The economics and utility of a sun lounger at the peak of the holiday season, and how to increase the collective lounger utility of all guests.

As the peak holiday season draws to a close and we head back to the office we can look back with yearning on those beautiful holiday snaps of us mountaineering in the Himalayas, exploring ancient temple ruins in Cambodia, studying the architectural delights of central European cities or boating in the Lake District. Or, for those of us with young children, fighting each morning for a sun lounger around a Spanish hotel swimming pool destined, as soon as the lifeguard allows us in, to become as densely populated as a mosquito-infected stagnant pond.

I will do my best here not to be excessively cynical about a style of holiday that many people enjoy year after year. (Spoiler alert: I fail.)

There we were one morning, the pool still not that crowded, looking for a spot to put our towels. We don’t do the sunbathing thing, contrary to the Brits-on-holiday stereotype. But we do like a little corner of a chair or table to keep dry things dry. Although few people were on the loungers, every single one had been reserved by the pre-breakfast towel drop race.

Much as I love watching my children develop, by the 836^th “Watch this, Daddy!” my mind had turned to economics and the utility of a sun lounger, and how to increase the collective lounger utility of all guests. To keep numbers simple, suppose there are 1,000 hotel guests, 250 loungers and 8 scarce hours during the day. By scarce I exclude times of day for which supply exceeds demand. I will also assume diminishing marginal utility: each additional hour in the sun adds less “benefit” than the previous hour, though at different rates for each guest.

Model SL1: Current. This is highly inefficient, though does exhibit elements of fairness (we can all get up early to deposit towels). The inefficiency is caused primarily by (1) unused loungers, during which time utility is zero, and (2) diminishing marginal utility, in which one lounger hog will gain less benefit than several users switching after a few hours each.

The overwhelming benefit of model SL1 is that it is easy to administer: staff do nothing, though do occasionally have to mediate in fights.

Model SL2: the Restricted Busker System. Apparently at the start of each day at certain busking spots budding musicians can write their name down to reserve a time slot. One presumes that each potential busker is limited to a time period, say of an hour. With loungers this would need to be centralised (250 bits of wet paper won’t reduce the fighting), and each guest would need to be allocated, say, two lounger hours (call this LH) per day. At whatever time the day’s bookings begin a family can reserve two hours for everyone. As for SL1 the model is first come, first served.

This model needs calibrating. Using the specified parameters, guests have an average of 2LH (i.e. 250 SL x 8 hours ÷ 1,000 guests) per day. This fails to account for differing demands: one family may be dedicated sun-worshippers; other families may be buffet- and bar-worshippers. Dare I even suggest cultural activities? Hence it could be that 3LH are offered per person, 4LH if poor weather is forecast. This variability makes model SL2 feel rather clumsy.

Model SL3: Variable Pricing System. This builds on SL2 but includes differing pricing, e.g. LH pricing is at 50% off-peak, but 200% during those busy afternoon hours of maximum music-blasting, child density and skin burning. Hence a notional 2LH allowance may buy four off-peak hours, but just one during the rush hour.

With SL3 I wouldn’t fancy the chances of the staff telling red-bodied beer-filled sunbathers that their hour is up.

Model SL4: Active Trader System. The Coase Theorem states that if trading costs are zero then a limited resource (e.g. carbon permits, radio broadcasting frequencies or sun lounger hours), regardless of how initially distributed, would find an efficient allocation – this is because if one unit has greater value to Party A than Party B, then Party A would buy a unit from Party B. This (1) reduces marginal utility to Party A but (2) increases it to Party B.

Now apply this to loungers. Each guest is allocated 2LH per day over their stay. Some form of electronic trading order book could display potential trades: high demand would increase the price, allowing a seller to exchange a high demand LH for multiple low demand LHs, should she wish.

This also permits a family that prefers the buffet (or culture) over the swimming pool to splash out (excuse the pun) on the last day, paying all their LH credits for a couple of peak hours on their last day.

Although SL4 could in theory be automated, it does involve an element of technological infrastructure. Not to mention, guest training. Ignoring such “real world” constraints my preferred solution is:

Model SL5: Active User System. This is essentially a variant on first come, first served. Anyone can put towels where they want, but only if they are actively using the lounger. Given the small number of hours during which at least 250 guests wish to sunbathe simultaneously, I believe this produces the highest collective utility of all the SL models. Towels need to be removed after, say, half an hour’s inactivity. This is easily monitored using a drone and image comparison software. For guests who are in the pool, simple waterproof GPS or RFID devices could pair a pool-inhabitant with a towel. If towels are unique (or fitted with in-built tracking devices) then lounger-hopping abuse can be detected with a tagging system, or an artificial intelligence towel matching system.

It is possible that when next year’s holidays are booked the travel agents will proudly display the sun lounger management system used by each hotel. I probably won’t see this – I am planning to go caravanning in Wales.