A

B

C

D

E

F

G

H

I

J

K

L

M

N

$0$

P

Q

R

S

T

time or reorder period$).$ Additionally, there is a holding cost of $$20$ per inventory unit per year.

Q$1$: Without more information provided, the manager, Jay, assumes the demand is stabe throughout the year because he has not seen considerable variability in the demand since he joined ProTech less than a year ago. What is the optimal order quantity when placing a purchasing order?

Q$2$: Continued from Q$1,$ what is the reorder point $($ROP$)$ so that no old inventory units are expected to remain when the new order arrives and no stockouts occur during the lead time?

Q$3$: ProTech was considering whether to use an order quantity $5$ times as much as the above order quantity from Q$1($i$.$e$.,$ place a larger order$)$ to receive a $5\%$ discount incentive offered by the vendor for the purchasing price. Should TechGear place a larger order every time when reordering from the vendor? You must show your calculation to justify the answer.

Q$4$: Continued from Q$2,$ the manager, Jane, proposed the company work with another vendor in China for a much better price. However, an order to this Chinese vendor tak ${?}^{C}17$ days to arrive. So$,$ if ProTech accepts Jane's proposal, what should the ROP in Q$2$ be$?$

Q$5$: TechGear did not use Jane's proposal and decided to stay with the current vendor. The management recently has been selling the product in boxes and will continue to$,$ where a box includes $10$ units. After looking into the sale data of $250$ observations for a reorder period $($or lead time$),$ only $6$ situations were found: either $21$ boxes, $22$ boxes, $23$ boxes, $24$ boxes, $25$ boxes, or $26$ boxes had been sold during a reorder period. The frequencies for each situation are listed below.

The management has been using the above ROP in Q$2.$ To achieve a service level of $90\%$ or better, the management calculated the minimum safety stock $($SS$)$ needed $($such SS $=0$ if it is not needed$)$ to add to the ROP in Q$2.$ There may be an impact on the inventory costs for the year due to the above SS$.$ Considering the maximum potential impact, would it be an increase or decrease in the inventory costs for the year? What is this max. potential impact $($in $$)?$

$\backslash$table$[[,]]$

Boxes

Units

Frequency

sold

sold $($observations$)$

$210$

$21$

$22$

$23$

$24$

$25$

$26$

Problem $1$

Problem $2$

Problem $3$

Problem $4$

Problem $5$

Problem $6$