Supermarket O.R. (1) Changing the service time

I have written elsewhere ( about the example of everyday Operational Research that I use to explain a little about what the subject is about, and where people encounter the "Hidden Science" in day-to-day life.
Supermarket queues -- like all kinds of queues -- demonstrate the interaction of science and mathematics with the psychology of human behaviour, and are therefore a useful reminder that O.R. needs to be put into practice, and that needs psychology.  As some of the best writers about the subject have pointed out, psychology enters in two places; (1) understanding the behaviour of the people in the "system" and (2) understanding the psychology of the managers and people who may implement the O.R. solution.  (The latter gives rise to the maxim: "A manager would rather live with a problem he/she cannot solve than accept a solution he/she does not understand.
David Kendall has given his name to the notation for describing queues succinctly, with later additions, principally by Alec Lee -- hence the Kendall-Lee notation.  Kendall's simpler notation describes a queue according to three aspects, the way that customers arrive, the way in which they are served, and the number of servers.  Write down M/D/2 and any queue modeller will know what is meant (Poisson arrival process, constant service time, 2 servers).  And then, anyone who is trying to implement changes to a queue will know that to reduce congestion, you need to increase the time between arrivals or reduce the variability of the time between arrivals, or reduce the service time, or increase the number of servers.
In the big four supermarkets, the check-outs area designed so that the goods accumulate in a trough where they are packed and the packing and payment must be complete before the next customer can be served.  So service time depends on the time taken to cost the shopping basket and the time for the customer to pack their purchases.  Some will offer "Do you want help with your packing", not out of politeness, but to reduce the service time and hence the congestion.
But in the budget supermarkets, another policy is used.  Customers are deterred from packing at the checkout point.  There is no room for an accumulation of goods.  Instead, there is a dedicated packing shelf away from the checkouts and tills.  Goods are swept from the conveyor belt past the checkout and laser scanner as rapidly and the customer places them into the trolley (urged on by the cashier, or the cashier's behaviour!)  That reduces the service time and hence reduces congestion, or perhaps more subtly, reduces the number of cashiers needed!


  1. In the States, self-service lanes excepted, the supermarket provides both a cashier (who may also bag purchases once payment is handled) and one our occasionally two baggers (who float). I heard a presentation once by a professor woo had done a simulation model for a major chain. Managers thought the key to keeping queues short during peak times was the number of cashiers. His model favored adding baggers before adding cashiers. (This was back when batters also offered to take your purchase out to your car.)


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