Operations Research Course ISC612 - Project material - Chance-constrained spare parts optimization problem

To do

• We start from your problem description and formulation.
• Here is an interesting work on probabilistic programming (also known as chance-constrained programming).
• First, prove that your problem, as formulated here, can be decomposed in two separate problems that have the same formulation and can be solved separately (consider critical and non-critical items). From now on we only deal with one of the two problems (call it P), as the other can be solved in exactly the same way.
• Secondly, the current notation is not very clear. I would like you to use the following notation: set of items A, unit costs c, demands d, probabilities associated to each item p, decision variables x (all these symbols are indexed by i in A); global probability q. Re-write the formulation of P using these symbols.
• Third, reformulate P such that no variables ever appear on the sum limits. This can be done by introducing binary variables. You have up to 10th january to do all this. If you can't do it, contact me.