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You have been asked to help schedule production on two assembly lines where six different products
are assembled. The two lines are identical and the demand rate (
) per day, production rate (
) per
day, holding cost (
), setup cost (
) and setup time (
) for each product is as follows:
Line 1 Line 2
Product A B C D E F
Demand rate (
) 4 4 6 6 3 3
Production rate (
) 30 30 40 30 40 40
Holding cost (
) 1 1 6 6 4 4
Setup time (
) 4 4 0.25 0.25 2 2
Setup cost (
) 1400 1400 87.5 87.5 700 700
While the production rates of each product are identical for both lines, the setup time (and hence cost,
which is simply proportional to the setup time) depends on the sequence of how they are assembled.
Specifically, the setup time is given as follows:
Setup Time for Product (Days)
A B C D E F
Previous Product
A 0.00 4.00 0.25 0.25 1.50 1.50
B 4.00 0.00 0.25 0.25 1.50 1.50
C 4.00 4.00 0.00 0.00 2.00 2.00
D 4.00 4.00 0.00 0.00 2.00 2.00
E 5.00 5.00 0.25 0.25 0.00 2.00
F 5.00 5.00 0.25 0.25 2.00 0.00IE 312 Optimization Fall 2013 Siggi Olafsson
Mike, the manufacturing engineering in charge of these lines, remembered from an IE undergraduate
course that it is possible to calculate the optimal cycle length for rotation schedules1
using the following
formula:
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Since that seemed like an easy approach for minimizing cost, Mike decided to set up a rotation schedule
for each line, but allow the two lines to have separate cycle times. He then assigned three products to
each line (product A,B and C to Line 1 and products D, E and F to Line 2), and by using the formula
above, found that the optimal cycle length should be 12.4 days and 7.6 days, for Line 1 and Line 2,
respectively.
Mike then calculated the required production runs to meet demand within each cycle using the formula
, resulting in runs of 1.65, 1.65, 1.86, 1.53, 0.57 and 0.57 for products A through F,
respectively. But he then discovered that there is a problem on Line 1. The total run time is 5.2 days and
the total setup time is 8.3 days, so during each 12.4 day cycle the line will be busy for 13.5 days! This
“optimal” solution cannot even be implemented as there is not enough time within the cycle to
complete the scheduled work.
Mike realizes that the solution he came up with is only optimal given the assumptions that he made, and
it unfortunately does not account for the setup times. It also makes other simplifying assumptions that
may not be needed. Since you are a well-known optimization expert, he has asked you to help find a
better solution for scheduling these assembly lines in the best possible manner.
1
A rotation schedule is a schedule where each item is run once each cycle.IE 312 Optimization Fall 2013 Siggi Olafsson
Project Details
This is a group project. You can form your own group of 2-3 people in each group. If you have problems
finding partners let me know as soon as possible and I will pair you up.
There are the following deliverables:
A PowerPoint presentation of your plan to solve the problem (5%). I will give you feedback on
the quality of the plan, but the grading will focus on the communication aspect, that is, the
quality of the presentation.
o Make sure that you correctly address the audience, which should be someone who does
not have a background in optimization (or even engineering), such as your boss or
another decision maker. In this presentation it is, for example, appropriate to talk about
what decisions need to be made but not to formulate decision variables.
o I do not have a fixed number of slides, but keep it short (3-5 slides).
This presentation is due November 15th
.
A report of your solution and final recommendation (80%). The expectations for the solution
and final report are as follows:
o I expect you to formulate the problem as a mathematical programming problem. There
are multiple ways to intuitively find a feasible solution to this problem. I expect you to
aim for an optimal solution.
o I expect you to use LINGO to solve this project.
o I expect you to use sensitivity analysis in interpreting the output when appropriate.
o The grading will be on how well you formulate this problem, how well you code your
formulation in LINGO, and how well you interpret the output.
o Note that there is no single correct formulation for the problem – assumptions will have
to be made, so make sure all of them are well justified. In fact, you may have more than
one formulation. For example, it is common to first come up with the most
comprehensive formulation that you can do, which would have high validity but be very
difficult to solve, and then a simplified version that you solve.
A PowerPoint presentation of your solution to your boss, that is, a high level description of the
report (15%). Again, the grading will focus on the communication aspect, that is, the quality of
the presentation.
The final report and second presentation are due December 13th
.
