Russel, Lda $($RSS$)$ imports sweets. Drops are supplied from Spain by BARCINO, a company located in Barcelona. Both RSS and BARCINO work $52$ weeks a year. RSS has its warehouse in Carregado. From this warehouse it supplies its $4$ retail stores. RSS receives daily orders from the stores from Monday to Saturday. Stores are open from Monday to Saturday, from $10$:$00$ to $22$:$00.$ The warehouse supplies one day after the order, $6$ days a week. BARCINO supplies every Tuesday before $10$:$00$ at the central warehouse, according to the orders placed on Friday until $10$:$00.$ Note that the warehouse works $6$ days a week, from Monday to Saturday. The daily demand from each store, and daily standard deviation in demand, in boxes, are as follows $($demand $($standard deviation$))$:

Drops

$25(2)$Lisbon

Porto

Braga$$Set$$bal

$35(4)25(3)20(2)$Note: RSS places orders in boxes, is supplied in boxes and delivers in boxes

BARCINO $($drops$)20$ per order

$125$ per box $50$ per box $56\%/$ year Z$=3,09$

$330$ boxes

$0$ boxes $1$ week $6$ days

a$)$ Today is Friday $9$:$00$am$.$ RSS Logistics Director asks you to identify how many boxes should be ordered.

b$)$ Knowing in advance that BARCINO is willing to change the time between orders and keep lead time, the Director of RSS is not satisfied with the average inventory level of drops as they consider that it is too high. The following suggestion is made:

$$Without changing the inventory model, I think we should change our time between orders $($TBO$)$ to become closer to the economic time between orders $($TBO$*).$ I think that this would decrease the average level of inventory of drops$.$ Comment on this statement and justify your position.$$Ordering cost

Selling price $($box$)$

Cost price $($box$)$

Carrying cost $($per year$)$

Service level $(99,9\%)$

Stock on hand, in the warehouse

Orders already placed