Inventory Analysis

Question 1

What are Dell’s revolvers?

Answer 1

• To compensate for long lead times and to buffer against demand variability, Dell requires its suppliers to keep inventory on hand in revolvers, small warehouses located within a few miles of Dell’s assembly plant.
• Each revolver is shared by several suppliers who pay rent for using them, but decide how much inventory to order and when to order based on target levels set by Dell

Question 2

Inventory Classification:

Answer 2

• Input Inventory, e.g. raw materials and parts
• In-process Inventory
  
  • Work-in-process inventory
  • In-transit inventory
• Output Inventory

Question 3

Why Should We Keep Inventory?

Answer 3

• Economies of scale
  
  • A process exhibits economies of scale when the average unit cost of output decreases with volume
    
    • Fixed ordering cost: the administrative cost of processing the order, transporting the material, and receiving and inspecting the delivery that is independent of order size
    • Fixed setup cost: the time and material required to set up a process
    • Price discounts
• Production and Capacity Smoothing
  • When demand fluctuates seasonally, it may be economical to maintain a constant processing rate and build inventories in period of low demand and deplete them when demand is high. Inventories maintained to absorb seasonal fluctuations of demand and supply are called seasonal inventories
• Stock-out Protection
  
  • Inventories are held to protect against unexpected supply disruptions, due to supplier strikes, fire, delays and foul weather, or surges in demand.
  • Inventory maintained to insulate the process from unexpected supply disruptions and surges in demand is called safety inventory.
• Price Speculation
  • Inventories are held to profit from probable changes in market price of inputs or outputs.

Question 4

Why Should We Avoid Inventory?

Answer 4

• Physical holding cost:

• The cost of storing inventory, including insurance, security, warehouse rental, lighting, heating and cooling, plus all the costs that may be entailed before inventory can be sold, including spoilage, obsolescence, pilferage, and rework.
• Physical holding cost per unit of time (a year) is often expressed as a fraction h of the variable cost C of acquiring (or producing) one unit of inventory
• Opportunity cost
• The forgone return on the funds invested in inventory which could have been invested in alternate projects.
• The opportunity cost of holding one unit of inventory is usually expressed as rC where r is the firm’s annual rate of return.

Cost of holding one unit of inventory for one year H = (h+r)C

Question 5

Optimal Order Size:

Answer 5

In general to find the optimal size of order, we take derivative from the total cost function with respect to Q and set it equal to 0, which gives

TC(Q)=H Q/2+S R/Q+RC

dTC/dQ = H/2-RS/Q² = 0

→ Q^∗=√(2SR/H)

The model above is called the Economic Order Quantity (EOQ) model.

Question 6

Inventory Management:

Answer 6

Inventory management is about finding the right balance between keeping too much and too little inventory.

• Two Inventory questions
  
  • When we should place an order?
  • How much we should order?
• Two Assumptions
  
  • Items are procured in batches
  • Processing (consumption) of items takes place continuously at a constant rate of R

Question 7

Total Annual Cost =

Answer 7

Annual Purchasing Cost + Annual Ordering Cost + Annual Holding Cost

TC(Q) = RC + SR/Q + HQ/2

• RC = Annual Purchasing Cost
• R/Q*S = Annual Ordering Cost
• HQ/2 = Annual Holding Cost

Question 8

Lead Time =

Answer 8

The time lag between the order being placed and its arrival is called replenishment lead time, and denoted by L.

In the EOQ model, we should order L units of time before we expect the inventory level drop to zero.

Instead of keeping track of time, we can keep track of inventory level and reorder as soon as the inventory level drops below a certain reorder point.

Question 9

Impact of Lead time

Answer 9

In general

• If L ≤ Q/R → ROP = L×R
• If L > Q/R → ROP = (L×R)/Q (the remainder of L×R divided by Q)

Our assumption is that we can keep track of inventory continuously over time. This is known as a continuous review policy.

A period ordering system is used when inventory cannot be continuously monitored.