MATH3202/7232 Operations Research & Mathematical Planning 2021
Practical 10 – Travelling Artist Problem
An artist has the possibility to visit a number of different exhibitions in different cities over the next four days. Based on her experience, she has estimated the probabilities of sales at each exhibition, given that she attends the exhibition for a day. Each of her paintings sells for $500. She also knows how much it costs to travel between exhibitions and from her home to each of the exhibitions. She can only attend each exhibition once.
The data for sales and travel costs are given below. (You can download these in Python from Blackboard.)
Exhibition
Probability of Paintings Sold 012
A 0.3
B 0.2
C 0.2
D 0.3
E 0.3
F 0.4
G 0.0
H 0.1
0.4 0.3 0.5 0.3 0.7 0.1 0.5 0.2 0.6 0.1 0.3 0.3 0.3 0.7 0.1 0.8
ABCDEFGH
Home 143 108 118 121 88 A 35 63 108 228 B 45 86 193 C 46 190 D 172 E
F G
121
182
165
203
224
174
57 92 73 162 42 129 73 105 98 71
160 108 129 212 117
a) The artist wants to maximize her expected profit from a tour of four exhibitions. What path should she take?
b) Suppose now that the artist only has 5 paintings to sell. What is her optimal strategy for a tour of at most four exhibitions assuming that she will return home once all paintings are sold?