MSC 385 Production/Operations Management Dr. Stafford, Summer I, 2003
Practice Examination Questions: Operator-Machine Assignment Problem
The purpose of these, and all other sets of practice examination questions, is to help each student prepare
for the examinations in MSC 385. All questions provided are from old examinations given by Dr. Stafford.
A copy of all questions will be available on the MSC 385 web page. Copies of the keys (answers) to these
problems will also be available on the web page. Watch the course bulletin board for notice of when each
assignment and answer key has been posted to the web.
Question 1
A company produces a critical part on a set of multiple, identical machines. These machines are semi-
automatic in that, after they have been loaded and started, they process the part without need of further
human intervention until the part processing is completed. At that time, an operator must unload the
machine, reload it, and press the start button once more. Run time on these machines is 11 minutes.
The "setup time" consists of unloading (2 minutes) and loading (2 minutes). Each machine produces two
identical parts each machine processing cycle. Fully fringed labor for operating one or more of these
machines is $24/hour. Operating expenses for each machine are estimated to be $48/hour.
Part I Currently, the company assigns one machine to each operator. For this arrangement, answer
the following questions.
__________1 What is the cost per unit to produce the critical part under the one man-one machine
arrangement?
__________2 What is the operator idle time (in minutes) per hour under this arrangement?
__________3 What is the output per operator per 8-hour shift under this arrangement?
__________4 What is the machine idleness (interference) (in minutes) per machine per cycle under this
arrangement?
__________5 What is the cycle time under this arrangement?
Part II The company has decided to investigate the assignment of more than one machine to each
operator. The plan is to assign K machines to each operator such that the average
manufacturing cost of the critical part is minimized, where K = 1, 2, 3, .... Perform the necessary
calculations and analyses to answer the questions below.
__________6 What is the optimal number of machines to assign to a single operator in order to
minimize per-unit manufacturing cost?
__________7 For the number of machines determined for question 6, what is the minimum per-unit
manufacturing cost?
__________8 For the number of machines determined for question 6, what is the cycle time?
__________9 For the number of machines determined for question 6, what is the amount of time per
cycle (to the nearest 0.1 minute) that the operator is idle?
_________10 For the number of machines determined for question 6, what is the amount of time per
hour (to the nearest 0.1 minute) that each machine is idle?
_________11 What is the machine idleness (interference) per machine per cycle if 5 machines are
assigned to a single operator?
_________12 What is the operator idleness per hour if 4 machines are assigned to a single operator?
_________13 What is the cycle time, in minutes, if 5 machines are assigned to a single operator?
