His objective function is wrong, I think: it considers only the total number of people we can accommodate with all spacings >= 2, but if that were the only thin

His objective function is wrong, I think: it considers only the total number of people we can accommodate with all spacings >= 2, but if that were the only thing people cared about then we wouldn't have the "use the middle of the biggest gap" algorithm in the first place. And apparently no one ever finishes. The model would be appropriate for the following situation: people turn up sequentially but rapidly; once someone starts peeing they stay where they are for ever; anyone who arrives and is unable to find a urinal whose neighbours are unused immediately commits suicide out of embarrassment.