Question

​Sam's Cat Hotel operates

52

weeks per​ year,

6

days per​ week, and uses a continuous review inventory system. It purchases kitty litter for

​$10.50

per bag. The following information is available about these​ bags:

follows≻Demandequals=85

​bags/week

follows≻Order

cost=​$50.00​/order

follows≻Annual

holding

costequals=35

percent of cost

follows≻Desired

​cycle-service

levelequals=80

percent

follows≻Lead

time=4

weeks

​(24

working​ days)

follows≻Standard

deviation of weekly

demand= 15

bags

follows≻Current

​on-hand inventory is

320

​bags, with no open orders or backorders.

a. Suppose that the weekly demand forecast of

85

bags is incorrect and actual demand averages only

65

bags per week. How much higher will total costs​ be, owing to the distorted EOQ caused by this forecast​ error?

B) Suppose that actual demand is 180 bags but that ordering costs are cut to only ​$15.00 by using the internet to automate order placing.​ However, the buyer does not tell​ anyone, and the EOQ is not adjusted to reflect this reduction in S. How much higher will total cost​ be, compared to what they could be if the EOQ were​ adjusted?

Answer 1

Given that:

d= 85 bag per week

n = 52 weeks * 6 days = 312

D = d * n

= 85 * 52

= 4420 bags per year

Cost = 10.50 per bag

Holding cost (H) = 25% of cost

35 / 100 * 10.50

= $ 3.675 per unit per year

Cycle service level (CSL ) = 80%

Value of Z (0.80) = 0.84

Lead Time (LT) = 4 Weeks

Standard deviation of weekly demand  = 15 bags

Current on-hand inventory (I) = 320 bags

Ordering Cost (S) = 50 per order

a) $EOQ = \Sqrt{(2DS)/H}$
$\sqrt {( 2 * 4420 * 50) / 3.675}\\ = \sqrt {( 442,000 / 3.675}\\ = \sqrt {120,272.1088}$
= 346.803 or
= 347 units

d = 65 bags per weeks
New D = 65 * 52
= 3,380 bags per year

$New EOQ =\sqrt {( 2 * 3,380 * 50) / 3.675}\\ = \sqrt {( 338,000 / 3.675}\\ = \sqrt {91,972.789}$
= 303.270 or
= 303 units

Total cost = annual ordering cost + annual holding cost

Difference = TC_303 - TC_347
= 1,286.136 - 1,274.501
= $11.635 (Answer)

b) d = 180 bags per week
D = 180 * 52 = 9,360 BAGS PER YEAR

$EOQ = \Sqrt{(2DS)/H}\\ = \Sqrt{(2 * 9360 * 50)/3.675}\\ = \Sqrt{936,000/3.675}\\ = \Sqrt{254,693.878}\\ = 504.672 OR\\ = 505 Units$

New ordering cost (S) = 15
So,

$New EOQ = \Sqrt{(2DS)/H}\\ = \Sqrt{(2 * 9360 * 15)/3.675}\\ = \Sqrt{280,800/3.675}\\ = \Sqrt{76,408.1633}\\ = 276.420 OR\\ = 276 UNITS$

Difference = TC_276 - TC_505
= 2,202.802 -1,854.673
= $348.129 (Answer)