Assume that during minute t (the current minute isminute 1), the following sequence of events occurs: (1) Atthe beginning of the minute, xt customers arrive at the cashregister; (2) the store manager decides how many cashregisters should be operated during the current minute;(3) if s cash registers are operated and i customers arepresent (including the current minute’s arrivals), c(s, i)customers complete service; and (4) the next minute begins.A cost of 10¢ is assessed for each minute a customerspends waiting to check out (this time includes checkouttime). Assume that it costs c(s) cents to operate s cashregisters for 1 minute. Formulate a dynamic programmingrecursion that minimizes the sum of holding and servicecosts during the next 60 minutes. Assume that before thefirst minute’s arrivals, no customers are present and thatholding cost is assessed at the end of each minute.
Assume that during minute t (the current minute is
minute 1), the following sequence of events occurs: (1) At
the beginning of the minute, xt customers arrive at the cash
register; (2) the store manager decides how many cash
registers should be operated during the current minute;
(3) if s cash registers are operated and i customers are
present (including the current minute’s arrivals), c(s, i)
customers complete service; and (4) the next minute begins.
A cost of 10¢ is assessed for each minute a customer
spends waiting to check out (this time includes checkout
time). Assume that it costs c(s) cents to operate s cash
registers for 1 minute. Formulate a dynamic programming
recursion that minimizes the sum of holding and service
costs during the next 60 minutes. Assume that before the
first minute’s arrivals, no customers are present and that
holding cost is assessed at the end of each minute.
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