priority classes.  The priority classes are used by the production scheduler as constraints on what can be scheduled in a production period.  If any job in a priority class is started in the production period, then all jobs in priority class i-1 must be completed within the production period.

Priority Class Scheduling Continued  This is the only constraint on the production scheduler and allows the scheduler to concentrate on optimizing manufacturing efficiency within the production period.  The constraint is so simple that its consequences are easily understood by those who assign jobs to priority classes but at the same time allows manufacturing some flexibility in scheduling.  the production scheduler can schedule a priority three job to be completed early in the production period as long as all priority one and priority two jobs are completed within the production period.

Priority Class Scheduling Continued  If only some priority three jobs can be completed in the production period, the selection of which jobs to produce is made entirely on the basis of production efficiency.  This gives some flexibility to manufacturing to optimize production efficiency.  The production scheduler only considers the priority classes when scheduling and does not even need to know the due dates of the jobs.

Priority Class Scheduling Continued  The marketing alone, without any help from the production schedulers, could determine the priority class for each job and let the production schedulers concentrate on increasing production efficiency.  Theoretically, priority class scheduling would greatly reduce the conflict between marketing and manufacturing.

Scheduling Police Stations  Attributes  Foot Patrol  Car Patrol  Detective Analysis  Office Work

Foot Patrol  Walking police to provide safety to especially urban areas such as assessing and solving conflicts between two or more citizens, arresting guilty or disobedient people if necessary

Car Patrol  Policemen or police women patrolling roads and highways, to control speeding, attend to broke down cars, attending vehicular accidents and or attending other suspicious activity in vehicles and police cars attending any disputes on the roads or in stores or in homes that cannot be reached by foot but still within the city limits

Detective Analysis  Detective analysis for crimes committed within the city limits but not yet solved  The evidence collected by detectives are to be used by prosecuting attorney in litigation of crimes committed against the public or the city

Office Work  Office and other miscellaneous work is used to ensure the city police department is working efficiently  The tasks may involve personnel attending the police department and answering any questions that general public might have, also serving as guards in city jail, as well as booking and finger printing arrested people, and performing arrested individuals their initial questioning

Trade-offs  Determine the correct balance between the jobs given the resources available.  Doing too much foot patrol takes resources away from car patrol and detective analysis, while doing no foot patrol would not be acceptable to the tax payers.

Maximin Objective Function  The Police Chief is trying to decide how many times the detective analysis or the office work will be done in lieu of foot patrol or car patrol.  The decision should be how much foot or car patrol should be completed in lieu of office work or detective analysis in a period in his district.  The police chief’s perfect complements preference structure is determined by having him or her complete a table.

Constraint Choice Table for Police Station Table 1: Constrained Choice Table for City Police Departments DESIRABLEPERCENT OF DESIRABLE QUANTITY ATTRIBUTESQUANTITY Foot Patrol20 Officers Car Patrol20 Cars Detective Analysis10 Detectives Office Work10 Officers Totals UTILITY

Attribute Value Table for Police Station Table 2: Attribute Value Table for City Police Departments LABORATTRIBUTE VALUES ATTRIBUTEHOURS0122A 2B Foot Patrol Car Patrol Detective analysis Office Work TOTAL LABOR HOURS UTILITY

Police Station Trade-0ffs  Suppose the only limiting resource needed to accomplish the jobs is labor measured in hours  The police chief estimates that one foot patrol requires 80 labor hours, one car patrol requires 40 labor hours, one detective analysis requires 150 hours, and one office work requires 40 labor hours. These estimates are entered in the LABOR HOURS column of Table 2 column 2A.

Police Station Trade-0ffs Continued  The labor hours needed to accomplish the attribute values in columns 0, 1, 2, 3, 4, 5, and 6 are computed and entered in the TOTAL LABOR HOURS row.  Suppose the police chief has 2074 labor hours available this winter. Then the amount of each attribute that provides the best balance while using no more than 2074 labor hours can be found by linear interpolation in Table 2.

Police Station Trade-Offs Continued  Suppose the city asked the Police Department what it could accomplish if the labor hours were increased from 2074 to  Using linear interpolation, Table 2 column 2B shows that 2438 labor hours would increase the detective analysis from 5.79 to 6.56, increase office work from 5.27 to 10.39, increase for foot patrol from 8.53 to 9.04, and increase car patrol from approximately 15 to 16.

Conclusions  The police chief avoided the job control obstacle as the police department viewed the computer schedule as simply a starting point and was free to change it as conditions warranted.  The computer schedule only gave the amounts of each job that could be accomplished and did not tell the chief what personnel should be assigned to which job or like priority class scheduling when the jobs should be done within the period.  The chief was free to devise his own work schedule within the computer schedule framework so he was hopefully motivated to design an efficient schedule and could not blame any inefficiency on the computer schedule.

Conclusions Continued  The chief were also free to respond to both short term physical changes and priority changes as they saw fit.  The preference and knowledge input obstacle and the tradeoffs obstacle were for the most part avoided by using the maximin value function supplied by the police department to drive the determination of the computer schedule.  Although there was some minimal training on how the quantitative scheduling algorithm worked, hindsight says that more effort should have been directed into training.

Overcoming Obstacles  Probably the most important idea is to make the quantitative scheduling technique accessible to the police chief as an integral tool in their day-to-day work.  Police chief must understand how the scheduling algorithm works so he knows not only its strengths but its weaknesses. Much more time must be spent in educating the chief so he can view the scheduling algorithm as an important tool that he can use.

Overcoming Obstacles Continued  Police chief must have constant access to the scheduling algorithm so he can run what if analyses. However, today the power of laptop computers and the internet make this access possible but the designers and programmers of the scheduling system must make this access the top priority in the design and implementation of the computerized quantitative scheduling system.  Ways to measure a chief’s value function and integrate that value function into his model must be invented. If this is done, the chief will feel ownership of the model and will not be afraid to use its results.