**Tuesday, 15:15 - 15:40 h, Room: H 2033**

**Alfredo MarĂn**

Discrete ordered non-linear median problem with induced order

**Abstract:**

The Discrete Ordered Median Problem (DOMP) has many discrete location problems as particular cases. Some examples are the *p*-median problem, the *p*-center problem, the *k*-centrum problem and several equitable location problems.

In the DOMP, distances between medians and allocated points are sorted. The sorted distances are then multiplied times a vector of coefficients which determines the particular problem that is being solved. Sorting values of variables inside a linear integer programming formulation was a matter of past research.

In this work we deal with an extension of the DOMP where the order in which the variables are multiplied by the coefficients is determined by a second set of variables. That is to say, pairs of variables are sorted with respect to the first component of the pair, and it is the second component which is multiplied by the coefficients. In this way, new problems can be modeled at the expense of increasing the difficulty of the formulation.

We also show that non linear objective functions can be incorporated to the formulation without additional effort. The results of a preliminary computational study will be presented.

Talk 1 of the contributed session Tue.3.H 2033

**"Location problems"** [...]

Cluster 11

**"Integer & mixed-integer programming"** [...]