Inventory Management: Strategies and Optimization

Posted on Mar 17, 2025 in Public Administration, Management, and Governance

Inventory Management

Definition of Inventory: The stock of any item or resource used in an organization to satisfy customer demand or to support the production of services or goods.

Types of Inventory

  1. Raw material inventory
  2. Work-in-process (WIP) inventory
  3. Finished product inventory

Purpose of Holding Inventory

Why Hold Inventory?

  • Uncertainty in customer demand
  • Uncertainty in supplies
  • Incentives for larger shipments (economies of scale)

Why Not Hold Too Much Inventory?

  1. Inventory increases certain costs such as:
  2. Holding cost (reduces working capital)
  3. Overstock cost
  4. Cost of production problems

Inventory Decisions and Costs

Inputs:

  • D = Annual demand (units/year)
  • K = Ordering cost/set up cost ($/order)
  • c = Cost per unit ($/unit)
  • I = Holding cost rate
  • h = I × c = Holding cost per unit ($/unit/year)

Decisions:

  • Q = Order quantity (units)
  • T = Reorder interval (year, month, week, or day)

Economic Order Quantity (EOQ)

The trade-off considered: large vs. small Q?

  • Annual cost of items sold: c × D (independent of the policy parameter Q)
  • Policy-related costs (depending on the order quantity Q)
  • Annual ordering costs: (D/Q)K
  • Annual holding costs: (Q/2)h

Objective: Find the Q that minimizes the total annual policy-related cost:

TC = (Q/2) h + (D/Q)K

EOQ = √ (2KD/h)

Annual Holding Cost = h

T = Q*/D = √ (2KD/h)/D = √ (2K/Dh)

Observations

  • In deciding the optimal lot size, the trade-off is between setup (ordering) cost and holding cost.
  • If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often.
  • If lot size is to be reduced, one has to reduce fixed ordering cost. To reduce lot size by a factor of 2, ordering cost has to be reduced by a factor of 4.

Probability Calculations

Prob(D

(Prob D > 48.5) = 1 − NORM.DIST(48.5, 50, 25, 1)

Single-Period Inventory Model

D = Demand (a random variable)

p = sale price (per unit)

c = purchase price (or cost per unit)

s = outlet price or salvage value (per unit)

Cu = p − c, underage cost per unit (too little)

Co = c − s, overage cost per unit (too much)

α = Prob(D ≤ Q), probability that demand D will be at or below order quantity Q (in-stock probability)

(1 − α)Cu = αCo

α = Cu/(Cu + Co)

Optimal order quantity Q* = NORM.INV(α, μ, σ)

If demand during the selling season is normally distributed with mean μ and standard deviation σ, and if we use an order quantity Q, then:

Expected Overstock (leftovers) = Q − μ ⋅ NORM.DIST(Q, μ, σ, 1) + σ ⋅ NORM.DIST((Q − μ)/σ, 0, 1, 0) = Q − μ ⋅ NORM.DIST((Q − μ)/σ, 0, 1, 1) + σ ⋅ NORM.DIST((Q − μ)/σ, 0, 1, 0) (The average number of units left over at the end of the season.)

Expected Understock (lost sales) = Expected Overstock − Q − μ (The average number of units of demand in excess of the order quantity)

Expected (Optimal) Profit = Cuμ − (Cu + Co)σ x NORM.DIST((Q* − μ)/σ, 0, 1, 0) = (p − c)μ − (p − s)σ x NORM.DIST((Q* − μ)/σ, 0, 1, 0)

optimal order quantity = Q*

Replenishment Policies

Two Replenishment Policies:

  • Continuous Review: Monitor or review inventory continuously; Order fixed quantity Q whenever total inventory drops below Reorder Point (s)
  • Periodic Review: Review and check inventory periodically, say, every T days or weeks; At each review, place an order to raise inventory position to Order-Up-To Level (S)

Continuous Review Policy

α: Cycle service level (given)

L: Lead time for replenishment

D: Average demand per time unit (mean of demand)

σ: Standard deviation of demand per time unit

K: Fixed ordering cost per order

h: Holding cost per unit

Use formulas to calculate:

Q: Order quantity

DL: Mean demand during lead time L

σL: Standard deviation of demand during lead time

z: Safety factor

s: Reorder point

Average Inventory Level = (Q/2 )+ Safety Stock average cycle stock level

Order-Up-To Level S = s + Q

Average inventory × h = average weekly IHC

Average weekly Ordering cost = K(D/Q)

Average weekly total cost = Average inventory(h) + K(D/Q)

Safe Stock = NORM.INT(α, 0, 1) x σ √ L

Periodic Review Policy

Given Inputs:

α: Cycle service level (CSL)

L: Lead time for replenishment

r : Reorder interval (review period)

D: Average demand per time unit

σ: Standard deviation of demand per time unit

Use formulas to calculate:

Dr+L: Mean demand during the period of r+ L time units

σr+L: Standard deviation of demand during the period of r+ L time units

z: Safety factor

S: Order-up-to level (base-stock level)

Continuous Review Safety Stock = NORM.INV(α, 0, 1) × σ √ L

Periodic Review Safety Stock = NORM.INV(α, 0, 1) × σ √ r + L

Inventory Pooling

Efficiency vs. Responsiveness

Ch.4 Efficiency vs. Responsiveness

  • Efficiency for functional products
  • Responsiveness for innovative products

Distribution Strategies

Direct shipping?

Items shipped directly from the supplier to retail stores without going through distribution centers

+ve: Avoids the expenses of operating a distribution center Reduced lead time

Cross-docking?

Warehouses function as inventory coordination points rather than as inventory storage points

Advantages:

  • Reduced transportation cost (like warehousing)
  • Lower storage time than warehousing lower inventory cost; shorter lead time

Requirements:

  • Advanced information systems to coordinate pickups and deliveries
  • Information sharing
  • A responsive material handling system
  • Cross-docking is effective only for large distribution systems

Strategic Alliances

Retailer-Supplier Partnerships

Quick Response (QR)

QR is an industry initiative launched in 1985 to make the textile/apparel sector speed up the product flow

QR entailed the retailer sharing point-of-sale (POS) data with the manufacturers/suppliers

Demand information sharing by a retailer to its supplier is the cornerstone of QR

Suppliers use this information to synchronize their production and inventory activities with actual sales at the retailer

Continuous Replenishment (CRP)

In a Continuous Replenishment strategy, vendors receive POS data and use these data to prepare shipments at previously agreed upon intervals to maintain specific levels of inventory

In an advanced form of CRP, suppliers may continuously improve the inventory levels. These inventory levels could be based on sophisticated inventory models.

Vendor-Managed Inventories (VMI)

In VMI, the supplier decides on the appropriate inventory levels of each of the products (within previously agreed-upon bounds) and the appropriate inventory policies to maintain these levels

Retailer-Supplier Partnerships (RSP) Graph Distributor Integration (DI)

  • To create a large pool of inventory across the distributor network
  • To create a pool of different expertise

Third-Party Logistics (3PL)

What is 3PL?

Use of an outside company to perform all or part of the materials management and product distribution functions

How do 3PL providers differ from traditional trucking and warehousing service providers?

Traditional service providers: transaction based, single-function

3PL: long-term commitment, multi-function

Advantages of using 3PL
  • Focus on core strengths
  • Technological flexibility
  • Avoid capital investments
Disadvantage of using 3PL
  • Loss of control

Economic Packaging and Transportation

Ch.6 ECONOMIC PACKAGING AND TRANSPORTATION

  • Design products so that they can be efficiently packed and stored
  • Design packaging so that products can be consolidated at cross-docking points
  • Design products to efficiently utilize retail space

Example:

  • Hewlett-Packard Deskjet printers were placed in a special pallet packing device that allowed twice as many printers in a container
  • Ikea
    • Large furniture stores, centralized manufacturing, compactly and efficiently packed products
  • Rubbermaid Clear Classics food storage containers designed to fit 14”x14” Wal-Mart shelves

Concurrent/Parallel Processing

  • Objective is to minimize lead times
  • Achieved by redesigning products so that several manufacturing steps can take place in parallel

Standardization and Postponement

Standardization:

  1. Aggregate demand information is more accurate than disaggregate data.
  2. Standardization: Use common parts (components) or common process across many products (e.g., personal computer, Lego).
  3. By effectively using standardization (e.g., using common parts or standardizing processing equipment), it may be possible to make effective use of demand aggregation.

Value of Postponement with Dominant Product:

Postponement is effective if the firm produces large variety of products whose demands are not positively correlated and of about the same size.

Mass Customization

MASS CUSTOMIZATION:

  • Mass production:
    1. Efficient production of a large quantity of a small variety of goods.
    2. High priority on automating and measuring tasks
  • Craft production:
    1. Create unique or personalized products/services
    2. Involves highly skilled and flexible workers (often craftsmen)
    3. In the past, managers often had to make a decision between craft production and mass production with their inherent trade-offs.

DEVELOPMENT OF MASS CUSTOMIZATION IMPLIES THAT IT IS NOT ALWAYS NECESSARY TO MAKE THIS TRADE-OFF

  • Mass customization:
    1. delivers a wide variety of customized goods or services quickly and efficiently at low cost
    2. captures many of the advantages of both the mass production and craft production systems
    3. is not appropriate for all products
    4. gives firms important competitive advantages
    5. helps to drive new business models

Making mass customization work:

  1. Highly skilled and autonomous workers
  2. Modular units
  3. Managers can coordinate and reconfigure these modules to meet specific customer requests and demands
  4. Advanced SCM techniques and Information technology are essential
  5. Postponement can play a key role in implementing mass customization

Bullwhip Effect

ch.7 Bullwhip Effect: The demand order variability in the supply chain are amplified as they move up the supply chain

What Causes the Bullwhip Effect?

Demand Forecasting

  • No visibility of end demand: Demand forecast is made based on orders and not on the true consumer demand
  • Long lead time makes forecasts less accurate
    • With long lead time, a small change in the estimate of demand variability implies a significant change in safety stock, leading to a significant change in order quantity
    • Continuous Review Safety Stock = Safety Factor × σ L
    • Periodic Review Safety Stock = Safety Factor × σ r+L

Batch Ordering

  • Retailers may be required to order in integer multiples of some batch size, e.g., case quantities, pallet quantities, full truck load, etc.
  • Reasons for batch ordering
    • High ordering cost
    • Quantity discounts

Price Fluctuation

  • High-low pricing leads to forward buying
    • Manufacturer gives retailer a temporary discount (a trade promotion). Then retailer purchases enough to satisfy demand until the next trade promotion.
    • Estimated 80% of transactions in grocery supply chains between manufacturers and distributors are forward buy
    • Example: Campbell’s Chicken Noodle Soup over a one year period:

Inflated Orders

  • If a manufacturer’s production is less than orders, orders are rationed, i.e., retailers are “put on allocation”.
  • Thus, to secure a better allocation, the retailers inflate their orders, i.e., order more than they need…
  • So retailer orders do not convey good information about true demand…
  • Unrestricted orders and free return policy encourage shortage gaming behavior

Coping with Bullwhip Effect

  • Avoid multiple demand forecast updates
  • Make demand data at downstream site available to upstream site
    • Information sharing: Actual demand information sharing between the stages of supply chain. Also share information regarding pricing, promotion, and advertising
    • Vendor Managed Inventory (VMI): delegation of stocking decisions
      • Retailer no longer decides when and how much to order
      • The supplier decides the timing and quantity of shipment to the retailer
      • Retailer shares with the supplier demand data
      • The supplier and the retailer eliminate trade promotion
      • Used by Barilla, P&G/Wal-Mart and others.
  • Reduce lead time e.g., cross-docking, direct delivery
  • Reduce information lead time
    • e.g., electronic ordering
  • Break order batches
    • Reduce cost of placing an order (e.g., adopt electronic ordering)
    • Avoid full truckload ordering (e.g., mixed SKU ordering, third party logistics, cross-docking)
  • Stabilize prices
    • Every day low price (EDLP)
    • Scan-based promotions: retailer receives credit for promotion discount for every unit sold
  • Eliminate gaming in shortage situations
    • Restrict returns and order cancellations
    • Order allocation based on past sales in case of shortages
    • Shared capacity and supply information

Supply Contracts

Lectures 9&10 :Supply Contracts

SUPPLY CONTRACT: Supply contract (or supply chain contract): a voluntary arrangement between two or more supply chain parties that is enforceable by law as a binding legal agreement.

Involves:

  • Pricing and volume discounts
  • Minimum and maximum purchase quantities
  • Product return policies
  • Delivery lead times
  • Product or material quality

Outline:

  • Quantity Discount (with fixed demand):
    • Two types of discounts:
      1. All-units discount
      2. Marginal unit discount
  • Double Marginalization
  • Design coordinating contracts
    • Two-part tariff ~ Buyback
    • Revenue sharing

Two-Part Tariff

  • For products for which a firm has market power (using price to influence demand), a two-part tariff contract can be utilized to coordinate the supply chain.
  • To achieve the maximum total SC profit (i.e., eliminate double marginalization), the wholesale price c should equal to the manufacturer’s unit production cost. Double marginalization leads to a loss in total supply chain profit
  • Contract solution: Supplier bears part of the risk of overstocking and under-stocking to induce retailers to order quantities that will increase total supply chain profit
    • Buyback contract
    • Revenue sharing contract

Buy-Back Contract:

Cu = p − c (underage cost per unit)

Co = c − s + b (overage cost per unit)

Let v denote the unit production cost, manufacturer’s expected profit is: =Q×(c–v) –b×(expected overstock at retailer), price=b.

Procurement and Outsourcing Strategies

Lecture 12: Procurement and Outsourcing Strategies

Benefits:

  • Economies of scale
    • Aggregation of multiple orders from many different buyers reduces costs, both in purchasing and in manufacturing
  • Risk pooling
    • Demand uncertainty transferred to the suppliers
    • Suppliers reduce uncertainty through the risk-pooling effect
  • Reduce capital investment
    • Capital investment transferred to suppliers.
    • Suppliers’ higher investment shared between customers.
  • Focus on core competency
    • Buyer can focus on its core strength
    • Allows buyer to differentiate from its competitors
    • Nike focuses on innovation, marketing, etc, rather than manufacturing
  • Increased flexibility
    • The ability to better react to changes in customer demand
    • The ability to use the supplier’s technical knowledge to accelerate product development cycle time
    • The ability to gain access to new technologies and innovation.
    • Critical in certain industries:
      1. High tech where technologies change very frequently
      2. Fashion where products have a short life cycle

Outsourcing Risks

  • Conflicting objectives between buyers and suppliers
    • Demand Issues
      • In a good economy
        • Demand is high
        • Conflict can be addressed by buyers who are willing to make long-term commitments to purchase minimum quantities specified by a contract
      • In a slow economy
        • Significant decline in demand
        • Long-term commitments entail huge financial risks for the buyers
    • Product design issues
      • Buyers insist on flexibility and would like to solve design problems as fast as possible
      • Suppliers focus on cost reduction that implies slow responsiveness to design changes
  • Loss of competitive knowledge
    • Outsourcing critical components to suppliers may open up opportunities for competitors
      • Contract manufacturer may enter the market
      • Knowledge spillover for competitor
    • Outsourcing implies that companies lose their ability to introduce new designs based on their own agenda rather than the supplier’s agenda
    • Outsourcing the manufacturing of various components to different suppliers may prevent the development of new insights, innovations, and solutions that typically require cross-functional teamwork

Outsourcing Problems: Shanzhai/High Imitation Products

  • Contract manufacturer may copy the same design and produce a similar product to sell in the local market
  • Shanzhai products/High imitation products: some has the same quality and produced by the same contract manufacturer

Make vs. Buy Decisions

  • Two major categories of outsourcing reasons:
    • Dependency on capacity
      • Firm has the knowledge and the skills required to produce the component
      • For various reasons decides to outsource, such as lack of capacity, etc.
    • Dependency on knowledge
      • Firm does not have the people, skills, and knowledge required to produce the component
      • Outsources in order to have access to these capabilities.
    • Modular product:
      • Capturing knowledge is important, whereas having the production capacity in-house is less critical.
    • Modular product
      • Made by combining different…

Pricing and Demand

ch.11 Pricing and Demand

  • All things being equal
    • Demand for a product/service will typically (not always) go up as the price goes down
    • Certain products/services more or less sensitive to price changes
    • In general, the property holds:
      • Downward-sloping demand curve
      • Except Veblen goods (e.g., luxury products)

Pricing and Demand: Example

  • A company wants to sell a new product and needs to decide the price for the product. Through analysis, management estimates that the relationship between demand and price is: D = 10,000 – 2000×p
    • When the p=$1, D=8,000
    • When the p=$2, D=6,000
    • Revenue is 𝑝⋅𝐷=𝑝(10,000−2000×𝑝)

Optimal Single Price

Given demand function: 𝐷=𝐴−𝐵⋅𝑝, if the firm sets a single price to maximize its revenue:

The optimal price that maximizes the revenue is given by: 𝑝∗= 𝐴/2𝐵

The maximized revenue is: 𝑝∗𝐴−𝐵⋅𝑝∗ =𝐴^2/4𝐵

  • In many realistic cases:
    • In the beginning of selling season, the company will charge an original (or regular) price for the new product
    • At the end of a selling season, the company will employ a markdown or sale to dispose the remaining inventory

Think about demand from the customer’s perspective:

Each customer has a maximum price that he or she is willing to pay for the product, which is called as “reservation price”. When the price is below or at a customer’s reservation price, he/she will buy.

  • The company first charges price $3.5, then 3000 consumers will purchase the product (the demand at price $3.5 is 10,000−2000× 3.5=3000).
  • Then in the end of selling season, the company offers sales by charging a lower price $2, then another 3000 consumers will purchase. (The demand at price $2 is 10,000−2000×2=6000, and 3000 among those 6000 have purchased already at price $3.5. Thus, the number of remaining consumers who are willing to purchase is 6000-3000=3000.)
  • This practice of charging different prices to different customers segments is known as price differentiation

Price Differentiation

  • Charge different customers different prices according to their price sensitivity
  • Difficult to do in many cases: price discrimination

Fundamental Approaches to Smart Pricing

  • Differential Pricing
    • Charging different prices to different customer segments
  • Dynamic pricing
    • Charging different prices over time

Differential Pricing Strategies

  • Strategies for differential pricing:
    • Group pricing: Giving discounts to specific groups of customers (e.g., student discounts for movie tickets)
    • Channel pricing: Charging different prices for the same product sold through different channels (e.g., online price is lower than retail-store price for the same product)
    • Regional pricing: Exploiting different price sensitivities at different locations (e.g., Coke Cola is much more expensive in Ocean Park or Disneyland)
    • Time-based differentiation: Setting prices based on service time durations, delivery times, etc (e.g., Amazon charges a higher shipping fee for faster shipping)
    • Coupons and rebates: Use coupons and rebates to distinguish between customers that place a high value on time or flexibility and those who are willing to spend the time to get a lower price by using a coupon (e.g., hidden offers or mail-in rebate)
    • Product versioning: Offering slightly different products to differentiate between customers with different price sensitivities

Dynamic Pricing

  • Dynamic pricing: Changing prices over time without necessarily distinguishing between different types of customers explicitly.
  • Purposes of dynamic pricing:
    • Get rid of excess inventory. For example, fashion clothing retailers may offer discounts later in the season to reduce inventory, and this discount is the same for all customers at a given time.
    • Offer periodic sales (e.g., Black Friday, Double 11 shopping festival)
    • Use surge pricing as a tool to better match demand and supply (i.e., air ticket, hotel)

Caveats of Smart Pricing:

Unfair Treatment

of their customers! CAVEATSOFSMARTINGPRICING: STRATEGICCONSUMER BEHAVIOR ▪The problem of dynamic pricing: Strategic consumer behavior refers to consumers willing to delay purchase in anticipation of price discounts. ▪The higher fraction of strategic customers, the more important it is to integrate strategic consumer behaviorinto pricing decisions. ▪How to mitigate strategic consumer behavior: oWait Time and Price: The firm can build fences by delaying the discount time and optimizing price so that this combination of delay and lower discount curb strategic consumer behavior. o Inventory:By focusing on product scarcity, the firm motivates consumers to purchase early rather than wait for a discount (i.e.,Zara) REVENUEMANAGEMENT ▪Revenue Management is the use of pricing to increase the profit generated from a limited supply of supply chain assets ▪Revenue management has been described as “selling the right inventory unit to the right type of customer, at the right time, and for the right price.” ▪Revenue management techniques have been traditionally applied in the airline, hotel, and rental car industries.  EXAMPLE: AIRLINES ▪Leisure travelers o Highly sensitive to price oNot generally sensitive to the duration of the trip oWilling to book non-refundable tickets far ahead of time ▪Business travelers oNot particularly price-sensitive o Highly sensitive to trip duration oNeed high flexibility to adjust their travel plans as needed EXAMPLE: AIRLINES ▪“Build fences” to prevent business travelers from buying tickets targeting leisure travelers o Require weekend stays and early booking OVERBOOKING ▪In many industries (i.e., car rentals, hotels, airline), a fraction of reservations may get cancelled by customers at some point in time. ▪Problem:The company may fail to fill the seat (room, car) if the passenger cancels at the very last minute or does not show up. ▪Solution:Sell more seats (rooms, cars) than capacity. ▪Danger:Some customers may have to be denied a seat even though they have a confirmed reservation. OVERBOOKING ▪Overbookingoccurs when a seller with limited capacity sells more units than it has. ▪Airlines often overbook to ensure that planes do not leave with empty seats. ▪The question of overbooking: How many quantities should be overbooked (sold in excess of capacity)? ▪Basic trade-off: o Excessive cancellations ⇒wasted capacity Few cancellations ⇒shortage of capacity OVERBOOKING Solving the overbooking problem is similar to the newsvendor model: ▪Assumption: Cancellation is normally distributed with mean 𝜇and standard deviation 𝜎 ▪Let 𝐶𝑢= marginal cost of having wasted capacity (i.e., marginal cost of overbooking too little) ▪Let 𝐶𝑜= marginal cost of having a capacity shortage (i.e., marginal cost of overbooking too much) ▪Critical fractile, CF=𝐶𝑢/(𝐶𝑢+𝐶𝑜) ▪Optimal overbooking level = NORM.INV(CF,𝜇,𝜎)

OVERBOOKING: EXAMPLE ▪An apparel supplier is taking orders for dresses with a Christmas motif. It must decide on how many orders to commit to at this time. ▪Production capacity available with the supplier is 5000 dresses. ▪The supplier makes a margin of $80 for each dress sold. ▪If it has orders that exceed capacity, it has to arrange for backup capacity and incur a loss of $40 per dress. ▪Retailers have been known to cancel their orders near the winter season as they have better visibility into expected demand. Cancellations are normally distributed with a mean of 800 and a standard deviation of 400. A simple example: o Two segments of customers: lower-price and higher-price segments o Total capacity is limited o Demand from the lower-price segment arises earlier in time, andsuppose that there aresufficient customers in this segment(i.e., more than the capacity limit) o Demand for the higher-price segment is uncertain and is normally distributed with mean 𝐷𝐻and standard deviation 𝜎𝐻 o The prices for the two segments are fixed: oQuestion: How much capacity should be reserved for higher-price segment? 30 𝑝𝐿= price charged to the lower price segment (i.e., economy class) 𝑝𝐻= price charged to the higher price segment (i.e., business class) ALLOCATINGCAPACITYTOMULTIPLEPRICESEGMENTS: EXAMPLE ▪ ABC Trucking Co. serves two segments of customers. ▪ Segment Ais willing to pay $1000 per cubic meter but wants to commit to a shipment with only 24 hours advance notice. ▪ Segment Bis willing to pay only $600 per cubic meter and is willing to commit to a shipment with up to one week notice. ▪ With two weeks to go, demand for segment Ais forecast to be normally distributed with a mean of 90 cubic meters and a standard deviation of30. MULTIPLECUSTOMERSEGMENTS Complexity of real-life analysis not captured by this example: • Can have more than two customer segments • There may be capacity limit in each segment •Overbooking of each segment may be allowed