BGSC-inventory management and risk pooling

What are key factors affecting inventory policy?

• First and foremost is customer demand, which may be known in advance or may be random. In the latter case, forecasting tools may be used in situations in which historical data are available to estimate the average customer demand, as well as the amount of variability in customer demand (often measured as the standard deviation).

• Replenishment lead time, which may be known at the time we place the order, or it may be uncertain.

• The number of different products stored at the warehouse.

• The length of the planning horizon.

• Costs, including order cost and inventory holding cost. a. Typically, order cost consists of two components: the cost of the product and the transportation cost. b. Inventory holding cost, or inventory carrying cost, consists of: (1) State taxes, property taxes, and insurance on inventories. (2) Maintenance costs. (3) Obsolescence cost, which derives from the risk that an item will lose some of its value because of changes in the market. (4) Opportunity costs, which represent the return on investment that one would receive had money been invested in something else (e.g., the stock market) instead of inventory.

• Service level requirement. In situations where customer demand is uncertain, it is often impossible to meet customer orders 100 percent of the time, so management needs to specify an acceptable level of service

Define the difference between inventory on-hand vs inventory level

• Inventory level

What inventory you currently have plus what is unrealized of incoming

• Inventory on-hand

Real inventory that is avilable at your warehouse

What is the economic lot size model?

The model illustrates the trade-offs between ordering and storage costs.

Explain the assumptions of the model

• D items per day (Demand is constant at a rate)

• Q items per order (Order quantities are fixed)

• K: fixed setup cost (incurred every time the warehouse places an order)

• h: holding cost/ inventory holding cost (is accrued per unit)

• Lead time = 0

• Initial inventory = 0

• planning horizon is long(infinite)

Explain the Formulas of EoQ model  

• order quantity Q:            

  _Q*=√2KD/h     

• Total cost in Cycle of length T:   

  hTQ/2+k           

• Inventory holding cost:         

    hQ/2

• Setup cost per unit time:

   KD/Q

• Holding cost per unit time:

  hQ/2           

• When the optimal order quantity is achieved at the point at which inventory setup cost per unit of time equals inventory holding cost per unit of time.
  KD/Q=hQ/2

• Total relevant costs(TRC/TC):

  KD/Q+hQ/2

What is Continuous Review Policy?

The inventory position at any point in time is the actual inventory at the warehouse plus items ordered by the distributor that have not yet arrived minus items that are backordered

What are the assumptions of the Continuous Review Policy?

• Daily demand is random and follows a normal distribution

• Ordering costs: Every time the distributor places an order from the manufacturer, the distributor pays a fixed cost, K, plus an amount proportional to the quantity order

• Inventory holding cost is charged per item per unit time

• Inventory level is continuously reviewed, and if an order is placed, the order arrives after the appropriate lead time

• If a customer order arrives when there is no inventory on hand to fill the order, the order is lost

• The distributor specifies a required service level. The service level is the probability of not stocking out during lead time.

• AVG=Average daily demand faced by the distributor

• STD =Standard deviation of daily demand faced by the distributor  

• L=Replenishment lead time from the supplier to the distributor in days

• h=Cost of holding out unit of the product for one day at the distributor

• ɑ= Service Level

• 1-a=The probability of stocking

How to calculate the Safety stock?

z*STD *√L     

Z is a constant, referred to as the safety factor

How to calculate the reorder level?

R=L*AVG+Z*STD*√L                                                                 

How to calculate the order quantity, Q?

Q=Q*=_{√2KD/h=√2AVG/h}     

Describe (Q,R) policy

Depend on the deterministic model of known demand    

What is (s,S) policy?

Whenever inventory drops to s, order S

Define periodic review policy

The inventory level is reviewed at regular intervals and appropriate quantity is ordered after each review

What is Base-stock policy?

This policy is used for longer review intervals(e.g., weekly or monthly), which is always ordered after each inventory review and fixed order cost is considered a sunk cost. The policy is characterized by a single parameter: the base-stock level, ordering enough to raise inventory position to the base-stock level.

What does the base-stock level include?

average demand during an interval of r+L days and the safety stock

How to calculate the average demand during an interval of r+L days?

(r+L)*AVG                 

How to calculate the safety stock under the periodic review policy?

r*AVG/2*r*STD*√(r+L)=z*STD*√(r+L)                                            

What are the 3 key aspects of risk pooling?

• Centralizing inventory reduces both safety stock and average inventory in the system

• The higher the coefficient of variation, the greater the benefit obtained from centralized systems; that is, the greater the benefit from risk pooling

• The benefits from risk pooling depend on the behavior of demand from one market relative to demand from another. The benefits from risk pooling are decreased the more positively correlated demand is between 2 marketsCentralizing inventory reduces both safety stock and average inventory in the system

• The higher the coefficient of variation, the greater the benefit obtained from centralized systems; that is, the greater the benefit from risk pooling

• The benefits from risk pooling depend on the behavior of demand from one market relative to demand from another. The benefits from risk pooling are decreased the more positively correlated demand is between 2 markets