Question

A local store sells toilet paper to people in the surrounding communities. The demand for the toilet paper has been increasing and management needs to ensure that enough rolls are available to meet the increasing demand. The daily demand for the toilet paper is 400 rolls. The store operates 250 days per year. The following information is also available about the product. The cost of each roll……………………….…..$2. Ordering costs………………………………..……$100 per order Annual holding costs per unit…………… 10% of the costs per unit Desired cycle service level …….……………... 95% Lead time:……………………………………………… 3 days Daily demand is normally distributed with a standard deviation of 20 rolls. 95% service level is equivalent to 2 standard deviations i.e. Z = 2 Current on-hand inventory is 1300 units, with no open orders or backorders. 1. Calculate the average time between orders 2. Calculate the ROP? 3. An inventory withdrawal of 100 units was just made. Is it time to reorder given the reorder point? 4. If the store currently uses a lot size of 8000 units, determine the annual holding cost and the annual ordering cost of this policy? 5.What would be the annual cost saved, if any, by shifting from the 8000-unit lot size to the EOQ

PLEASE CALCULATE THE ROP AN INVENTORY WITHDRAWAL OF 100 UNITS WAS JUST MADE . iS IT TIME TO REORDER GIVEN THE REORDER POINT. PLEASE NOTE WITH THE SCENARIO THE ROP DO NOR HAVE TO USE THE SQUARE ROOT

EOQ?

Answer 1

EOQ = ( 2*annual demand x cost of order / holding cost per year)^0.5

= [ 2*250*400*100/0.2]^0.5

=10000 units.

Number of orders = 250*400/10000= 10

Time between orders = working days / number of orders

= 250/10 =25

Rop = demand during lead time + safety stock

= 3 *400+ z*SD *( lead time)^0.5

1200+2*20*(3)^0.5 = 1269.28 = 1270

Yes.if withdrawal is made for 100 unirs, the reorder point if 1270 is passed hence order needs to be placed.

For lot size of 8000,

Inv cost = (4000+70)*0.2 =814

Order cost =( 250*400/8000)*100 = 1250

Cost with EOQ =( 10000/2+70)*0.2 = 1014

Order cost = 100000/10000*100=1000

TC = 2014

Savings = 2064-2014 =50