ISD 599/MFG 599 XXXXXXXXXXHomework No. 1
Module 3: SMART PRODUCTION SYSTEMS XXXXXXXXXXDue Feb 10, 2023
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• Reading Assignment: Lecture Notes 1 and 2.
• Problems:
Problem 1. The efficiency, ??, of a machine can be increase by either increasing its average uptime,
??????, or decreasing its average downtime, ??????????. Is it better to increase ?????? by a certain factor or
decrease ?????????? by the same factor, so that ?? is maximized?
Problem 2. Consider a serial production line with eleven identical machines and ten identical
uffers. Assume that one of the machines can be replaced by a more efficient one. Which
machine should it be so that the throughput of the system is maximized? (Hint: Use the
eversibility law to answer this question.)
Problem 3. Consider a serial production line with ten identical machines and nine identical
uffers. Assume that the capacity of one buffer can be increased. Which one should it be should
e so that the throughput of the system is maximized?
Problem 4: The layout of a production system for an automotive ignition device is shown in Figure
1. It consists of four main operations: Housing Subassembly, Valve Body Assembly, Injector
Subassembly, and Injector Final Assembly. In addition, the system contains Shell Assembly, three
Welding operations (L.H.W., U.H.W., and Weld), two Overmold operations (O.M.1 and O.M.2),
two Set Stroke operations (Stroke 1 and Stroke 2), one Leak Test operation (L.T.) and one High
Potential operation (Hi Pot). Finally, the system includes five buffers positioned as shown in
Figure 1 and conveyor buffering among all other operations. Construct a structural model for this
system and simplify it to an assembly line with one merge operation.
XXXXXXXXXXFigure 1
Problem 5. The layout of a production system for another automotive ignition device is shown in
Figure 2. It consists of 15 operations, separated by buffer- conveyors. Construct a structural model
for this system and simplify it to a serial line.
XXXXXXXXXXFigure 2
Problem 6. Consider a two-machine Bernoulli line and assume that N = 5 and ??1??2 = 0.81.
XXXXXXXXXXa) Under this constraint, find ??1 and ??2, which maximize PR. (You may use the trial and e
or
method to accomplish this; alternatively, you may think a little bit, look at the expressions for ????,
make an “educated guess” and verify it by calculations.)
XXXXXXXXXXb) For these ??1 and ??2, calculate PR, WIP, ????1 and ????2. What can you say about qualitative
features of WIP, ????1 and ????2?
XXXXXXXXXXc) Interpret the results and formulate a conjecture concerning the optimal allocation of ????’s.
XXXXXXXXXXd) What is the inte
elation of ????1 and ????2 under this allocation?
XXXXXXXXXXe) What is the relationship between ?????? and buffer capacity?
Problem 7. Consider a two-machine Bernoulli production line and suppose that each machine
produces a good part with probability ???? and a defective part with probability 1 − ???? , ?? = 1,2.
Assume that quality control devices operate in such a manner that a defective part is removed from
the system immediately after the machine that produced this part. Derive the formulas for the
production rate of good parts, ??????, and for ??????,????1 and ????2 in this system. (Hint: Use ??1??1 as
the new parameter, ??1′ , of the first machine.)
Problem 1. From the reading materials PDF file
Page 114, Question #5. You do NOT need to draw the string diagram, multicolumn process
chart, and the from-to chart. Please consider a sequential layout of 1->3->4->5->6-2->7,
(1) compute the layout efficiency based on string diagram
(2) Generate from-to chart, assume all the products are the same in weight.
(3) Compute the penalty points of the layout based on the from-to chart. Assume no penalty fo
ack-tracking. Also, computer the layout efficiency based on the from-to chart.
Problem 2.
Problem 3. Page 246, 12.3 (please indicate the detailed sequence of departments going into the
picture).
Problem 1. There are 8 departments in the plant and the relationship chart is given as
follows. Consider SLP method.
Table 1.1 Value chart
XXXXXXXXXXImportance value
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
6 - 0 1
7 - 0
8 -
A semiscale grid representation of a layout is given as
8 8 2 2
8 8 2 2
1 8 2 2
1 3 3 2
1 3 3 2
1 3 3 4
1 3 3 4
1 3 3 4
5 3 3 6
5 7 7 6
Table 1.2 Efficiency evaluation (i.e., flow multiply by distance)
XXXXXXXXXXEfficiency
value
1 -
2 -
3 -
4 -
5 -
6 -
7 -
8 - 0
Please answer the following questions:
(1) Fill in the importance values in table 1.1. Based on the importance value, what is the
sequence of the departments going into the nodal representation diagram? (10 points)
(2) Please fill in the efficiency values of department 2 and 4 only in Table 1.2 based on the
semi-scale layout and Table XXXXXXXXXXpoints)
Problem 2
(1) How do you suggest this module should be updated to deliver the best value possible
within 4 lectures ? (5 points)
homework3
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