-Catawba Valley Highway Patrol

Case Problem CATAWBA CATAWBA VALLEY VALLE Y HIGHWAY HIGH WAY PATROL PATROL

Broderick Crawford is the district commander for the Catawba Valley highway patrol district in western Pennsylvania. He is attempting to assign highway patrol cars to different road segments in his district. The primary function of the highway patrol force is to patrol roads outside incorporated city and town limits in the district to deter traffic violators and accidents. This objective is typically achieved by maintaining a visible presence letting motorists see patrol units on a regular basis and giving out warnings citations and so forth. !econdary activities of a patrol unit include providing pr oviding assistance to motorists answering distress calls handling emergencies and accidents when called to the scene and occasionally apprehending criminals. Commander Crawford has "# patrol cars that he wants to assign to the following si$ major road segment areas% road segment & interstate north road segment " urban area north road segment # four'lane highway east road segment ( two'lane highway west road segment ) interstate*four'lane highway south road segment + two'lane highway ,heavy truck traffic- south ach of these road segments includes the primary arteries as indicated earlier plus adjoining roads. /ll the road segments have different levels of traffic density and accident rates which are key factors in determining how many patrol units to assign. However these factors do not always coincide. 0or e$ample interstate highway segments typically have high traffic density but low accident rates whereas some two'lane highways high ways have low traffic density but high accident rates. 1ifferences often occur because of variations in road conditions ,such as sharp curves visibility visibility and width-. 2ther conditions such as heavy truck traffic ,as on segment +- also contribute to high accident rates. ach segment re3uires different operating costs including maintenance and repair fuel and so on because of different operating conditions. The commander4s most pressing objective is to limit daily operating costs to 5()6. The daily dail y operating costs per road segment are as follows% Road Segment & " # ( ) +

Operating Cost !" "6 &7 "" "( &8 &9

The commander would like to reduce the accident rate for the district as well as increase both physical and sight contacts which are deterrents to potential traffic violators. The commander would also like to achieve a reasonable average response time for a patrol unit to respond to a call for each road segment. The average accident rate reduction ,per million miles traveled- and physical contacts and sight contacts per car for each road segment are shown in the following table% Patrol #nit Physical /ccident :eduction ,per million !ight Contacts Contacts miles traveled,per day,per dayRoad Segment & 6."8 &7 &866 " 6."& "+ 966 # 6."7 &6 +)6 ( 6.&9 #( "#6 ) 6."# ") &+66 + 6.## &8 )"6 The commander4s second'most'important goal is to reduce the average accident rate for the district by five accidents per million miles traveled. The commander4s ne$t goals ,in order- are to achieve #)6 physical contacts and #6666 sight contacts per day in the district. ;f no patrol units are assigned in the district the average time to respond to a distress call anywhere in the district from the main district head3uarters and motor pool is "7 minutes. ach car assigned to a road segment reduces the overall average response time in the district by the following amounts% Red$%tion in A&erage Response Road Segment Time min'" & 6.#" " 6.+) # 6.(# ( 6.78 ) 6.)) + 6.(9 The commander4s last objective is to achieve an average response time to distress calls of &) minutes. Because of local and political pressure the commander has to assign at least two patrol units to each road segment. ;n addition the commander believes that a ma$imum of five patrol units is sufficient for any particular road segment. 0ormulate and solve a goal programming model to determine the number of patrol units to assign to each road segment to achieve the commander4s goals.