Question

An order is placed to a clothing distribution center on average every 10 seconds, but the time between orders has uncertain variability associated with it. Orders are independent. The fulfilment manager needs to collect orders that have been received and release them to an order picker who will retrieve the order’s items from storage locations.

a. If the manager releases all orders received in 1 minute to an order picker, what is the average number of orders and the CV of the number of orders that any one picker is given?

b. What assumptions did you rely on for (a)?

c. What happens to the average and CV if the managers collects orders for 10 minutes before giving them to an order picker?

CV = coefficient of variation

Answer 1

Let xdenotes he af mkers eceived in 1 inutt 1-4.X i3 4he ne. of mders ang der hickeris given $ince, a prder is ylaced setmds, x Polssm (mean en average ever 10 60x L 1D s.d. [x) me N Var lx) meanlx) ava Can(X) NG 0.41 b) time w mders is ass umel to foller exponential dist with (Tate per secmnds) 1 Trate parameter As, minute -60 Secomds and by thear This is the assumptim for a) Teceived in 10 minutes let =no f mders YN Poisson 10 V60 varlx) S-d. lx) 09(413: .13 60 Els) 60 1. of rders in creases by the deereases Taverage Amont of time increas es and ie voriabihty (relative) Bof #rdens decredes with imtrease overals time