Lecture 14

 

Held on: Monday, September 11, 2000.

 

Notes by: Shantanu Mathur & Saiket Sen Gupta

 

 

INVENTORY THEORY

 

Motivation for keeping inventory

 

1.      Transaction motive(reduce cost/transaction)

§         Large lots imply è reduction of fixed cost

§         Production setup reduced è cost/unit comes down

§         Economics of scale

§         Efficient inventory management can lead to significant impact on bottomlines.

 

2.      Precautionary motive

§         Inventories introduced as a hedge, i.e. insurance against uncertainties like

§         Supply

§         Demand

§         Lead times(time between placing of order and receipt time)

 

3.      Speculative method

§         If cost of obtaining or producing is going to increase in the near future it is advantageous to hold inventories in the anticipation of price rise.

§         E.g. Paper industry: most of it imported from Indonesia. The prices oscillate a lot and hence when to buy and how much to buy.

§         If demand is anticipated to increase, (due to seasonality, etc) it may be more advantageous to increase inventory rather than capacity.

 

However inventory build up usually occurs due to lack of sales reflection on poor health of the economy.

 

MAIN INVENTORY STOCK POINTS

 

 

 

 

 

 

 

1.      Raw material and supplies

§         Carry out production process

§         Minimum cost according to plan

§         No compromise on production.

§         How much and when to order

 

2.      Work in progress (WIP) and Finished goods

§         Lot sizes

§         Timing

§         Usage rates of distributors

§         How much to produce at a time and how often

 

3.      Distributors and retailers

§         They store different goods of different companies.

§         Large number of items

§         How often and how much to order?

 

 

INVENTORY MODELS

 

We will be looking at single product single location models as of now.

The three key variables from modeling viewpoint are

1.      Nature of Demand

2.      Cost to be incorporated

3.      Physical Aspects of the system

 

 

1.      Demand Patterns

 

There are three type of demand patterns:

a.       Deterministic Demand and stationary demand i.e. independent of time eg. EOQ model

b.      Deterministic and time varying demand. Seasonality, Trend are some of the factors on which the demand may be dependent.

c.       Uncertain Demand: Probability distribution is known.

 

2.      Costs

a)      Average cost vs discounted cost

For large time horizons time value of money should be accounted for and discounted cash may be considered.

 

r : return on investment

a = 1/(1+r) ; C_i: Cash flow in period I

                                      _¥

Present value of cost = S aⁱ C_i

                                     ⁰

If avereage cost considered then,

                                _¥ 

Avg Cost: lim (1/n) S C_i

                ^{nॠ           1}

b)      Structure of order cost

Whether cost consists of variable and/or fixed components

 

Typically cost = c.y + K.d(y)

            d(y) = 1 if y >0

            d(y) = 1 otherwise

 

c)      Penalty Cost for unfulfilled demand.

 

 

3.      Physical Aspects

 

a)      Assumptions on lead times

§         EOQ model: zero lead time or constant lead time.

§         Variable lead time

 

b)      Back Ordering Assumptions (The way system reacts when demand exceeds supply)

§         All excess demand is backordered

§         All excess demand is completely lost

§         Something in between

 

c)      Review Process

How often inventory reviewed

§         Continuous Review: monitored at all times and order can be placed anytime

§         Periodic Review: monitored at predetermined time

§         In large companies too many components hence continuous review is not feasible, so we go for review at periodic review.

§         We may have continuous monitoring of inventory for critical components

 

d)      Changes in inventory during storage

§         Traditional models did not take these into account

§         Eg. Petrol may evaporate

§         Food products may decay

§         Technology may become obsolete

 

 

EOQ MODEL

 

Assumptions

1.      Constant known Demand

2.      Shortages not allowed

3.      Lead time is instantaneous for delivery

4.      No time discounting for money

5.      Costs include K per order and h per unit held per unit time

h: cost of capital invested, insurance, storage, handling cost, etc

 

Since lead times are 0 and demand is know with certainty, orders are given only when inventory level hits zero.

 

Say order size Q

Cycle time: time between 2 successive arrivals of orders

è T = Q/l

T = Q/l

Q5

Q4

Q3

Q1

Q2

Inventory

Level

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

If we order different quantities then the average cost is higher as compared to when we order 1 optimum quantity always.

 

		T = Q/l