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 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?

Answer 1

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

Function Library hed Names Formula Auditing G15 Annual demand Purchase price per unit Ordering cost per order Holding cost per unit per year Number of periods 21840 14 0.2 D3 365 SQRT(2 D2 D4/D5) -D2/D8 -D6/D9 -D8/2 9 10 Total number of orders per year Annual demand, D /Order quantity,Q Time between orders-Total number of periods/ number of orders Average cycle inventory 12 13 14 Ordering cost Annual cycle inventory Holding cost -D9 D4 -D5 D11 16 17 18 19 Product cost -D2 D3 Total Annual inventory costs(if product cost is included) D18+D13+D14 21

Function Library G21 Annual demand Purchase price per unit Ordering cost per order Holding cost per unit per year Number of periods 21840 14 50 2.8 365 4 883.18 9Total number of orders per year 10 Annual demand, D /Order quantity,Q 24.73 Time between orders-Total number of periods/ number of orders Average cycle inventory 14.76 441.59 12 13 14 15 16 17 18 19 20 21 Ordering cost Annual cycle inventory Holding cost 1236.45 1236.45 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

Annual demand Purchase price per unit Ordering cost per order Holding cost per unit per year Number of periods 21840 14 50 2.8 100.00 218.40 1.67 50.00 9 | Total number of orders per year= Annual demand. D / Order guantityQll 10 Time between orders-Total number of periods/ number of orders Average cycle inventory 12 13 14 15 16 17 18 19 20 21 Ordering cost Annual cycle inventory Holding cost 10920.00 140.00 Product cost 305760.00 Total Annual inventory costs(if product cost is included) 316820.00 23

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

Function Library E13 21840 13.85 50 2.77 365 Annual demand Purchase price per unit Ordering cost per order Holding cost per unit per year Number of periods 4 1000.00 9 Total number of orders per year Annual demand, D 10 Time between orders-Total number of periods/ number of orders Order quantity,Q 21.84 16.71 500.00 Average cycle inventory 12 13 14 15 16 17 18 Ordering cost Annual cycle inventory Holding cost 1092.00 1385.00 Product cost 302484.00 Total Annual inventory costs(if product cost is included) 304961.00

Function Library f 50 D4 Annual demand Purchase price per unit Ordering cost per order Holding cost per unit per year Number of periods 21840 13.7 50 2.74 365 4 2000.00 9 Total number of orders per year Annual demand, D /Order quantity, 10 Time between orders-Total number of periods/ number of orders 10.92 33.42 Average cycle inventory 1000.00 12 13 14 15 16 Ordering cost Annual cycle inventory Holding cost 546.00 2740.00 Product cost 299208.00 19 20 21 Total Annual inventory costs(if product cost is included) 302494.00

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

JUse in Formula Trace DependentsError Checking Remove Arrows Watch Calculation Calcu Insert AutoSum Recently Financial Logical Text Date &Lookup & Math More Function Create from Selection Defined Names Evaluate Formula Window Options Time. Reference. & Trig. Functions. Manager Used Function Library Formula Auditing Calculation 123 Annual demand Purchase price per unit Ordering cost per order Holding cost per unit per year Number of periods(days) 21840 6 50 2.8 365 9 10 Average demand for the period(daily demand),d S.D of demand (per day) Lead timeldays),L S.D of Lead time (days) Service level -C5/C9 12 13 14 15 16 17 18 19 20 21 15 0.96 EOQ S.D of demand during lead time -NORMSINV(C15) -C11 C13 -C19 C18 mean demand during lead timend L Safety stock zservice level) "sd ofdemand during lead time Reorder point R mean demand during lead time +saftey stock 23 24 C20 C21

U23 Continous review-fixed quantity//EOQ Annual demand Purchase price per unit Ordering cost per order Holding cost per unit per year Number of periods(days) 21840 6 50 2.8 365 9 10 Average demand for the period(daily demand),d S.D of demand (per day) Lead time(days),L S.D of Lead time (days) Service level 59.84 15 12 15 16 17 18 19 20 21 0.96 833.18 30 1.751 239.3424658 52.52 S.D of demand during lead time mean demand during lead time dL Safety stock- z service level) "sd ofdemand during lead time Reorder point R-mean demand during lead time +saftey stock 291.86 23

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