##### 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.

- What is the order quantity that minimizes total annual cost of

inventory (TAC)? What is the minimum TAC? - 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

$13.70The 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