Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision.

The table below shows the cost ($ per item) for shipping from each DC to each region.
Region
$$\begin{array} { | c | c | c | c | c | }
\hline \mathrm { DC } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } \
\hline 1 & 1 & 3 & 3 & 2 \
\hline 2 & 2 & 4 & 1 & 3 \
\hline 3 & 3 & 2 & 2 & 3 \
\hline
\end{array}$$ The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units.
Assume that Xij = quantity shipped from distribution i to region j. i = 1,2,3 and j = 1, 2, 3, 4.
Assume that Yi = 0 or 1 where i = distribution center 1, 2 or 3.
-You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:
Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7.
Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5.
Restriction 3. Of all the sites, at least 3 should be assessed.
Assuming that Si is a binary variable, write the constraint(s) for the second restriction.
A) S2 + S5 ? 1
B) S4 + S5 ? 1
C) S2 +S5 + S4 + S5 ? 2
D) S2 +S5 ? 1, S4 + S5 ? 1

Question

Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision.

The table below shows the cost ($ per item) for shipping from each DC to each region.
Region
 $$\begin{array} { | c | c | c | c | c | } 
\hline \mathrm { DC } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } \
\hline 1 & 1 & 3 & 3 & 2 \
\hline 2 & 2 & 4 & 1 & 3 \
\hline 3 & 3 & 2 & 2 & 3 \
\hline
\end{array}$$ The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units.
Assume that Xij = quantity shipped from distribution i to region j. i = 1,2,3 and j = 1, 2, 3, 4.
Assume that Yi = 0 or 1 where i = distribution center 1, 2 or 3.
-You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:
Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7.
Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5.
Restriction 3. Of all the sites, at least 3 should be assessed.
Assuming that Si is a binary variable, write the constraint(s) for the second restriction.
A) S2 + S5 ? 1
B) S4 + S5 ? 1
C) S2 +S5 + S4 + S5 ? 2
D) S2 +S5 ? 1, S4 + S5 ? 1

Quizplus · Accepted Answer

The second restriction states that evaluating either S2 or S4 will prevent the assessment of S5, which means you cannot choose S2 and S5 or S4 and S5 at the same time. This is represented by two separate constraints: S2 + S5 ≤ 1 and S4 + S5 ≤ 1, ensuring that if either S2 or S4 is chosen (value 1), then S5 cannot be chosen (value would exceed 1), and vice versa.

Due to Increased Sales, a Company Is Considering Building Three