# Question: A job shop is being laid out in a square

A job shop is being laid out in a square area with 600 feet on a side, and one of the decisions to be made is the number of facilities for the storage and shipping of final inventory. The capitalized cost associated with providing each facility would be $10/hour. There are just four potential locations available for these facilities, one in the middle of each of the four sides of the square area as shown in the figure.

The loads to be moved to a storage and shipping facility would be distributed uniformly throughout the shop area and they become available according to a Poisson process at a mean rate of 90 per hour. Each time a load becomes available, an appropriate materialshandling vehicle would be sent from the nearest facility to pick it up (with an expected loading time of 3 minutes) and bring it there, where the cost would be $40/hour for time spent in traveling, loading, and waiting to be unloaded. The vehicles would travel at a speed of 20,000 feet per hour along a system of orthogonal aisles parallel to the sides of the shop area.

Another decision to be made is the number of employees (m) to provide at each storage and shipping facility for unloading arriving vehicles. These m employees would work together on each vehicle, and the time required to unload it would have an exponential distribution, with a mean of 2/m minutes. The cost of providing each employee is $15/hour.

Determine the number of facilities and the value of m at each that will minimize expected total cost per hour.

The loads to be moved to a storage and shipping facility would be distributed uniformly throughout the shop area and they become available according to a Poisson process at a mean rate of 90 per hour. Each time a load becomes available, an appropriate materialshandling vehicle would be sent from the nearest facility to pick it up (with an expected loading time of 3 minutes) and bring it there, where the cost would be $40/hour for time spent in traveling, loading, and waiting to be unloaded. The vehicles would travel at a speed of 20,000 feet per hour along a system of orthogonal aisles parallel to the sides of the shop area.

Another decision to be made is the number of employees (m) to provide at each storage and shipping facility for unloading arriving vehicles. These m employees would work together on each vehicle, and the time required to unload it would have an exponential distribution, with a mean of 2/m minutes. The cost of providing each employee is $15/hour.

Determine the number of facilities and the value of m at each that will minimize expected total cost per hour.

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