Wayne Winston - Operations Research

Case 8 - Emergency Vehicle Location in Springfield

Those are all the info available.

Can someone help me defining the objective function for this exercise? I am trying to minimze the total costs,however I do not really know which variables and parameters to include in the objective function.

I need to hand in the case by the end of the week, so your help would be highly appreciated. I am completely stuck!!

Cheers!

You are the logistics manager for the Springfield Fire Department. You are asked to develop a recommendation for providing emergency service to Springfield for next year. The department's resources include engine trucks, ladder trucks, and paramedic vehicles. The budget enables the operation of at most 15 vehicles for next year. Currently, seven engines, three ladder trucks, and five paramedic vehicles are in operation. This system runs 24 hours per day. The city has been divided into 10 zones as shown in Figure 1. The map is drawn to scale. Figure 1: Map of the city (17 miles by 11 miles) - X marks the spot of the existing sites and the possible sites in each one For each zone, the department has estimated the number of fire calls, the number of false alarms, and the number of medical calls per 12-hour day. These data are listed in Table 1). Currently, there are five fire stations in the city: these are listed in Table 1 Each existing station costs $20,000 per year to operate. The yearly costs for each potential station (including the amortized cost of construction) are also listed in Table ! Each station can hold three vehicles at most. For fire calls, an engine and a ladder truck must respond. For medical calls, a paramedic vehicle always responds and an engine also goes when one is available and closer than the nearest paramedic vehicle. On average, fire calls take 2.5 hours, false alarms 10 minutes, and medical calls 45 minutes. When vehicles are dispatched on a call, the closest idle vehicle is dispatched first. If no vehicles are idle, then the call must be sent to a private provider; these responses cost the Table 1: Demand information per year Zone Fire Calls False Alarms Medical calls 100 200 100 100 CRO- 1000 450 600 1300 1400 1000 800 1000 Base Cost (S/year) 40,000 Existing 35,000 50,000 Existing 50,000 Existing Existing Existing 35,000 300 650 city $5,000 per medical call, $15,000 per fire call, and $200 per false alarm. There is no queueing. The street network is largely rectangular, and the fire department estimates that the cost per mile for travel is $1.50 per mile for engines and ladders and $0.75 per mile for paramedic units. Your Goal Your job is to design a system for the fire department. The questions that should be considered are these What sites should be selected and how should the vehicles be distributed? Moreover, decide on the composition of the fleet of vehicles. If travel gets more expensive, how is the recommendation affected? If the cost of using the private provider increases, then how should the system be changed? Is all of this equipment needed to serve the public? How much more demand can be handled with the full complement of vehicles? Your report should include a description of your models and any assumptions made in model formulation