2.2 Variability and Inventory in the Supply Chain

Question 1

Deterministic Inventory Management

Answer 1

▪ Demand, replenishment times and costs are known
▪ Fixed costs incurred per order
▪ Inventory holding costs
→ Determine the optimal cycle inventory (adjusting order quantities and replenishment times to minimize costs)
→ Determine optimal lot sizes

Question 2

Inventory Management under Uncertainty

Answer 2

▪ Demand, replenishment times, revenues and costs are uncertain
▪ However, models generally assume revenues and costs to be certain
▪ Inventory holding costs
▪ Understock result in costs
▪ Overstock result in costs
→ Identify the inventory / service level to maximize profit
→ Identify the safety inventory to minimize costs

Question 3

Fig. The Role of Inventory in Supply Chains

Answer 3

Question 4

Lot Size (𝑸)

Answer 4

Lot or batch size is the quantity that a stage of a supply chain either produces or purchases at a time

Question 5

Cycle Inventory (𝑪𝑰)

Answer 5

Cycle inventory is the average inventory in a supply chain due to either production or purchases in lot sizes that are larger than those demanded by the customer (D).

Question 6

Average Flow Time Resulting from Cycle Inventory

Answer 6

Average time that a product is in the SC in addition to the production-related lead time.

Question 7

Ordering / producing larger lot sizes

Answer 7

to take advantage of economies of scale:
→ Decrease of ordering costs
→ Increase of holding costs

Question 8

Lot Sizing for a Single Product

Answer 8

▪ Material cost (average price per unit purchased) 𝐶
▪ Holding cost 𝐻 = ℎ𝐶 (with inventory cost rate ℎ as fraction of the unit cost of the product)
▪ Fixed ordering cost incurred per lot 𝑆
▪ Steady demand 𝐷
▪ No shortages allowed
▪ Fixed replenishment time
→ Minimizing the sum of material cost 𝐶, fixed ordering cost 𝑆 and holding cost 𝐻=hC

Question 9

Cycle Inventory Insights

Answer 9

▪ Cycle Inventories are caused by deviations between lot sizes and demand, due to economies of scale
▪ High cycle inventories lead to a high capital commitment / current assets
▪ Cycle inventories lead to an increase of the average flow time
▪ When demand fluctuates, high flow times may be problematic
▪ Larger lot sizes cause an increase in variability in subsequent stages
→ Aggregating orders of multiple products to reduce fixed costs, despite small lot sizes of the individual products

Question 10

Ordering Separately or Collectively for Multiple Products

Answer 10

▪ 4 Products:
▪ Demand 𝐷𝑖 = 1,000 𝑢𝑛𝑖𝑡𝑠/𝑚𝑜𝑛𝑡ℎ = 12,000 𝑢𝑛𝑖𝑡𝑠/𝑦𝑒𝑎𝑟
▪ Material cost 𝐶𝑖 = 500 €/𝑢𝑛𝑖𝑡
▪ Fixed ordering cost 𝑆 = 4,000 €/𝑜𝑟𝑑𝑒𝑟
▪ Holding cost ℎ = 20 %/𝑦𝑒𝑎r (annual interest rate)

Question 11

Collective Orders

Answer 11

Aggregation of orders over products or suppliers causes the total lot size to decrease due to the allocation of fixed ordering costs and transportation costs. Further, cycle inventory and average flow time decrease as well.
→ However, some types of costs might increase with an increase in product variety (e.g., processing and handling costs) whereas others are independent of product variety (e.g., transportation costs)

Question 12

Estimating Cycle Inventory Related Costs in Practice

Answer 12

Calculating inventory holding and ordering costs is often difficult in practice; use quick but good approximations instead.
→ Identify costs which depend on the lot size
→ Account for marginal costs

Question 13

Inventory Holding Cost

Answer 13

▪ Cost of capital
▪ Obsolescence cost
▪ Handling cost
▪ Holding cost
▪ Energy costs
▪ Insurance
▪ Tax
▪ Miscellaneous costs

Question 14

Ordering Cost

Answer 14

▪ Personnel Costs (Salaries)
▪ Transportation costs
▪ Receiving costs / quality control
▪ Other costs

Question 15

Safety Inventory

Answer 15

Safety inventory is carried to satisfy demand that exceeds the amount forecasted.

Question 16

Safety Inventory - Trade-off

Answer 16

▪ High product availability
▪ High level of service
vs.
▪ High inventory holding costs
▪ Risk of obsolescence

Question 17

Factors Affecting the Level of Safety Inventory - Sources/Reasons of Uncertainty

Answer 17

1. Uncertainty of demand = the demand quantity is uncertain
2. Uncertainty of supply = the replenishment lead time of an order is uncertain
3. Uncertain delivery quantities = delivery quantities deviate from order quantities

Question 18

Factors Affecting the Level of Safety Inventory - Product Availability

Answer 18

▪ Cycle service level = fraction of replenishment cycles in which all customer demand is met
▪ Product fill rate = fraction of product demand satisfied from inventory
▪ Order fill rate = fraction of orders filled from available inventory

Question 19

Factors Affecting the Level of Safety Inventory - Demand Uncertainty

Answer 19

Demand Uncertainty:
- 𝐷 Average demand per period
- 𝜎𝐷 Standard deviation of demand (forecast error) per period
- 𝐿 Lead time (number of periods)
Distribution of Demand During the Lead Time 𝑳:
- 𝐷𝐿 Expected demand during the lead time
- 𝜎𝐿 Standard deviation of demand (forecast error) during the lead time

Question 20

Factors Affecting the Level of Safety Inventory - Supply Uncertainty

Answer 20

• 𝐷 Average demand per period
• 𝜎𝐷 Standard deviation of demand (forecast error) per period (uncertainty due to customers)
• 𝐿 Average lead time (in periods)
• 𝑠𝐿 Standard deviation of the lead time (uncertainty due to supplier)
  Distribution of Demand During the Lead Time 𝑳
  (Uncorrelated demand, 𝜌𝑖𝑗 = 0)

Question 21

Product Availability

Answer 21

Product availability reflects a firm’s ability to fill a customer order out of available inventory.
→ Essential to measure the responsiveness of a supply chain.

Question 22

Cycle Service Level – CSL (alpha service level)

Answer 22

Fraction of replenishment cycles that end with all the customer demand being met
→ Event-oriented performance indicator: 𝛼 = 𝐶𝑆𝐿 = 𝑃 𝐷𝑒𝑚𝑎𝑛𝑑 ≤ 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦

Question 23

Product Fill Rate (beta service level)

Answer 23

Fraction of product demand satisfied from product in inventory
→ Quantity-oriented performance indicator

Question 24

Order Fill Rate

Answer 24

Fractions of orders filled from available inventory

Question 25

Determining the Optimal Safety Inventory Under Demand and Lead Time Uncertainty

Answer 25

Question 26

Safety Inventory Insights

Answer 26

▪ A higher safety inventory leads to a higher CSL and product fill rate.
▪ The required safety inventory increases with a higher standard deviation of lead time and demand.
▪ The required safety inventory increases over-proportionally with an increase in the desired product availability.
▪ A reduction of supply uncertainty allows for a significant reduction of the safety inventory while maintaining the same product availability.

Question 27

Product Availability

Answer 27

▪ Achieving a balance between product availability and cost of inventory
▪ The optimal level of product availability maximizes the expected SC profits
▪ Consideration only makes sense if uncertainty is explicitly included in the decision

Question 28

Factors Affecting the Optimal Level of Product Availability (CSL)

Answer 28

▪ Cost of overstocking (𝐶𝑂):
− Cost for unsold units
− Correspond to the purchase cost 𝑐 minus the salvage value 𝑠
− 𝐶𝑂 = 𝑐 − 𝑠
▪ Cost of understocking (𝐶𝑈):
− Penalty cost, lost profits, lost sales
− Corresponds to the retail price 𝑝 minus purchase cost 𝑐
− 𝐶𝑈 = 𝑝 − 𝑐
▪ High cost for understocking → high product availability / high CSL
▪ High cost for overstocking → low product availability / low CSL

Question 29

Determining the optimal level of product availability

Answer 29

by weighing cost for understocking and overstocking

Question 30

Managerial Levers to Improve Supply Chain Profitability

Answer 30

▪ Increasing the Salvage Value of Unsold Units
→ Outlet stores, exploiting other markets
▪ Decreasing the Margin Lost from a Stockout
→ Back-up sourcing

Question 31

“Synchronization” of Production and Demand

Answer 31

▪ Production quantity = demand quantity
▪ Reactive strategy: Execute orders upon receipt
▪ Requirements: Available personnel and technical production capacities correspond to the maximal demand
→ Disadvantage: Utilization fluctuates strongly
→ Advantage: No inventory costs

Question 32

“Emancipation” of Production and Demand

Answer 32

▪ Keep production quantity constant
▪ Meet demand by build-up and reduction of inventory
→ Disadvantage: Inventory costs, shortages
→ Advantage: Uniform production quantity allows for production at optimal intensity