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A gourmet coffee shop in downtown San Francisco is open 200 days a year and sells an average of 75 pounds of Kona coffee beans a day. (Demand can be assumed to be distributed normally, with a standard deviation of 15 pounds per day.) After ordering (fixed cost 5 $16 per order), beans are always shipped from Hawaii within exactly 4 days. Per-pound annual holding costs for the beans are $3.

a) What is the economic order quantity (EOQ) for Kona coffee beans?

b) What are the total annual holding costs of stock for Kona coffee beans?

c) What are the total annual ordering costs for Kona coffee beans?

d) Assume that management has specified that no more than a 1% risk during stockout is acceptable. What should the reorder point (ROP) be?

e) What is the safety stock needed to attain a 1% risk of stockout during lead time?

f) What is the annual holding cost of maintaining the level of safety stock needed to support a 1% risk?

g) If management specified that a 2% risk of stockout during lead time would be acceptable, would the safety stock holding costs decrease or increase?

Respuesta :

abiolataiwo2015

Answer and Explanation:

Gourmet coffee shop

(a) d= 75 lbs/day 200 days per year

D= 15,000 lb/year

H= $3/lb/year

S= $16/order

EOQ= √(2*15,000*16)/3

=400 lb of beans

(b)Total annual holding cost =

Q/2 * H

= 400/2 * 3

= $600

(c)Total annual order cost

= D/Q * S

= 15,000/400 * 16

= $600

(d) LT= 4 days with σ = 15

Stockout risk = 1%

Z= 2.33

ROP = Lead time demand + SS, where SS= (Z)(σd*LT) and lead time demand = (d)(LT)

σd*LT= (√LT) * 15 = √4 * 15 = 30

ROP = 369.99

where ROP = (d)(LT) + SS

(e) SS= 69.99 from part (d)

(f) Annual safety stock holding cost = $209.97

(g)2% stockout level →Z= 2.054 SS= (Z) * (σdLT)

= 61.61

chilljain33

A- The Economic Order Quantity for Kona coffee beans is 400 pounds.

B- Total annual holding costs of stock for Kona coffee beans $600.

C- Total ordering cost for the Kona coffee beans is also $600.

D- Reorder point at 1% risk will be 369.9

E- This can be achieved with (D) as 70.

F- The safety stock's annual holding cost at 1% risk $209.97

G- The safety stock holding costs will increase if the risk of stock out is 2%.

  • The above calculations can be achieved with the form of calculations as shown below.

  • For A

  • [tex]\rm Economic\ Order\ Quantity= \sqrt \dfrac {2\ x\ \$15000\ x\ 16} {3} }\\\\\\\\\rm Economic\ Order\ Quantity=400\ pounds[/tex]

  • For B

  • [tex]\rm Total\ annual\ holding\ cost= \dfrac{400}{2}\ x\ 3 \\\\\\\rm Total\ annual\ holding\ cost= \$ 600[/tex]

  • For C

  • [tex]\rm Total\ annual\ ordering\ cost= \dfrac{15000}{400}\ x\ 16\\\\\\\\\rm Total\ annual\ ordering\ cost= \$ 600[/tex]

  • For D

  • [tex]\rm Reorder\ point\ = \sqrt{4\ x\ 15}\\\\\\\rm Reorder\ point\ = \$400- \$30\\\\\\\rm Reorder\ point\ = \$369.99[/tex]

  • For F

  • [tex]\rm Annual\ Safety\ Stock\ Holding\ Cost = \$209.97[/tex]

  • For G

  • [tex]\rm Safety\ Level = \$61.11[/tex]

Hence, the solutions for all the queries have been given above by the use of calculations by applying the given values to the formulae.

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