Cutting Workshop 3 Operations
Uploaded by
ScribdTranslationsCutting Workshop 3 Operations
Uploaded by
ScribdTranslationsInventory Model Workshop
Group BN
The B & S Novelty and craft shop in Bennington, Vermont, sells to tourists
various quality handmade items. La B & s has 300 for sale.
hand-carved miniature replicas of a colonial soldier, every year, but the
The annual demand pattern is uncertain. The replicas are sold for $20.00.
each one, and the company uses an annual maintenance cost rate of
15% inventory on the annual holding cost of the inventory. The
Ordering costs are $5 and the demand during the waiting time
follows a normal distribution with a mean of 5 and a standard deviation
standard of 6 units.
a) What is the optimal order quantity?
DATA:
annual demand = 300 replicas
$20
CM (maintenance cost) = 15%(PV) = 15%($20) = $3
$5
µ = 5 units
σ = 6 units
√ √
2( D)(CO) 2( 300)(5)
Q*= = = 31.62 = 32 replicas.
CM 3
b) If you decide to accept a depletion of two times a year, what point of
What reorder would you recommend? What is the probability that the company
Did you experience a shortage in any order cycle?
R = µ + Zσ
PAE (probability of depletion of existence) = depletion of
stocks/N
Exhaustion of existence = 2
N (number of orders) = D/Q = 300/32 = 9.375 = 10 orders per year
0.2
P (no exhaustion of existence) = 1 - PAE = 1 - 0.2 = 0.8
P (0 exhaustion of existence) = 0.8, then Z = 0.84, table of
normal distribution.
R = 5 + (0.84*6) = 5 + 5.04 = 10.04 = 11
P (probability of exhaustion in any cycle) = exhaustion of
existence/N
Depletion of existence = 1
P (probability of depletion in any cycle) = 1/10 = 0.1 = 10%.
c) What are the annual costs of the safety stock of this?
product?
Annual security existence costs = CM*B
B (safety stock) = Z*σ = 0.84*6 = 5.04 = 6 replicas
Annual existence costs = 3*6 = $18
A retail store sells a seasonal product for $10 per unit.
the cost of the product is $8 per unit. All units that are not sold
during the regular season they are sold at half the retail price in a
clearance sale at the end of the season. Assume that the demand for
the product is uniformly distributed between 200 and 800.
a. What is the recommended order quantity?
DATA:
PV (selling price) = 10 $/unit
8 $/unit
PL (liquidation price) = PV/2 = 10/2 = 5$/unit
(200<Q<800)
Cu (costo por unidad de subestimar la demanda) = PV – CV = 10 – 8 = 2
Co (cost per unit of overestimating demand) = CV - PL = 8 - 5 = 3
Cu 2
P ( demand ≤ Q
=
) Cu+ What 2+ 3 0.4
=
Q* = 200 + ((800 - 200) * 0.4) = 200 + 240 = 440 units
b. What is the probability that at least some customers will order the product
after the stock has run out? That is to say, what is the
probability of exhausting stock using your order quantity of the part
a)?
P (demand > Q) = 1 - P (demand ≤ Q) = 1 - 0.4 = 0.6 = 60%
c. To keep customers happy and make them return to the store later, the
the owner thinks that stockouts should be avoided if it is
possible. What is your recommended order quantity if the owner is
willing to tolerate a 0.15 probability of stock exhaustion?
15% = 0.15
P (margin of tolerance) = 1 - P (tolerance) = 1 - 0.15 = 0.85 = 85%
Q* = 200 + ((800 - 200) * 0.85) = 200 + 510 = 710 units
d. Using your answer from section C. What is the cost of appreciation that
would ensure the depletion of stock?
CP (capital gains tax) = Q*Co = (710 units)*(3$/unit) = $2130
3) Foster Drugs, Inc., handles a variety of health and beauty aid products.
The particular hair conditioner product costs Foster $2.95 per unit. The annual holding
cost rate is 20 percent. Using an EOQ model, they determined that an order
quantity of 300 units should be used. The lead time to receive an order is one
week, and the demand is normally distributed with a mean of 150 units per week
and a standard deviation of 40 units per week.
a. What is the reorder point if the firm is willing to tolerate a 1-percent chance of a
stockout during an order cycle?
DATA:
PV (selling price) = $2.95/unit
$0.59
Q* = 300 units
1 week
µ = 150 units/week
σ = 40 units/week
1% = 0.01
P (margin of tolerance) = 1 - P (tolerance) = 1 - 0.01 = 0.99 = 99%
Z = 2.33 normal distribution table.
R = dL + ZσL
dL = µL = (150 units/week) * (1 week) = 150 units
σL = σd* √ L (40 units/week)* √ 1 week = 40 units
R = 150 + (2.33*40) = 150 + 93.2 = 243.2 = 244 units
b. What safety stock and annual safety stock cost are associated with your
recommendation in part a?
Safety stock = ZσL = (2.33*40) = 93.2 = 94 units
Annual existence costs = CM*B = 0.59*94 = $55.45
c. Foster is considering making a transition to a periodic-review system in an
attempt to coordinate ordering of some of its products. The review period would be
two weeks and the delivery lead time would remain one week. What target
What inventory level would be needed to ensure the same 1 percent risk of stock out?
DATA:
sales price = $2.95/unit
$0.59
Q* = 300 units
1 week
P (review period) = 2 weeks
µ= 150 units/week
σ = 40 units/week
1% = 0.01
P (margin of tolerance) = 1 - P (tolerance) = 1 - 0.01 = 0.99 = 99%
Z = 2.33 normal distribution table.
R = d(P+L) + Zσ(P+L)
d(P+L)=µ(P+L)=(150 units/week)*(2 weeks+1 week) = 450
units
σ(P+L) = σd* √ P+L (40 units/week) * √ 2weeks+1 week = 69.28
units
R = 450 + (2.33 * 69.28) = 450 + 161.42 = 611.42 = 612 units
d. What is the safety stock associated with your answer to part c?
What is the annual cost associated with holding this safety stock?
B (safety stock) = Zσ(P+L) = (2.33*69.28) = 161.42 = 162
units
Annual existence costs = CM*B = 0.59*162 = $95.58
e. Compare your answers to parts b and d. If you were the manager of Foster
Drugs, would you choose a continuous or periodic review system?
If I am the manager of the company, when comparing the answers to the questions
It is observed that with a system of periodic review there is greater
safety stock and therefore, higher annual costs of
existence.
162 units is greater than 94 units and $95.58 is greater than $55.45.
consequently, if the continuous review system is chosen, the company will
saves ($95.58 – $55.45) a total of $40.13 in the year.
In conclusion, the system of continuous review is chosen.
f. Would it be ok for the continuous review system for more expensive items? For
For instance, suppose that the product is sold at $2.95 per unit. Explain.
Yes, a continuous review system would be good because the company when selling
the 300 units that is the optimal quantity to order annually and sell them at
$2.95 generates an annual income of $885 and the annual inventory costs
Security costs $55.45, therefore a profit of $829.55 is obtained.
Clearly, this does not include ordering costs and maintenance costs.
of the inventory.