The number of arrivals per period is distributed according to the poisson with the expected value of 0.75 unit per period. the cost of waiting per unit per period is $3.20. The facility cost for serving one unit per period is $5.15. What expected service rate should be established if the service duration is distributed exponentially? What is the expected total system cost?

1 answer

Expected number of units per period(λ)=0.75unit per period
Cost of waiting per period(C_W)=$3.20

Facility cost per unit per period(C_f)=$5.15

The formula for calculating expected service rate is as follows
= λ+√((λC_W)/C_f )
 = 0.75 + √([(0.75)($3.20)]/$5.15) = 1.4326 units per period

TC_m = [($3.20 × 0.75)/(1.455 – 0.75)] + ($5.15 × 1.455) = $10.8975