Question: Trucks arrive at a distribution center at a rate of 3 trucks/hour. The average truck contains 50 pallets and it takes a forklift, on average, 0.5 minutes to unload a single pallet. Dock doors are unavailable 60 minutes per shift due to employee breaks, thus a single dock door is available for 7.0 hours of an 8 hour shift. Assume each dock is 97% reliable and has 100% performance [Make sure to use consistent units throughout the problem].

Based on averages determine the number of dock doors required to service the truck demand using the forklift processing time as the unit (truck) service/processing time (i.e. time to unload one truck).

Assume that truck arrival follows a normal distribution with a standard deviation of 0.5 trucks/hour. Draw the truck arrival normal distribution PDF and highlight the area of the truck arrival distribution that the number of dock doors designed in part (a) will be able to sufficiently service. Now, determine the number of dock doors required to cover 85% of the truck arrival normal distribution (z value = 2).

Assume that the truck inter-arrival time and service time follows an exponential distribution, allowing for the use of the (M/M/c):(GD/Inf/Inf) queuing theory model. Determine the expected number of trucks in queue (Lq) and the expected wait time in queue (Wq) for the dock doors specified in part (a) and part (b).

Comment on the differences between designing the number of dock doors using part (a), (b), and (c) and how this may impact the physical facility operations.