# Math

Topics: Inventory, Trigraph, Newsvendor Pages: 6 (1157 words) Published: August 26, 2013
NAME : NURUL SYAIEDAH BINTI ZULKEFLI
I/C NUMBER : 941128-04-5238
CLASS : PU/13/A4
TEACHER’S NAME : PN . CHAH HUA LIN

INTRODUCTION

As an inventory control manager at hypermarket XYZ, you need to ensure a good stock of a health supplement drink under the name JUSMANGGIS. Customers are willing to wait for the drink to arrive at the hypermarket since the hypermarket sells the drink for 12.5 percent less than its competitors. The demand data shows that the customers of hypermarket XYZ purchase an average of 2400 bottles of JUSMANGGIS per month (30 days). The supplier charges the hypermarket a wholesale price of RM5.40 per bottle. The annual holding cost (based on 360 days) for the inventory is 10 percent of the capital tied up in the inventory of JUSMANGGIS. It takes about 20 minutes to place each order. Your salary and benefits add up to RM112.50 per hour. 1. Create an optimal inventory policy where no planned shortages are allowed and the lead time is zero. The optimal inventory policy shold include a) a list of assumptions,

b) the quantity of an order each time,
c) the cycle time,
d) the numbers of orders per year,
e) a graph of inventory level as a function of time.
2. a) If a hypermarket XYZ has to wait 8 days after it places an order to receive the shipment, determine i. the number of bottles of JUSMANGGIS that should be ordered each time, ii. the cycle time,\

iii. the numbers of orders per year,
iv. the reorder point.
b) If hypermarket XYZ has to wait 2 days longer than the cycle time as in part 1 after it places an order to receive the shipment, determine the reorder point. 3. Suppose that you change your policy in part 1 such that planned shortages are allowed and the lead time is 15 days. Customers are willing to wait to purchase the JUSMANGGIS at hypermarket XYZ due to its low price. They would, however, become unhappy about the prospect of having to return for the JUSMANGGIS. a) If the estimated cost of dealing with the dissatisfaction and future sales is RM0.75 per bottle short per year, i. calculate the number or bottles of drink that should be ordered , ii. calculate the maximum shortages under this optimal inventory policy, iii. determine the reorder point,

iv. determine the total variable inventory cost per year, v. sketch a graph of inventory level as a function of time.

b) If the estimated cost of dealing with the dissatisfaction and future sales is RM0.30 per bottle sort per year, i. calculate the number of bottles of drink that should be ordered, ii. calculate the maximum shortages under this optimal inventory policy, iii. determine the reorder point,

c) Discuss the significance of the relationship between the shortage cost and the holding cost.

1) a) list of assumptions
* The demand for the item is predetermined and occurs at a constant rate throughout the year. For instance, 5 units per day. * The ordering cost is constant and independent of the quantity ordered. * The holding cost per quantity unit per time period is constant. * The quantity ordered (per cycle) is supplied instantaneously whenever the inventory level reaches zero. * The lead time for an order is constant.

*

b)

3. a) i) Q* =2DCoCh Ch+CbCb
= 2 2880037.50.54 0.54+0.750.75
= 4000000 1.72
= 2622.98
≈ 2623 units
ii) M* = 2DCo ChCbCh+Cb
= 22880037.50.54 0.750.54+0.75
= 4000000 0.5814
= 1524.99
≈ 1525 units
iii) No of back orders = Q* ─ M*
= 2623 ─ 1525
= 1098 units
Reorder point, r = dl
= 28800360 (15) ─ (1098)
= 102
iv) T=cD+ DCoQ+ M2Ch2Q

Declaration
This is to certify that the assignment report submitted is based on my work.

Signature :
Name : Nurul Syaiedah...