Problem A1 Given a transportation problem:

i \ j 1 2 3 4 si

11 6 7 8 1 35 9 3 8 7

2 35 10 4 5 9

3 70

dj 25 30 40 45 a) Compute a base solution with a method of your choice b) Compute the optimal solution with the stepping stone algorithm

Problem A2

1) Given a directed graph:

(a) Determine the shortest path from 1 to 10 using the method by Bellman. (b) Determine the shortest path from 1 to 10 using the method by Dijkstra.

Problem A3 Two logistic companies, G and S, need special containers for some customers. There are 5 types of special containers. The two companies decided to share the containers since they are very expensive. The table below denotes how long each company would need those containers: G Container Time liquid fuel 4 solid fuel 3 acids 2 leach 5 toxic substances 1 Stefan Container Time liquid fuel 2 solid fuel 6 acids 2 leach 1 toxic substances 5 G needs the containers in the following order: liquid fuel, solid fuel, acids, leach, toxic substances. S needs the containers in the following order: solid fuel, leach, acids, toxic substances, liquid fuel.

a) Use the method by Akers to to determine all optimal schedules that minimize the total time.

2

0 4 2 0 8 6 12 10 16 14

4

6

8

10

12

14

16

b) Draw for those optimal solutions the job-oriented and the machine-oriented

GANTT chart.

Problem A4 The table below denotes processing times for 2 jobs of a 5 machine job shop problem:

M1 M2 M3 M4 M5 J1 3 4 1 3 5 J2 2 5 2 1 6

Job J1 has to be processed in the following sequence: M1, M2, M3, M4, M5, J2 needs M1, M3, M2, M4, M5.

a) Use the method by Akers to to determine all optimal schedules that minimize the total time.

2

0 4 2 0 8 6 12 10 16 14

4

6

8

10

12

14

16

b) Draw for those optimal solutions the job-oriented and the machine-oriented

GANTT chart.