10. Inventory Management (EOQ M

1. Inventory is a stock of any item or resource used in an organization.

2. Why Hold Inventory?

To meet predictable variability in demand or supply (seasonal inventories)

To provide a safeguard for unpredictable variability in demand or supply (safety stock)

To reduce the inter-dependence of various operations in production or service (decoupling/buffer inventory)

To take advantage of economies of scale (cycle stocks) in production & in logistics

To form the process flow (pipeline inventory)

To respond to price fluctuations (speculative inventories)

3. Why Not to Hold Too Much Inventory?

costly, risky, hides problems

4. Inventory management :

an analytical modeling approach to managing the inventory level: not too much, not too little, but just the right amount.

5.  analytical approaches used in modeling inventory decisions:

• Models without demand uncertainty: 

-Economic Order Quantity

• Models with demand uncertainty:

-Fixed-order quantity model

-Fixed-time period model (we skip this)

• Models with perishable products with demand uncertainty:

-Newsboy model 

6. Economic Order Quantity (EOQ) Model

• Key Assumptions: All aspects are known with certainty

-Constant demand stream: No demand variability (Pets eat steadily)

-Constant setup cost per order (Trip cost to Petco is constant per visit)

-Constant annual holding cost per unit (Products occupy spaces in my house)

-Constant lead time (= zero in the basic setting) (I can get products instantly)

-No backorders are allowed (I cannot let my dogs and cats starve!)

• Questions

1) When to order/produce (assuming zero lead time)?

(When your inventory reaches zero)

2) How much to order/produce?

• Data:

D = Demand rate (units / yr)

C = Cost of purchasing or producing a unit ($ / unit)

C is often decreased (discounted) if Q is large

S = Setup cost or cost of placing an order($)

H = Annual holding cost per unit of inventory ($ / (unit•yr))

H is often taken as a percentage of the unit cost:

H = i*C, where i is annual percentage holding cost

• Decision:

Q = Quantity of an order (units)

Objective: To minimize the total cost

• optimal order quantity:

• Total cost curve is fairly flat near the optimal point Q-OPT

EOQ is “robust”, i.e, some errors in parameters estimation will not lead to large cost increase.

At EOQ,  Holding cost = Setup (Ordering) cost

Is that always true if holding cost or setup cost take different forms? Answer: Not necessarily.

• when lead time>0

7.