Assignment 1

University of British Columbia
Sauder School of Business
COMM 399: Logistics and Operations Management

Problem Set 1
1. Solution:
(a) Inventory build-up diagram:

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(b) The average number of customers in the system is 12.95. Probably the easiest way to calculate this number is by calculating the area under the graph and then by dividing by the entire time. The area under the graph is a summation of four triangles or trapezoids which we obtain by drawing vertical lines at 9:00, 9:30 and 10:30. The areas of each triangle/trapezoid is
8:30-9:00:

0.5 · 15/2 = 3.75

9:00-9:30:

0.5 · (15 + 20)/2 = 8.75

9:30-10:30:

1.0 · (20 + 15)/2 = 17.5

10:30-11:15:

0.75 · 15/2 = 5.625

Thus, the total area is 35.625. Now, divide 35.625 by 2.75 hours and we find that on average there are 12.95 customers in the system.
(c) During the 2.5 hours, the number of customers is 30 + 15 = 45. Thus,
Throughput Rate = Actual Output Rate =

45 customers
2.75 hours

= 16.36 customers/hour
Average Inventory
12.95 customers
Average Flow Time =
=
Throughput Rate
16.36 customers/hour
= 0.792 hour = 47.5 minutes
1

2. Solution:
(a) The resource requirements are as follows:
Resource
Cut
Grilled cheddar
Veggies
Cream cheese
Wrap

Cheddar & veggie
3
10
5
2

Veggie only
3

Cream cheese
3

5
2

4
2

Product mix
540
300
700
160
360

The bottleneck for each kind of bagel is: Grilling for cheddar & veggie, Veggie for the veggie, and Cream cheese for the cream cheese.
The bottleneck for the product mix (30 cheddar & veggie, 110 veggie only, and 40 cream cheese) is Veggies, as shown above.
Note that the demand in this product mix cannot be fully satisfied – as Veggies requires
700 minutes per day while we have only 600 minutes available.
(b) If there are 700 minutes available,