A small cross-docking system has three incoming docks and four outgoing docks. Trucks arrive at each of the three incoming docks with interarrival times distributed as UNIF(35, 55)—all times are in minutes. Each arriving truck contains UNIF(14, 30) pallets (truncated to the next smaller integer), which we can assume are unloaded in 0 time. Each pallet has an equal probability of going to any of the four outgoing docks. Transportation across the dock is provided by three fork trucks that each travel at 60 feet per minute. Assume that the distance between any incoming dock and any outgoing dock is 50 feet. Also assume that the distance between adjacent incoming docks (and adjacent outgoing docks) is 15 feet.

(a) Develop a model in which the fork trucks remain where they drop off their last load if there are no new requests pending.

(b) Modify your model so that free fork trucks are all sent to the middle (Dock 2) incoming dock to wait for their next load.

(c) Modify your model so that each fork truck is assigned a different home incoming dock and moves to that dock when there are no additional requests pending. Compare the results of these three systems, using the pallet system time as the primary performance measure. Be sure to back up your comparison with a proper statistical analysis.