Sid Das Brick Distributors currently employs 1 worker whose job is to load bricks on outgoing company trucks. An average of 24 trucks per day, or 3 per hour, arrive at the loading platform, following a Poisson distribution. The worker loads them at a rate of 4 trucks per hour, following approximately the exponential distribution in his service times.
Das believes that adding a second brick loader will substantially improve the firm’s productivity. He estimates that a two-person crew at the loading gate will double the loading rate from 4 trucks per hour to 8 trucks per hour. The following is an analysis of the effect on the queue of such a change:
Number of Brick Loaders
1 2
Truck arrival rate (?) 3/hr. 3/hr.
Loading rate (µ) 4/hr. 8/hr.
Average number in system (Ls) 3 trucks 0.6 truck
Average time in system (Ws) 1 hr. 0.2 hr.
Average number in queue (Lq) 2.25 trucks 0.225 truck
Average time in queue (Wq) 0.75 hr. 0.075 hr.
Truck drivers working for Sid Das earn an average of $15 per hour. Brick loaders earn about $9 per hour. Truck drivers waiting in the queue or at the loading platform are drawing a salary but are productively idle and unable to generate revenue during that time.
What would be the HOURLY cost savings to the firm if it employed 2 loaders instead of 1. Be sure to show your work.