Operations Research 1, 2015-2016
Solutions Tutorial 5
Note: Only brief answers to the exercises of the practicals and tutorials will be provided on Nestor.
More detailed explanations will be given during the practicals and tutorials.
Solution Exercise 1
(

Operations Research 1, 2015-2016
Tutorial 5: Network Theory and Queueing Theory
Exercise 1: Travelling Salesman Problem
Consider a collection of 5 cities with pairwise distances as shown in the matrix below. The goal is
to nd a tour that starts in city 1,

Operations Research 1, 2015-2016
Solutions Tutorial 4
Note: Only brief answers to the exercises of the practicals and tutorials will be provided on Nestor.
More detailed explanations will be given during the practicals and tutorials.
Solution Exercise 1
(

Operations Research 1, 2015-2016
Tutorial 4: Integer Programming and Network Theory
Exercise 1: Shortest path
(a) Use the algorithm described in the lecture sheets to determine the shortest path from A to
H in Network 1.
(b) Determine the lengths of the s

Operations Research 1, 2015-2016
Tutorial 2: The Simplex Method and Sensitivity Analysis
Exercise 1: Work order planning (2)
The work order planning problem considered during the previous tutorial can be modeled by the
following mathematical model.
Let
T

Operations Research 1, 2015-2016
Tutorial 3: Sensitivity Analysis and Integer Programming
Exercise 1: Sensitivity analysis
Consider the following LP, where the value of c1 has not yet been ascertained.
Maximize
z = c1 x1 + x2 ,
subject to
x1
x1
+
+
x2
2x2

Operations Research 1, 2015-2016
Solutions Tutorial 3
Note: Only brief answers to the exercises of the practicals and tutorials will be provided on Nestor.
More detailed explanations will be given during the practicals and tutorials.
Solution Exercise 1
F

Operations Research 1, 2015-2016
Solutions Tutorial 2
Note: Only brief answers to the exercises of the practicals and tutorials will be provided on Nestor.
More detailed explanations will be given during the practicals and tutorials.
Solution Exercise 1
T

Operations Research 1, 2015-2016
Solutions Tutorial 1
Note: Only brief answers to the exercises of the practicals and tutorials will be provided on Nestor.
More detailed explanations will be given during the practicals and tutorials.
Solution Exercise 1
(

Operations Research 1, 2015-2016
Tutorial 1: The Graphical Method
Exercise 1: Work order planning
A shop that does custom order work has received two rush orders (to be nished in two working
days), one for tow bars and another for stabilizer bars. The own