good shephard home
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Good Shepherd Home
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ase Details The Good Shepherd Home is a long-
term care facility with an 80-bedcapacity
Mr. Scott, the administrator, is
concerned about rising food costs Mr. Scott decides to investigate food
services, due to increased in price
significantly.
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He has looked at 100 stock items and isconsidering tighter controls on the 40
stock items for which 400 order-units(dozens, cases, pounds, etc.) havebeen ordered.
Of particular interest is a problem withperishable good, bread.
Bread demand is uneven.
Fresh bread is delivered daily and isused that day for table meal serviceonly.
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-T h e d a y o ld b re a d is sa lva g e d fo r.d re ssin g a n d sim ila r d ish e s
S co tt e stim a te s th e co st o f b re a d to b e. / -$ 0 7 5 lo a f a n d th e co st o f d a y o ld b re a d
. / .to b e 0 2 5 lo a f
. M r S co tt is of th e o p in io n th a t b e in g-o u t o f b re a d it co st a d o lla r p e r lo a f
sh o rt in g o o d w illlo st fro m o u r
.re sid e n ts T h e fo o d se rvice s su p e rviso r h a s a/sta n d in g o rd e r fo r 3 0 lo a ve s d a y a n d.tw ice th a t a m o u n t o n S u n d a y
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The supervisor spends less than $5/day onfood for each resident on food
The supervisor says that she knows withcertainty that demand for hamburgerover a menu cycle is 200 pounds.
Costs : $12 to place an order and 20percent of the hamburger cost to carry
hamburger in inventory. Hamburger costs $1.55/pound.
Good Shepherd currently ordershamburger every week
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Typical Inventory Items
Number ofStock Items
QuantityOrdered (inunits)
Total Cost (in $)AverageInventory (in $)
3 50 3,500 1,200
12 150 2,500 900
20 200 1,500 600
40 400 2,000 20025 200 500 100
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The ABC classification process isan analysis of a range of items,
such as finished products orcustomers into three categories:
A - outstandingly important:
comprising items with a large dollarvolume.B - of average importance: comprising
items with moderate value andmoderate dollar volume.C - relatively unimportant as a basis
for a control scheme: comprisingitems with a lar e volume and small
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ABC Classification
Classification
Item no Monthly $usage
% of total$ wage
No ofitems
% of totalno ofitems
A 3, 12 6000 60 2 40
B 40 2000 20 1 20
C 20,25 2000 20 2 40
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ABC Classification
A-large $ items: item comprise 60%of total $ volume
B-moderate unit and $ value: itemcomprise of 20% of the total $volume.
C-large number of items but small $
value: item comprise 20% of total $value.
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Assuming
Mr. Scott is concerned with the 40item
because it involves a perishable itemie., Bread
and therefore he wishes to exercisegreater
control over it than the group A.In fact we can say that for Mr Scott
these 40 stock are graded as A
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Critical Fractile
Single Period Inventory Model.
Critical Factile is the service levelthat maximizes profit for theperishable goods case.
It is the ratio of the shortage(understock) cost and the sum of
shortage and overstock costs Critical Fractile (CF) = Cu / Cu + Co
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Critical FractileCalculation
Cost of fresh bread - $0.75/loaf
Cost of day old bread - $0.25/loaf
Understock cost = $1
Overstock cost = $ 0.5 (0.75 0.25)
Critical Factile = 1 / 1 + 0.5 = 0.66
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( )B re a d D e m a n d in lo a ve sD a y W e e k1 W e e k2M o n 2 0 1 9
T u e 1 5 2 7 W e d 2 1 2 0T h u 3 0 3 2Fri 3 1 2 7
S a t 1 9 1 6S u n 4 2 3 9
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For SundayRange = 3Economic order quantity (Q) = 41On Sunday 41 loaves is the ideal
quantity to be ordered.
Mean weekday Bread demand =23.083 23(approx)
Standard Deviation = 5.65
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% W e ca n b e 6 7 certa in th a t th ed e m a n d fo r b re a d lo a ve s w ill n o t
.e xce e d 2 6 o n w e e k d a y s % W e ca n b e 8 0 certa in th a t th e
n u m b e r o f u n its sold w ill n o t
.e xce e d 2 8 o n w e e k d a y s
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ComparisonStockout cost
Previously 65.5 $
Now 45 $
A d e clin e o f . %1 2 9 .in stockout cost
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Cost TradeoffsMultiperiod Inventory System.Objective in inventory control is to find
the minimum cost. To calculate thatwe need to consider all the following
costs.
Total Annual Relevant Cost = Cost of
the Items + Procurement Cost +Carrying Cost + Stockout Cost.
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Cost of Item:The cost of value of the item is usually its
purchase priceThat is the amount paid to the supplier for
the item.E.g.: from the case hamburger cost is
$1.55/pound
Procurement Costs:
Costs of placing an order or setup costs ifthe item is manufactured by the firm
E.g.: $12 to make an order for hamburger
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Carrying (holding) Costs:
Carrying or holding costs are the
costs of maintaining the inventory.E.g.: 20% p.a. of the hamburger cost .
= 0.20 x 1.55 / 26
= 0.01192 for 2 weeks
Stockout Cost:
Stockout cost are associated
with demand when stocks have beende leted,
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As theOrdering
costdecreases
the Carryingcost
.increases
It is saidthat there
is a casttradeoffbetween the
.two
EOQ
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Economic Order Quantity
EOQ is essentially an accountingformula that determines the pointat which the combination of order
costs and inventory carrying costsare the least.
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Economic Order Quantity(EOQ) Forthis case
Q* = (2 x D x S/IC) = [2 x 200 x 12 / 0.011] = 634.57 poundsWell as the demand is just 200 pounds
per week and hamburgers timeduration is only 2 weeks (Assumed)
we cannot order such a largequantity. So the ordering quantityshould be equal to demand i.e. 200
pounds
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Total Cost
Total cost = Procurement cost x No.of orders + Carrying cost of 1 unit xAvg. no. of units carried
TC = S x D + IC x Q Q 2
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TC = 12 x 200/200 + 0.011 x 200/2 = 13.192
TC = 12 x 200/100 + 0.005 x 100/2 = 24.298
. %5 7 0 of d e cre e sin to ta l
.cost
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Suggestion to Mr. Scott
Minimize the number of orders byordering for a entire meal cycleinstead of each week.
Implement proper inventory controlby making use of critical fractile.
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Thank