Lingo Programing

IE 312 Optimization Fall 2013 Siggi Olafsson

IE 312 Project

Problem Description 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

P re

v io

u s

P ro

d u

ct

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 0.00

IE 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 schedules 1 using the following

formula:

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 15 th

.

 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 13 th

.