## Contributed Session Tue.3.H 2033

#### Tuesday, 15:15 - 16:45 h, Room: H 2033

**Cluster 11: Integer & mixed-integer programming** [...]

### Location problems

**Chair: Wilbert Wilhelm**

**Tuesday, 15:15 - 15:40 h, Room: H 2033, Talk 1**

**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.

**Tuesday, 15:45 - 16:10 h, Room: H 2033, Talk 2**

**Wilbert Wilhelm**

The stochastic healthcare facility configuration problem

**Coauthors: David Carmona, Xue L. Han, Brittany C. Tarin**

**Abstract:**

The stochastic healthcare facility configuration problem, which is

essentially a supply chain design problem, is to prescribe the

location and size of each facility, allowing openings, expansions,

contractions, and closures; the healthcare services each is to offer;

and the capacity to be allocated to each service - all given that patient needs are uncertain. This topic is timely as countries seek to enhance access to healthcare services, including the U.S., which is working towards the goal of expanding access in underserved (e.g., rural) areas and through recent legislation. This presentation describes relevant practical features of the healthcare facility configuration problem and presents a framework for prescriptive models. Appropriate solution methods are proposed. The goal is a scalable methodology to plan healthcare-facility configuration, adjusting, for example, to demand and demographic changes, emigration, immigration, mergers, and acquisitions.