Buying information on travel distances.
A first step to solve delivery problems.

Description | In order to address delivery problems with P_1, …,P_n as possible origins/destinations and time intervals t_1, …, t_r, we need to know in advance (precisely or with an estimate) d_k(P_i,P_j), the travel distance between points P_i and P_j at time interval t_k for all i,j,k.

A company sells this information in small packets: at the price of c cents, one can buy the all-pairs distance matrix for m chosen points at one time interval. For instance, if n=6, and the small packets available are 3x3, we need to buy several all-pairs distance matrix 3x3 (at the cost c cents each) to construct the full matrix all-pairs distance 6x6. For example, if we buy the all-pairs matrix for P1, P2, P3 and the all-pairs matrix for P1, P3 and P6, at time interval t,

we don't have enough information since the distance between P2 and P6 at such time instant is not known.

The aim is to build a strategy to buy all-pairs matrices so that we have enough information to address the delivery problems using these points as origins/destinations at different time intervals.

Mathematical background | Integer programming, basic statistics.

Coordinators | Rafael Blanquero and Emilio Carrizosa, University of Sevilla.


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The 7IMW is supported by the Portuguese Network of Mathematics for Industry and Innovation, PT-MATHS-IN, and the Spanish Network for Mathematics & Industry, math-in.