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ASSIGNMENT TASK:

 


TASK 1 (logic puzzle)


In this task you will develop a Constraint Programming model that solves the following
logical puzzle:

Alice, Bob, Charlie, and Dave want to cross a river at night. There is a narrow bridge, but this bridge can only support two people at a time. They only have one torch, and
because it is dark this torch has to be used every time when crossing the bridge in either direction. Alice can cross the bridge in 5 minutes, Bob manages the crossing in
10 minutes, Charlie needs 20 minutes and Dave requires 25 minutes to get to the other side. When two people cross the bridge together, they have to move at the slower person’s pace.


The torch only lasts for 1 hour. How can they all make it across safely?
 

A. Identify the predicates describing the states of the puzzle and create the resulting decision variables in an OR Tools CP-SAT model.

B. Define the initial and goal state of the puzzle and implement the resulting constraints in the CP-SAT model C. For each operator define its pre- and post-conditions and implement the resulting constraints in the CP-SAT model . Make sure to clearly indicate which are the pre-conditions and which are the post-conditions for each operator.
D. Define and implement the frame axiom constraints in the CP-SAT model to ensure that state changes only occur due to operators being applied .
E. Define and implement the frame axiom constraints in the CP-SAT model to ensurethat state changes only occur due to operators being applied .
F. Define and implement the mutual exclusion axiom constraints in the CP-SAT model to ensure that the same person cannot simultaneously move across the bridge and back in a single time-step . Note, that more than one person can move in each timestep, though.
G. Define and implement the constraints in the CP-SAT model that a maximum of two people is allowed on the bridge at any given time.
H. Define and implement the constraints in the CP-SAT model to ensure that the total amount of time for all people to cross the bridge does not exceed 60 minutes 
 

. To achieve this, you will need to create additional variables in the CP-SAT model to reflect how much time each individual spends on crossing the bridge in
each time-step as well as the amount of time all people crossing together are spending on the bridge in each time-step.


. Solve the CP-SAT problem and determine the number of feasible solutions Output for all solutions who is crossing the bridge and in which direction for each time-step and the total time required to get everyone across the river 

TASK 2 (supply chain optimisation)
In this task you will optimise the cost of sourcing raw material from different suppliers, manufacturing products in different factories and delivering these products to customers.

TASK 3 (project planning)
In this task you will develop an Integer Linear Programming model for deciding what projects can be taken on and what companies need to be contracted to deliver on these projects.

 

 

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