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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.

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    $\begingroup$ 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? $\endgroup$
    – prubin
    Jul 7 at 18:23

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