Reference no: EM132224648

The grain harvesting season in the US Midwest is short, and farmers deliver their truckloads of grain to two identical, co-located giant central storage bins within a 2-week span. Because of this, grain-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bins. The two central bins are owned cooperatively, and it is to every farmer’s benefit to make the unloading/storage process as efficient as possible. The cost of grain deterioration caused by unloading delays and the cost of truck rental and idle driver time are significant concerns to the cooperative members. Although farmers have difficulty quantifying crop damage, it is easy to assign a waiting and unloading cost for truck and driver of $20 per hour. During the 2-week harvest season, the two storage bins are open and operated 16 hours per day, 7 days per week, and the two bins can together unload 30 trucks per hour on average, with an unload time coefficient of variation of 1.2. Full trucks arrive all day long (during the hours the bin is open) at a rate of about 25 per hour, following an exponentially distributed interarrival time.

To help the cooperative get a handle on the problem of lost time while trucks are waiting in line or unloading at the bin, we seek to find the following:

Note: Focus only on the two-bin storage system (ignore downstream grain processing, if any).

Show formulas.

Average Flow Time, T: The average time per truck in the system

Average Inventory, I: The average number of trucks in the unloading system.

Average Truck Waiting Cost: The total daily cost to the farmers of having their trucks tied up in the unloading process.

Bin Expansion Option: Farmers estimate that adding a new bin would cut unloading costs by about 65% next year. It will cost $8,000 to add the new bin during the off-season. Would it be worth the expense to add a new bin? Explain.