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Words 344

Pages 2

Ricky Norberg

Quantitative Methods - 1

Everest University Online

Date - 03/19/2016

Instructor: Robert Miner

1

1.

Over a three week (21-day) scheduling period, each unit will be scheduled for seven days. Normal staffing requires 186 firefighters to be on duty every day. Thus, each unit needs to provide staffing for 7*186=1302 firefighter days. During a three week period, each firefighter provides 6 days of service. Therefore, Base no of firefighters needed by each unit=1302/6 = 217 Base no of firefighters needed by each unit=217.

2.

Using the normal distribution, Z value corresponding to probability of 0.3548= - 0.3722 Optimal no of additional firefighters based on given distribution: Q*= μ+Ζσ μ=20 σ=5 Ζ=0.3772 Thus, Q*=20-0.3772(5) =18.14 Using minimum cost criteria, 18 firefighters should be added in each unit in order to cover daily absences.

3.

On a given day, what is the probability that Kelley-day firefighters will be called in to work overtime? Optimal probability that demand will exceed Q*: P (Demand>Q*) =1-((Cu/ (Cu +Co)) P (Demand>Q*) =1-0.3548 = 0.6542 the probability that Kelley-day firefighters will be called in to work overtime=0.6542

4.

Based on the three-unit organization, how many firefighters should be assigned to each unit? What is the total number of full-time firefighters required for the River City Fire Department? Firefighters for each unit=Base no of firefighters + Additional firefighters =217 +18 =235 2

Firefighters for each…...

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