ISDS 514 Exam #2 Review Dr. Z. Drezner

Question #1

The following is quarterly data of sales:

t / Xt
1 / 76
2 / 23
3 / 34
4 / 56
5 / 82
6 / 29
7 / 35
8 / 60
9 / 87
10 / 30
11 / 42
12 / 65
13 / 90
  1. Find the forecast for the next three quarters by using dummy variables.
  2. Find the forecast for the next three quarters by using index numbers and exponential smoothing using α=0.5, β=0.3.

Question #2

You have three plants that produce a certain type of boats. The capacity for next month is 38 in San Diego, 45 in Santa Ana, and 58 in San Jose. Production cost per boat is $1,065 in San Diego, $1,005 in Santa Ana, and $975 in San Jose. Demand for next month is 42 in Newport Beach, 33 in Long Beach, 14 in Ventura, 10 in San Luis Obispo, and 22 in San Francisco. The shipping costs per boat are summarized in the following table:

From / Shipping Cost to:
NB / LB / VEN / SLO / SF
SD / $200 / $220 / $280 / $325 / $500
SA / $125 / $125 / $280 / $350 / $400
SJ / $390 / $365 / $300 / $250 / $100

Develop a production and shipping schedule that minimizes the total cost of production and shipping while satisfying all the demand.

Question #3

Three suppliers provide two products to four factories. In the two tables below the cost of transporting each product from each supplier to each factory, the demand at each factory for each product and the availability of each product at each supplier are given.

Product 1 / Product 2
Suppl1 / suppl2 / suppl3 / demand / Suppl1 / suppl2 / suppl3 / demand
Fact 1 / 17 / 23 / 12 / 310 / Fact 1 / 25 / 22 / 19 / 210
Fact 2 / 15 / 19 / 24 / 250 / Fact 2 / 24 / 20 / 26 / 320
Fact3 / 18 / 22 / 21 / 300 / Fact3 / 33 / 24 / 29 / 180
Fact 4 / 14 / 12 / 18 / 240 / Fact 4 / 17 / 22 / 20 / 170
supply / 370 / 520 / 430 / supply / 530 / 420 / 380

The amount transported from each supplier to each factory of the two products combined, should not exceed 200 units. Find the amount transported from each supplier to each factory of each product to minimize the total transportation cost. Note that total supply exceeds total demand and not all the supply will be transported.

Question #4

Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table 2. The number of tons of coal demanded by each customer is given in Table 3. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 4. The total amount of coal shipped must contain at most 6% ash and at most 3.5% sulfur. Show Coalco how to minimize the cost of meeting customer demands.

Table 2: Cost and Other Data for Coalco Problem

Production Cost Capacity Ash Content Sulfur Content

Mine 1$501200.08 ton0.05 ton

Mine 2$551000.06 ton0.04 ton

Mine 3 $62 140 0.04 ton 0.03 ton

Table 3: Customer Demand for Coalco Problem

Customer 1 Customer 2 Customer 3 Customer 4

Demand 80 70 60 40

Table 4: Shipping Costs for Coalco Problem

Customer 1 Customer 2 Customer 3 Customer 4

Mine 146812

Mine 296711

Mine 3 8 12 3 5

Question #5

You can invest in 5 projects in multiple of 1 million dollars. You have 10 million dollars to invest. Your objective is maximizing profit. You expected profit by investment in each project is as follows (all numbers are in millions of dollars):

Investment / Project 1 / Project 2 / Project 3 / Project 4 / Project 5
0 / 0 / 0 / 0 / 0 / 0
1 / 52 / 63 / 41 / 59 / 62
2 / 110 / 120 / 130 / 100 / 110
3 / 180 / 170 / 160 / 190 / 190

Hint: Similar to the assignment problem. Define 20 0-1 variables. For each project you have to select one of the 4 options (0,1,2 or 3) and the variable is 1 if the investment is selected and zero if not.

a. Solve the problem without integrality constraints, i.e. you can invest parts of a million.

b. Solve it again with integrality constraints.