The central research question is:
In which cities should depots be located in order to minimize annual costs (= depot costs + transport costs)?
We will distinguish two versions of this problem. In Assignment 1.1 we consider the case without capacity restrictions on the depots. In Assignment 1.2 we consider the case with capacity restrictions on the depots. Assignment 1.3 consists of some theory questions; try to prepare these at home (i.e., use your time during the exercise class for assignments 1.1 and 1.2).
For this assignment we use the mathematical programming software "OMST_LP_Shell". Before you start, make sure you copy all the files to a directory.Warning: make sure to save your files before you log out of the terminal server. The assignments must be handed in through Blackboard.Assignment 1.1. (A): no depot capacity restrictions
We will study two ways to model this problem.(first model option) Demonstrate that the problem can be formulated straightforwardly as an integer linear program (ILP), with the variables Xd (0-1, indicates whether depot d is opened) and Ysd (non-negative integer, indicates the number of product units delivered to city s from depot d)
(i) Write down a qualitative model formulation, i.e., describe the parameters, variables, restrictions and objective.
(ii) Write down an ILP formulation of the problem in (i) (i.e., not in the OMST_LP_Shell!).(iii) Write down the corresponding LP relaxation (i.e., not in the OMST_LP_Shell).
(iv) Formulate the problem in (ii) in the 'OMST_LP_Shell'. Use the file 'depotlocatie1a.olp', in which the required sets, parameters and data have already been defined. Determine the optimal solution. What depot(s) do you find? From what depot is each city delivered?
(v) What is the solution of the LP-relaxation? Is it feasible? How can you interpret / use the LP relaxation solution?
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