INVENTORY

1.Purchasing Problem with no shortage

Formula:

2. Production Problem with no shortages Formula:

3.PURCHASING PROBLEM WITH SHORTAGES

Formula:

4.PRODUCTION PROBLEM WITH SHORTAGES

Formula:

Buffer Stock

B = Ld * r

Ld = Difference Between maximum lead time and normal

lead time.

r- consumption rate during lead time

Reorder level

1. If buffer stock is not maintained

ROL = L* r units

2. If we maintain buffer stock with B units then

ROL = B+L* r units

3. Average Inventory = B + (Q/2)

4. Maximum Inventory = B + Q

PROBABILISTIC MODELS

Problem

1. A manufacturer has to supply his customer with 600 units of the

product per year. Shortages are not allowed and the storage cost amounts

to Re.0.60 per unit per year. The set-up cost per run is Rs.80.Find the

optimum run size and the minimum average yearly cost.

2. A manufacturer has to supply his customer with 24,000 units of his

product per year. This demand is fixed and known. Since the unit is used

by the customer in an assembly line operation and the customer has no

storage space for the units, the manufacturer must ship a days supply

each day. If the manufacturer fails to supply the units he will lose the

account and probably the business. Hence, the cost of storage is assumed

to be infinite, and consequently, none will be tolerated. The inventory

holding cost amounts to 0.10 per unit per month, and the set up cost per

run is Rs.350.Find the optimum lot size and the length of optimum

production run.

3.

4. A bush manufacturing company has a contract to supply 5000 bushes

to an automobile factory per day. The company has capacity to

manufacturer 8000 bushes and holding cost of 1000 bushes is 8 paise.

Setup cost is Rs.20.What would be the frequency of production run?

5. Find the most economic batch quantity of a product on a machine if

the production rate of that item on the machine is 200 pieces per day and

the demand is uniform at the rate of 100 pieces per day. The set-up cost

is Rs.200 per batch and the cost of holding one item in inventory is

Re.0.81 per day. How will the batch quantity vary if the machine

production rate is infinite?

6. The demand for an item is Rs. 18,000 units per year. The holding cost

per unit time is Rs.1.20 and the cost of shortage is Rs.5.00, the

production cost is Rs.400.Assuming that replenishment rate is

instantaneous determine the optimal order quantity.

7. A certain product has a demand of 25 units per month and the items

withdrawn uniformly. Each time a production run is made the setup cost

is Rs.15. The production cost is Rs.1 per item and inventory holding cost

is Rs.0.30 per item per month. If shortage cost is Rs.1.50 per item per

month, determine how often to make a production run and what size it

should be?

8. A dealer supplies you the following information with regard to a

product dealt in by him.

Annual demand 5000 units

Buying cost Rs.250 per order

Inventory carrying cost Price Rs.100 per unit 30% per year

The dealer is considering the possibility of allowing Home back orders

to occur for the product. He has estimated that the annual cost of back

ordering (allowing shortages) the product will be Rs.10.00 per unit.

(i) What should be the optimum order number of units of the product he

should buy in one lot?

(ii) What quantity of the product should he allow to be back-ordered?

(iii) How much additional cost will he have to incur on inventory if he

does not permit back-ordering?

9. A commodity is to be supplied at a constant rate of 200 units per day.

Supplies for any amounts can be had at any required time, but each

ordering costs Rs. 50.00. Cost of holding the commodity in inventory is

Rs.2 per unit per day while the delay in the supply of items induces a

penalty of Rs.10 per unit per delay of one day. Formulate the average

cost function of this situation and find the optimal policy (q, t) where t is

the reorder cycle period and q is the inventory level after re-order. What

should be the best policy if the penalty cost becomes infinite?

10. The demand for an item in a company is 18,000 units per year, and

the company can produce the item at a rate of 3000 per month. The cost

of one set up is Rs.500 and the holding cost of one unit per month is 15

paise. The shortage cost of one unit is Rs.20 per month. Determine the

optimum manufacturing quantity and the number of shortages. Also

determine the manufacturing time and time between set-ups.

11. A contractor undertakes to supply diesel engines to a truck manufacturer at the rate of 25 per day. There is a clause in the contract

penalizing him Rs. 10 per engine per day late for missing the scheduled

delivery date. He finds that the cost of holding a completed engine stock

is Rs.16 per month. His production process is such that each month he

starts a batch of engines through the shops, and all these engines are

available for delivery any time after the end of the month. What should

his inventory level be at the beginning of each month?

12. The following information is provided: Annual usage is 24,000 units, Ordering cost is Rs.120 per order,

Carrying cost is 20%, Price of each item is Rs.20 and lead time is 10

days. There are 240 working days per year. Determine the EOQ and

orders per year. In the past two years, the usage rate has gone as high

as 140 units per day. For a reordering system based on inventory level,

what safety stock is required to protect against this higher usage rate?

What should be the reorder point at this safety stock level? What should

be the carrying cost for a year?