We went to London for a two-day break last week, and, inevitably, I looked at some of the experience with a pair of O.R.-problem-seeker's spectacles. Two of the things I saw are worth recording.
We went to the theatre (Phantom of the Opera); earlier in the year we had booked online and bought the cheapest tickets on sale ... even for a treat like this, we couldn't face paying some of the prices. The cheapest seats are £25; in Exeter and Taunton, where we generally go to the theatre, the most expensive seats are less than £20. When we got to the theatre, we discovered that the section in which our seats were located was closed for the evening, and we were bumped up to higher quality seats ... in fact the most expensive ones, at £59 each. At no charge, of course. So here is the cheapskate's optimal policy for theatre-going. Book well in advance, for a midweek (less popular) evening, in the cheapest section fof the theatre. Then wait and see what happens when you arrive. At worst, you have your seats. But you may get an upgrade instead. (Oh, and take your own chocolates ... theatre prices are high!)
We bought Oyster cards to pay for the trips around London on the bus and tube. The cost of fares is deducted from the balance on the card, up to a daily maximum, which depends on where you travel and when. So, off-peak, in zones 1-2, the cap is £5.60, which is also the price of a day card. We didn't save much except time with that. We did save when we used the tube in the morning rush-hour. Even then, the scheme has a cap on the day's deduction. Looking at the calculation of caps, we spotted an anomaly. For someone whose use of the system consists of one journay in the morning rush-hour and a number of journeys in the off-peak season, the cap may be more than the combined rush-hour fare and the cost of the day card. So it is better not to use the same Oyster card for the rush-hour and the rest of the day. So here's the optimal strategy for anyone doing this type of day's travelling very often. Have two cards. Use one for the rush-hour, and the other for the wandering about. It depends on what zones you are using, so I am not going to spell out what to do ... an exercise for the reader.