Question 4: Transportation, Assignment and Transhipment problems [30]

4.1. The three plants that process and pack potatoes are coordinated from a central office that facilitates delivery of sack of potatoes to the mentioned towns/cities. The cost of transporting a sack of potatoes per unit (i.e. 7kg potatoes sack) from each plant to each town/city is shown below. Moreover, the numbers of units of potatoes available from each plant as well as the number of requested units of potatoes at each city/town are provided in the table below.

Town 1 Town 2 Town 3 Town 4 Supply

Plant 1 $ 8 $ 9 $ 11 $ 16 $50

Plant 2 $ 12 $ 7 $ 5 $ 8 $ 80

Plant 3 $14 $10 $ 6 $ 7 $120

Demand 90 70 40 50 250/250

Formulate the linear programming model (i.e. objective function) and the corresponding constraints including the lower bounds of the decision variables.

How many shipments must be made from each plant to each different town/city so that the cost can be minimized

Suppose that as a supervisor, you need to optimally assign drivers to different locations to deliver purchased stock to factories located in different provinces. The hours required for each job on each machine are given by:

Town 1 Town 2 Town 3 Town 4

Driver 1 10 12 9 14

Driver 2 14 13 12 16

Driver 3 16 15 12 18

Driver 4 13 12 11 16

Assuming that as a supervisor you want to allocate drivers such that the total time is minimized, what is the optimal solution? (Write the linear programming model in full before using some software to solve this question)