Inventory Management

Question 1

Reasons to (not) hold inventory

Answer 1

• Why to hold inventory:
  
  • meet predictable variability in demand
  • provide safeguard against unpredictable variability in demand
  • deal with variability in production or service operations
  • take advantage of economies of scale in production/logistics
• Why not:
  
  • costly: storage cost, spoilage cost, opportunity cost of capital, insurance costs
  • risky: obsolescence, over-supply
  • substitutable: by information or capacity
  • hides problems in a sea of inventory

Question 2

Inventory cost components

Answer 2

• Purchase costs (per unit), incl. order size discounts
• Ordering costs (per order): paperwork etc.
• Holding costs (per unit per time): warehousing, insurance… ≈ 15-35% of actual unit value per annum
• Shortage/stockout costs (?): missed sales, costs of rush order…

Question 3

Inventory Management: ABC Analysis

Answer 3

• Different items require different amount of management’s attention, based on their “value” to the organization:
  
  • A: 20% of items - 80% of value: require frequent monitoring and management via advanced inventory management techniques
  • B: 30% of items, 10-20% of value: require less frequent monitoring and less advanced techniques
  • C: 50% of items, 5-10% of valie: require infrequent monitoring and easy-to-implement techniques

Question 4

Economic Order Quantity Model

w/ instant lead time

Total Cost

Answer 4

• D = Demand rate (number of orders / year)
• Q = Order quantity (units)
• S = Setup costs or cost per order (€/order)
• H = Holding costs per year (€/unit/year); sometimes they are i*C
• C = Cost of purchasing a unit (€/unit)

Objective => minimize total costs so that TC’(Q)=0

Q* = sqrt [(2*D*S) / H]

If there is lead time, reorder as soon as inventory = D*L, also dem demand, der während der lead time herrschen wird

Question 5

EOQ Insights

Answer 5

• Order size Q and average inventory (Q/2) are directly related
  
  • trade-off between ordering and holding costs
• The total cost curve is “flat” near the optimum
  
  • EOQ is robust
• EOQ is driven by cost minimization: not always best

Question 6

Continuous Review & Periodic Review

Pros & Cons

Answer 6

Continuous review:

• Pros:
  
  • knowledge of an item’s inventory levels at all times
  • less inventory needs to be kept at hand
• Cons:
  
  • costs of monitoring inventory levels

Periodic review:

• Pros:
  
  • review periods are known in advance
  • allows for better coordination across products and management of ressources
• Cons:
  
  • Requires keeping more inventory on hand to achieve similar service level

Question 7

Continuous Review

Fixed Order Quantity Model: Safety Stock

Answer 7

• Order Quantity: get it from EOQ => Q* = sqrt(2DS/H)
• Reorder point ROP = D * L + SS
  
  • Safety stock provides cushion against demand variability
  • Shortage occurs when Demand over Lead time > ROP
• Factors that influence Safety Stock
  
  • Demand variability +
  • Service level (self chosen) +
  • Delivery Lead time +
• SS = z * σ_L = z * σ_D * sqrt(L)
  
  • z=NORMSINV(service level)
  • σ_L = σ_D [std. of daily demand] * sqrt(L)

Question 8

Risk Pooling to reduce Safety Stock

Answer 8

• Idea: Supplyng independent demand streams from one location rather than multiple locations requires less safety stock
• Tool: Adding independent and identically distributed random variables:
  
  • Mean Σµ_i
  • Std. Dev.: sqrt( Σ(σ_i²)
• Example:
  
  • 4 Locations, each daily demand of µ=100, std. dev=50
  • 1 centralized location: µ=400, std. dev=sqrt(4*250)=100
• Benefits:
  
  • Cost savings are proportional to the square root of the number of locations pooled!
  • Reduces safety stocks: better service for same total inventory level OR same service for a smaller total inventory

Question 9

Periodic Review + Order-up-to-Level

Answer 9

• Order up to a predefined level on predefined time intervals
• Exposure period = T [Review Period] + L [Lead Time]
  
  • time between placing order n and receiving order n+1
• I+q is the order-up-to-level
• Safety Stock:
  
  • z * σ_L+T [Std. dev of demand during exposure period]
• Current Inventory = I
• Target Inventory
  = D * (L + T) + z * σ_L+T
• Order Quanity
  = D * (L + T) + z * σ_L+T - I
  = Target - Current Inventory
• Average Cycle Stock:
  
  • (D * T) / 2

Question 10

Newsvendor Model

Answer 10

• Based on marginal analysis: with what probability will the 88th newspaper be sold/not sold and how does that affect profits?
• Buy the Q+1st unit, as long as
  
  • Loss < Gain (or)
  • P(D≤Q) * C_o < P(D>Q) * C_u (or)
  • P(D≤Q) < C_u / (C_u + C_o)
• Stop at P(D≤Q*) ≥ C_u / (C_u + C_o)
• Service Level = Critical Ratio
• For normal demand:
  
  • Q* = µ + z * σ
  • with z = NORMSINV(C_u / (C_u + C_o))

Question 11

Newsvendor Application: Revenue Management

Answer 11

• Technique to maximize revenue by matiching fixed supply with uncertain demand
• When to use it:
  
  • fixed inventory/capacity which is expensive or impossible to store
  • inventory/capacity is committed to a customer before all demand is known
  • different customer segments can be price discriminated
  • same unit of inventory can satisfy different customer segments
• Calculate Cu and Co

Question 12

Inventory: functional classifications

Answer 12

• Cycle inventory: inventory being shipped to different production stages
• Safety inventory: against demand fluctuations & peaks
• Decoupling inventory: buffers against blocks & starvation
• seasonal inventory
• pipeline inventory: products inside production
• speculative inventory: against cost increases for inputs