# Facility location over time - Parameter

I'm trying to model this scenario that each population group gets assigned to a hospital over a period of time. The time is divided into say a period of 30 weeks, and I have about 8 age-wise population data from every demand point. If I were to minimise the distance travelled by every patient to a hospital at every time period, how would I model this, given that the parameter for demand that I have is not sorted age wise.

For a closer look:

80+ = 70
70 -79 = 30
60 - 69 = 45
50 - 59 = 20
40 - 49 = 45
30 - 39 = 20
20 - 29 = 80
<= 19 = 80



Currently, I have the following parameters:

$$D_{ij}$$: Demand allocated from location i to hospital j

$$D_{it}$$: Demand at location i at according to age period t

$$x_{ijt}$$:1, if demand from location i is allocated to hospital j at age period t

Objective: Minimise $$\sum_{i \in I} \sum_{j \in J} \sum_{t \in T} x_{ijt} D_{it} D_{ij}$$

Subject to:

$$\sum_{ j \in J} x_{ijt} \geq 1$$ $$\forall i \in I, t \in T$$

The above constraint will ensure that every demand point i can be allocated to more than one facility in time t

I'm quite out of ideas on how to include the weekly period given that I don't have the right parameters for it. I'd sincerely appreciate any advise on how to model this problem.

• I'm afraid portions of your question seem self-contradictory in a number of respects. For instance, you say that demand allocated from location to hospital is a parameter. In that case, travel distance is fixed and you have nothing to minimize. Perhaps you can clarify the question? Jul 7 at 18:23