The Central Hydraulic Supply Company Is A

Question

The Central Hydraulic Supply Company is a distributor of hydraulic supplies in Central California. Central handles standard fittings, tubing, and similar items. Generally Central carries an entire pro…

The Central Hydraulic Supply Company is a distributor of
hydraulic supplies in Central California. Central handles standard
fittings, tubing, and similar items. Generally Central carries an
entire product line for each manufacturer it represents providing
local stock for rapid delivery to customers. Central stocks parts
that are used in the maintenance of large construction equipment.
The company operates 52 weeks per year, 6 days per week.

Central has grown from a small two-person operation to a
$75-million per year business in a span of 25 years. From its
inception Central has been a profitable business in sound financial
condition. Despite the continued growth of profits in absolute
terms, however, Central found that profits as a percentage of sales
have declined. When management became aware of the seriousness of
the problem, it was decided to undertake a thorough review of
policies and procedures in the area of inventory management.

One of the first items the company reviewed was the cost of
preparing and processing a requisition, preparing a purchase order,
and making necessary record changes. This was estimated to be $50
per order.

One of the typical items of inventory analyzed in detail was a
small hydraulic fitting. Central sells about 21,840 of these
fittings per year (each fitting is purchased for $14 and is sold
for $19). The

manufacturer from whom Central buys the fitting does not offer
any quantity discount. The manufacturer is located about 1,500
miles away and the fittings are shipped to Central by truck. They
all arrive at once.

The annual per unit inventory holding cost is 20% of the item’s
value.

  1. What is the order quantity that minimizes total annual cost of
    inventory (TAC)? What is the minimum TAC?
  2. Suppose that the supplier of the fittings only has the capacity
    to deliver the fittings at the rate of 100 per day. Recalculate the
    optimum order quantity and the minimum TAC.

    C. Suppose the supplier were to offer the following quantity
    discounts:

                           
    Quantity Ordered        
    Price per fitting=

                           
    <
    1,000                       
    $14.00

                           
    1,000 to
    1,999             
    $13.85

                           
    2,000 or
    more             
    $13.70

    The supplier is capable of delivering all the fittings order at
    once (instantaneous replenishment). Recalculate the optimum order
    quantity and the minimum TAC.     

    D. Suppose the supplier has a 4 day lead time and that the
    standard deviation of daily demand is 15 units. What is the
    necessary reorder point to achieve a 96% service level?

Solutions

Expert Solution

A.

The order quantity
that minimizes total annual cost of inventory (TAC)=EOQ

EOQ=SQRT(2*Annual
demand*ordering cost per order /   holding cost per unit
per year)

Annual
demand       21840

Purchase price per
unit        14

Ordering cost per
order       50

Holding cost per
unit per year         2.8

EOQ          
=883.18

Total number of
orders per year = Annual demand, D / Order quantity
,Q      24.73

Average cycle
inventory       441.59

Ordering
cost         
1236.45

Annual cycle
inventory Holding cost 1236.45

Total annual
inventory costs= some books also include product cost in inventory
costs

Product
cost     =     
305760.00

Total
Annual inventory costs(if product cost is included)  
308232.89

B

our
order quantity is 100 and is delivered daily

Annual
demand       21840

Purchase price per
unit        14

Ordering cost per
order       50

Holding cost per
unit per year         2.8

   

EOQ          
100.00

Total number of
orders per year = Annual demand, D / Order quantity
,Q      218.40

Average cycle
inventory       50.00

     Ordering
cost         
10920.00

Annual cycle
inventory Holding cost 140.00

    

Product
cost          
305760.00

Total Annual
inventory costs(if product cost is
included)       316820.00

C

We know EOQ, for
regular price 14, is   883.18. It does
not fit not any discount .

Total Annual
inventory costs(if product cost is included)    =
316820.00

We take other
minimal order quantities that qualify for the discount and use them
to calculate Total Annual inventory costs

The order quantity
that gives the least Total Annual inventory costs is chosen

Purchase
price per unit      13.85

Minimum order
quantity required to qualify for discount = 1000

Total Annual inventory costs(if product cost is
included)    = 304961

Purchase
price per unit      13.7

Minimum order
quantity required to qualify for discount = 2000

Total Annual
inventory costs(if product cost is included)    =
302494

We find that the
total annual inventory cost is lowest for Q= is   2000.
So we choose this as the optimal order quantity

Total Annual
inventory costs(if product cost is included)    =
302494

d.

Continuous review-
fixed quantity//EOQ       

      Annual
demand       21840

Purchase price per
unit        14

Ordering cost per
order       50

Holding cost per
unit per year         2.8

Number of
periods(days)     365

   
Average demand for the period(daily
demand),d       59.84

S.D of demand (per
day)     15

Lead
time(days),L    4

S.D of Lead time
(days)      0

Service
level          
0.96

    

EOQ          
=883.18

S.D of demand during lead time =
30

Z   
1.751

Mean demand during
lead time=d*L 239.3424658

Safety
stock=         52.52

Reorder
point         
291.86

asd


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