Catawba Valley Highway Patrol
Case Project #2: Catawba Valley Highway PatrolMS 5023: Decision Analysis and Production ManagementDue: March 21, 2016Joshua StevensStudent ID: @01099386I. Executive SummaryDistrict commander Broderick Crawford of the Catawba Valley Highway Patrol (in western Pennsylvania) is attempting to assign a total of 23 highway patrol units to six distinctive various road segments throughout his district. Commander Crawford has intentions of assigning a designated number of patrol cars to each distinctive road segment by optimizing his fleet in a way that best suits five primary “goals”/ objectives (listed in order of importance): maintain operating costs to less than $450/day, reduce average accident rate for the district by five accidents per million miles traveled, achieve at least 350 physical contacts/ day and at least 30,000 sight contacts/ day by patrol units, and lower average response time to distress calls from 28 minutes to 15 minutes. By setting up a linear goal programming equation, placing the set-up in Microsoft Excel, and using Solver to create a “solution” that optimizes the priorities of the objectives of commander Crawford, we are able to provide a model of the number of patrol units to assign to each of the six varying road segments. Based on the requirements set-forth by commander Crawford, we are able to create an optimal solution that keeps operating costs less than $450/ day, reduces accidents by 5 per million miles traveled, maintains at least 350 sight contacts/ day, with at least 2 patrol units’/ road segment; yet a maximum of 5 patrol units per road segment. We were short 4900 sight contacts/ day (from a 30,000 goal), and the average response rate was lowered from 28 minutes to 15.96 minutes.
II. Formulation of Goal Programming Problem/ SetupCatawba Valley Highway Patrol:x₁ = Road Segment 1: interstate, northx₂ = Road Segment 2: urban area, northx₃ = Road Segment 3: four-lane highway, eastx₄ = Road Segment 4: two-lane highway, westx₅ = Road Segment 5: interstate/four-lane highway, southx₆ = Road Segment 6: two-lane highway (heavy truck traffic), southObjectives (goals) in order of importance:Limit daily operating costs to $45020x₁ + 18x₂ + 22x₃ + 24x₄ + 17x₅ + 19x₆ ≤ 450Reduce average accident rate for the district by 5 accidents per million miles traveled0.27x₁ + 0.21x₂ + 0.28x₃ + 0.19x₄ + 0.23x₅ + 0.33x₆ ≥ 5