Tag: linear programming

OM Podcast #29: The Art & Science of Developing Supply Chain Strategies

Happy New Year!  After a brief end of semester break to enjoy the holidays with family, we’re back with the first podcast of 2025.  In this podcast, Barry Render interviews Alex Klein, Senior Manager of Supply Chain Solutions for APL Logistics, a third-party logistics provider.  Alex and Barry discuss the art and science of developing supply chain strategies for shippers with three fascinating, wide-ranging real world examples from Alex’s career.

Transcript

A Word document of this podcast will download by clicking the word Transcript above.

 

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Instructors, assignable auto-graded exercises using this podcast are available in MyLab OM. See our earlier blog post with a recording of author and user Chuck Munson to learn how to find these, or contact your Pearson rep to learn more! https://www.pearson.com/en-us/help-and-support/contact-us/find-a-rep.html

Guest Post: Building Furniture in a Linear Programming Class

Bob DonnellyToday’s Guest Post is by Dr. Robert Donnelly, Professor of Management at Goldey-Beacom College, in Delaware, who describes one exercise he uses to teach LP (Module B).

One of the challenges of teaching linear programming is the intangible nature of the topic which causes many students to have anxiety. One method that I use in my LP class is to pass out 6 large and 8 small Duplo-sized Legos to small groups of students and ask them to build tables and chairs. This is an example of a product mix problem with the objective of maximizing profit.

LP exampleAs you can see, each table has 2 large and 2 small blocks while each chair has 1 large and 2 small blocks. Each table contributes $16 in profit while each chair contributes $10 in profit.

Tables

Chairs

Availability
Large Blocks

2

1

6
Small Blocks

2

2

8
Profit

$16

$10

I start a class discussion on the feasible solutions that were discovered along the way to the optimal solution, which is to produce 2 tables and 2 chairs earning a profit of $52.

Tables

Chairs

Profit

0

4

$40

1

3

$46

2

2

$52

3

0

$48

I solve this problem graphically showing the 4 corner points and the optimal solution.

I introduce shadow prices by offering the students an additional large block and ask how much they are willing to pay for it (answer = $6). I show a second large block and ask how much the students are willing to pay for it (answer = $6). Finally, I show the students a third large block and ask how much they will pay for it (answer = $0).  I lead a discussion on the concept of shadow prices and finally wrap up with solving the Legos problem on Excel.

I find that playing with Legos in class lightens the mood and makes LP more understandable.

Guest Post: Making LP Relevant to Students

steve harrodDr. Steven Harrod is Assistant Professor of Operations Management at the University of Dayton. He shares a tip on teaching LP today.

It takes some creativity to make linear programming (see Module B in the Heizer/Render text) relevant to students. Here is an activity that offers a discussion of energy, transportation, and air pollution. The topic is coal-burning electric power plants, and it is an example of the blending problem.

Nearly half of all electricity in the U.S. is produced by burning coal, and nearly all of this coal moves by rail. Coal is an organic material that varies considerably in cost, power, and pollution content. Power plants frequently blend different coals to achieve their desired performance. Trains magazine published a detailed article on the movement of coal and its consumption by electric power plants in 2010. The readings and class materials may be downloaded here.

The documents package includes a quiz you may assign to motivate the reading assignment, a longer version of this Guest Post, and a sample spreadsheet model. Start the class discussion by drawing the class’s attention to the power plant at Monroe, Michigan. If you have an overhead projector with internet access, use Google maps to display a satellite photo of the plant. The lakeside plant has a prominent railroad loop and coal storage facility. You may also wish to explain how a power plant converts coal into electricity, and the environment concerns (sulfur causes acid rain and ash must be disposed of).

The challenge question for the students is: what coal should this plant purchase to satisfy energy and pollution limits at minimum cost? The formulated and solved LP leads to an optimal blend of three of the five coal sources. Ask the students, “is this intuitive?” Would you have been able to reach this conclusion without LP? Discuss at length and experiment with reducing or eliminating the pollution limits. This exercise may lead to a lengthy discussion of energy policy, environmental policy, and their joint effect on transportation demand.

Video Tip: Scheduling Employees at Hard Rock Cafe

One of my favorite videos is a short  (4.5 min.) study of how Hard Rock Cafe schedules its 160 servers at the giant 1,100 seat Hard Rock here in Orlando. I show it when I teach scheduling (Ch.15) and linear programming (Mod.B in the hard cover text). The  topic is one  many students relate to, especially if they have worked in retail or restaurants, where schedules are always a sensitive subject.

In Hard Rock’s case, the sales forecast is critical. Many factors are considered in deciding how many servers to call in, including historical sales, major conferences in town, season, etc. Each employee submits a weekly request form, and then an LP package takes over, with the objective of minimizing the number of employees per shift. It turns out that the system works quite well and employees are usually satisfied. Turnover, even during non-recession times, is 1/2 the industry average.

What we don’t mention in the video is that the managers never mastered the scheduling software, which is actually somewhat complex. But one, very enterprising, young server offered to handle the weekly task on his own. He collects all the forms, goes down into a basement office every Saturday, where it takes him about 6 hours to input the data and churn out the schedules. He does this for no additional pay! Why, you ask? Because  constraints and schedules are set by seniority, and he is allowed to assign himself the highest priority, a 9. It turns out that a great schedule, at the right work stations, can make the difference of $100’s a week in tips.

This topic is one that students with jobs are more than happy to discuss..