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# Process Flow Time - Queueing Problem and Critical Assumptions

See the attached file.
Fort Lost-in-the-Woods is a basic training center for new Army recruits. Upon arriving at the military post the new recruits are processed through the Induction Center that involves three steps: background information gathering, medical examination, and barracks assignment. Arriving inductees first enter the Center's Background Information room, which contains 5 computer terminals. The inductees complete in about 15 minutes a computerized questionnaire that covers personal and medical information. When done, the recruit moves to the medical exam wait area. Inductees are admitted to the examination area one-at-time when called by the nurse. The recruits move through a single channel series of stations in fixed sequence where individual test are completed. Space between test stations is minimal. Once the medical exam is finished, the inductee is assigned to a platoon and given directions to the barracks area.

The data below provide cycle times for each examination station and expected arrival rates for inductees for a typical week day. The Induction Center is fully staffed when it opens at 8 a.m. in the morning and continues processing until the last recruit is finished. (Assume inductees start arriving at 8 a.m.)

Medical Examination Stations Expected Inductees

Station No. Test Duration (minutes) Time Arrivals/hour
1 Vision 5 8 - 9 am 16
2 Nose & Throat 4 9 - 10 am 18
3 Hearing 3 10 - 11 am 18
4 Respiration 2 11 - Noon 9
5 Immunization 2

a) Estimate the number of medical exam wait area chairs needed for the waiting inductees at 10 a.m.?

b) What is the expected flowtime for the person entering the system at 11 a.m.?

c) What is your estimate of the maximum number of chairs needed in the medical exam wait area at any time in the morning?

d) What are the critical assumptions (not the stated constraints) for your answers in parts a and b? In other words, how good, qualitatively, are you answers?

#### Solution Preview

a). from 8 - 10 am, the number of arrivals is 16 + 18 = 34. The max number of those examined is determined by the bottleneck factor, which in this case is Vision testing (taking 5 minutes, whereares other takes from 2 - 4 minutes). So waiting area chairs are needed for those who cannot be examined, the number of which is 34 - 24 = 10. So we need 10 chairs.

b). From 8 - 11 am, the number of arrivals ...

#### Solution Summary

Process flow time is investigated and discussed. The solution is detailed and well presented.

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