Homework 4
Grad. Inst. Busi. Admin.
National Chung Cheng University
Introduction to Management Science 2022F
Notes:
⚫
繳交日期: 2022.11.09 (三)
⚫
請於當日第一節上課繳交給老師，遲交一日扣30%，最多遲交1日，逾時不接受補交(特殊
理由者請提前告知)。
⚫
A4空白影印紙書寫，一張以上請用釘書機固定，未用規定格式之白紙扣總分5分。
⚫
請按照題號依序作答，如有跳題請註記。
⚫
請用課堂上所使用之符號及解題流程作答。
⚫
請書寫詳細的解題過程(定義決策變數、完整的計算過程、依據題目回答完整的結論)。
⚫
請勿抄襲，違者該次作業將以零分計算。
I. Formulation (15 pts)
1. Mike has been approached by three telephone companies to subscribe to their
long-distance service in the United States. MaBell will charge a flat $18 per
month plus $.25 a minute. PaBell will charge $24 a month but will reduce the
per-minute cost to $.21. As for BabyBell, the flat monthly charge is $20, and the
cost per min is $.22. Mike usually makes an average of 150 minutes of longdistance calls a month. Assuming that Mike does not pay the flat monthly fee
unless he makes calls and that he can apportion his calls among all three
companies as he pleases, how should he use the three companies to minimize his
monthly telephone bill? Please formulate it as an integer program. Note that the
decision variables must be defined precisely and clearly. (15 pts)
II. Calculation (85 pts)
1. Compare the starting solutions obtained by the northwest-corner, least-cost, and
VAM methods: (15 pts)
5
0
2
1
6
2
1
5
7
2
4
3
7
5
10
2.
Three orchards supply crates of oranges to four retailers. The daily demand
amounts at the four retailers are 15, 15, 40, and 10 million crates, respectively.
Supplies at the three orchards are dictated by available regular labor and are
estimated at 15, 20, and 25 million crates daily. The transportation costs per crate
from the orchards to the retailers are given in Table as below:
Transportation Cost/Crate for Problem
Retailer
1
2
3
4
Orchard 1
$1
$2
$3
$2
Orchard 2
$2
$4
$1
$2
Orchard 3
$1
$3
$5
$3
(a) Draw the network representation of this TP with nodes and arcs. (8 pts)
(b) Set up the TP simplex tableau and using the VAM method to find the initial
BFS. Is it optimal? Why? (20 pts)
3.
[Class notes] Consider the following TP simplex tableau. Use NW rule to find an
initial BFS, and then solve it using the TP simplex algorithm, in which 𝑣2 = 2
is adopted in testing optimality. (20 pts)
4.
Set up the simplex tableau for the following transshipment network: (10 pts)
5.
[Class notes] Consider the following ILP:
max. 5𝑥1 + 4𝑥2
s. t. 𝑥1 + 𝑥2 ≤ 5
10𝑥1 + 6𝑥2 ≤ 45
𝑥1 , 𝑥2 ≥ 0 , 𝑥1 , 𝑥2 ∈ 𝐼
Solve it using B&B starting with 𝑥2 as the branching variable. Each LP subproblem can be solved using the graphical method discussed in class. (12 pts)
Total Points: 100
Good Luck and Check Carefully!