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Questions on problems whose solution space are one-to-one mappings between two sets.

6
votes
You can model this with a binary variable $x_{i,j}$ to indicate whether task $i$ is assigned to worker $j$, and a binary variable $y_{i,j}$ to indicate whether task $i$ is the first task assigned to w …
answered Jan 24 '20 by RobPratt
5
votes
You can formulate this as an instance of the quadratic assignment problem by duplicating the workers and incurring the batching cost only for pairs of duplicate workers. Here's an alternative MIQP fo …
answered Apr 5 '21 by RobPratt
4
votes
If I understand correctly, you can enforce the time constraint implicitly by omitting arcs. For each customer, there is a unique path by car and a unique path by bike. If the bike is too slow to mee …
answered Nov 13 '21 by RobPratt
8
votes
Maybe the unnecessarily large value for $A$ is causing numerical trouble. Try instead $A = \max_{i,j} p_{i,j} = 9$. Probably your $=0$ in the declaration of $x$ should be $\ge 0$. In fact, you gener …
answered Dec 5 '20 by RobPratt