Question

A small factory consists of a machining center and inspection station in series. Unfinished parts arrive to the factory with exponential interarrival times having a mean of 2 minutes. Processing times at the machine are uniform on the interval [0.65, 0.70] minute, and subsequent inspection times at the inspection station are uniform on the interval [0.75, 0.80]. Ninety percent of inspected parts are “good” and are sent to shipping; 10 percent of the parts are “bad” and are sent back to the machine for rework. Both queues are assumed to have infinite capacity.

        Let Y_i be a random variable representing the number of parts produced during the ith hour. Generate 10000 Y_is, and compute ten sample means and sample variances using 1000 Y_is each, respectively. Comment on the convergence of Y_ito the steady-state distribution Y.

Answer 1

YyHomework # 2 Solutions
Chapter 3 Questions:
1. What is a bottleneck station?
Answer: The bottleneck station is the slowest workstation in a production line, and therefore it limits the pace
of the entire line.
2. What is production capacity?
Answer: As defined in the text, production capacity is the maximum rate of output that a production facility
(or production line, work center, or group of work centers) is able to produce under a given set of assumed
operating conditions.
3. How can plant capacity be increased or decreased in the short term?
Answer: As listed in the text, the two ways that plant capacity can be increased or decreased in the short term
are (1) change the number of work shifts per week Sw or (2) change the number of hours worked per shift Hsh.
4. What is utilization in a manufacturing plant? Provide a definition.
Answer: Utilization is the amount of output of a production facility relative to its capacity. Expressing this as
an equation, U = Q/PC, where U = utilization, Q = actual output quantity produced during the period of
interest, and PC is the production capacity during the same period.
5. What is availability and how is it defined?
Answer: Availability is a reliability metric that indicates the proportion of time that a piece of equipment is up
and working properly. It is defined as follows: A = (MTBF – MTTR)/MTBF, where A = availability, MTBF =
mean time between failures, and MTTR = mean time to repair.
6. What is manufacturing lead time?
Answer: As defined in the text, manufacturing lead time is the total time required to process a given part or
product through the plant, including any lost time due to delays, time spent in storage, reliability problems,
and so on.
7. What is work-in