Problem 1: You are a retailer who buys a widget at a wholesale price $3.00 from a supplier and retails it for $4.00. It costs your supplier $2.00 to make the widget. Unsold widgets are marked down and sold for $1.50. Demand is uncertain and uniformly distributed between 6 and 10 units. That is, it is equally likely that demand is 6, 7, 8, 9, or 10 units. [Hint: Supply chain management problem]
a. How many widgets should you stock?
b. When will the channel (supplier and retailer) profits be maximized?
c. Assume demand is normally distributed with a mean demand of 8 units with a standard deviation of 2 units. How many units should he stock now?
Problem 2: Throughput analysis problems
a. You are traveling down a one lane highway, marked with mile markers. You are traveling the speed limit of 60 miles an hour. The average car length is 20 feet and the average distance between cars is 40 feet.
i) Assuming the portion of the "system" we are analyzing is the stretch of highway between two mile markers, what is the throughput time for one car?
ii) Assuming a steady flow of cars entering the "system" (between two mile markers), what is the cycle time?
b. You are traveling down a two lane highway marked with mile markers. You are traveling the speed limit of 60 miles an hour. The average can length is 20 feet and the average distance between cars is 40 feet.
i) Assuming the portion of the "system" we are analyzing is the stretch of highway between two mile markers, what is the throughput time for one car?
ii) Assuming a steady flow of cars entering the "system" (between two mile markers), what is the cycle time?
c. You are traveling down a one lane highway You are traveling the speed limit of 60 miles an hour. The average can length is 20 feet and the average distance between cars is 40 feet. In addition, the following conditions exist:
i) A gate at the beginning of the mile stretch opens every 5 seconds, letting one car in.
ii) Another gate, located at the half-mile, opens every 15 seconds, letting one car through.
iii) In the interest of simplicity, assume cars can go from 0 mph to 60 mph and from 60 mph to 0 mph in 0 seconds
- Where would the bottleneck be in this system? Why?
- What would the throughput time be?
- What is the cycle time for this example?
Problem 3: Stermon Mills: An Options Approach
Stan Kiefner was intrigued by Bill Saugoe's presentation, but was not at all happy with the marketing department's assessment of the value of flexibility to Stermon.
"Let's look at this another way," suggested Kiefner, "let's forget about customizing for now. Increasing the range of machine 4 would allow us to produce a lot of standard grades that our customers already want. We just don't offer them. Prices for sheet are so variable at the moment—I'm sure we could stabilize our revenues—maybe even increase them—if we only had the ability to make a few extra grades, and go after those grades where we can find the best price."
"Bill—how many grades do we make in a two-week run on #4?" asked Kiefner.
"Oh...about five—we pick the five that'll give us the best price and run through them. We usually have a good idea what the prices will be by Monday morning. We make pretty much equal tonnage of each of those five grades, giving us a total of about 3,920 tons in the two weeks"—replied Saugoe.
"But if we ran one-week cycles, we could pick a different five grades every week?"
"Yes—I guess, but that wasn't quite how we had been looking at it..."
"Well, why don't you get Elly and her Sales people to look at the prices our top ten merchants have been paying for the grades we could make on machine 4. Then let's figure out what advantage we'd get from broadening the range or going to a one-week cycle, or maybe doing both." suggested Kiefner.
Reluctantly, Saugoe relayed the instructions to Elly Ryesham. This was a different way of looking at it altogether. Ryesham did some investigation and sketched out a note to Saugoe.
Price per ton in dollars
Grade/Week 1 2 3 4 5 6 7 8 9 10
A 780 764 793 845 749 819 725 770 835 837
B 786 847 751 754 776 828 850 799 830 821
C 757 735 709 738 710 801 767 809 806 704
D 766 732 778 723 719 801 775 738 802 738
E 788 811 793 780 745 722 792 749 802 820
F 789 761 720 792 846 737 755 735 836 730
G 770 739 762 783 785 797 809 810 780 816
H 810 751 742 761 735 847 846 200 200 200
I 789 841 765 768 756 840 739 780 820 757
J 786 765 843 846 720 730 795 832 817 764
K 772 777 740 805 732 782 753 820 736 831
L 792 768 804 814 795 840 750 827 742 781
M 766 772 738 815 781 733 798 781 737 805
N 785 775 742 792 825 735 745 735 739 794
O 765 731 812 802 716 714 800 776 725 796
The following assumptions were made:
- Increasing machine range will allow grades A-D and L-O to be produced.
- Currently, five grades are selected every two weeks. One week cycle would allow selection every week.
- Grade H is the sweet spot of the machine but we can only get $200/ton for this when there is really no demand
Bill S. is interested in measuring the financial benefits of such flexibility. Provide an estimate of this for him. In order to simplify calculations, restrict your analysis below to weeks 5-8 inclusively.
Make a chart (outlined below) for each plan suggested by Kiefner. Indicate for each week the paper grades applicable and finally clearly show the $ effect of each plan.
Plan Grades produced
Week 5
Week 6
Week 7
Week 8