Acquisition and Supply Chain Mgmt Help Needed

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Supply Chain Management: Strategy, Planning, and Operation

Seventh Edition

Chapter 11

Managing Economies of Scale in a Supply Chain Cycle Inventory

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Learning Objectives (1 of 2)

11.1 Describe the role of cycle inventory in a supply chain.

11.2 Choose the optimal lot size given fixed ordering costs in a supply chain.

11.3 Evaluate how aggregation is best implemented to reduce cycle inventory in a supply chain.

11.4 Understand the impact of quantity discounts on lot size and cycle inventory.

Learning Objectives (2 of 2)

11.5 Devise appropriate discounting schemes for a supply chain.

11.6 Understand the impact of trade promotions on lot size and cycle inventory.

11.7 Develop replenishment policies to improve synchronization in multiechelon supply chains.

11.8 Identify managerial levers that reduce lot size and cycle inventory in a supply chain without increasing cost.

Role of Cycle Inventory in a Supply Chain (1 of 8)

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

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

Q: Quantity in a lot or batch size

D: Demand per unit time

Inventory Profile

Figure 11-1 Inventory Profile of Jeans at Jean-Mart

Role of Cycle Inventory in a Supply Chain (2 of 8)

Role of Cycle Inventory in a Supply Chain (3 of 8)

For lot sizes of 1,000 pairs of jeans and daily demand of 100 pairs of jeans

Role of Cycle Inventory in a Supply Chain (4 of 8)

Lower cycle inventory

Decreases vulnerability to demand changes

Lowers working capital requirements

Lowers inventory holding costs

Cycle inventory is held to

Take advantage of economies of scale

Reduce costs in the supply chain

Role of Cycle Inventory in a Supply Chain (5 of 8)

Average price paid per unit purchased is a key cost in the lot-sizing decision

Material cost = C

Fixed ordering cost includes all costs that do not vary with the size of the order but are incurred each time an order is placed

Fixed ordering cost = S

Holding cost is the cost of carrying one unit in inventory for a specified period of time Holding cost = H = hC

Role of Cycle Inventory in a Supply Chain (6 of 8)

Following costs considered in lot sizing decisions

Average price per unit purchased,

Fixed ordering cost incurred per lot,

Holding cost incurred per unit per year,

Role of Cycle Inventory in a Supply Chain (7 of 8)

Primary role of cycle inventory is to allow different stages to purchase product in lot sizes that minimize the sum of material, ordering, and holding costs

Ideally, cycle inventory decisions should consider costs across the entire supply chain

In practice, each stage generally makes its own supply chain decisions

Increases total cycle inventory and total costs in the supply chain

Role of Cycle Inventory in a Supply Chain (8 of 8)

Economies of scale exploited in three typical situations

A fixed cost is incurred each time an order is placed or produced

The supplier offers price discounts based on the quantity purchased per lot

The supplier offers short-term price discounts or holds trade promotions

Summary of Learning Objective 1

Cycle inventory builds up in a supply chain because product is produced or purchased in large lots to lower the sum of material, ordering, and holding costs by exploiting economies of scale. Opportunities to exploit economies of scale arise if a fixed cost is incurred each time an order is placed or produced, the supplier offers price discounts based on the quantity purchased per lot, or the supplier offers short-term price discounts. A reduction in cycle inventory improves a supply chain’s ability to match supply with demand.

Economies of Scale to Exploit Fixed Costs

Lot sizing for a single product (E O Q)

D = Annual demand of the product

S = Fixed cost incurred per order

C = Cost per unit

h = Holding cost per year as a fraction of product cost

Basic assumptions

Demand is steady at D units per unit time

No shortages are allowed

Replenishment lead time is fixed

Estimating Cycle Inventory Related Costs in Practice (1 of 3)

Inventory Holding Cost

Cost of capital

Where

E = amount of equity

D = amount of debt

Rf = risk-free rate of return

β = the firm’s beta

M R P = market risk premium

Rb = rate at which the firm can borrow money

t = tax rate

Estimating Cycle Inventory Related Costs in Practice (2 of 3)

Inventory Holding Cost

Obsolescence (or spoilage) cost

Handling cost

Occupancy cost

Miscellaneous costs

Theft, security, damage, tax, insurance

Estimating Cycle Inventory Related Costs in Practice (3 of 3)

Ordering Cost

Buyer time

Transportation costs

Receiving costs

Other costs

Lot Sizing for a Single Product (Economic Order Quantity)

Basic assumptions

Demand is steady at D units per unit time.

No shortages are allowed—that is, all demand must be supplied from stock

Replenishment lead time is fixed (initially assumed to be zero)

Minimize

Annual material cost

Annual ordering cost

Annual holding cost

Lot Sizing for a Single Product (1 of 3)

Lot Sizing for a Single Product (2 of 3)

Figure 11-2 Effect of Lot Size on Costs at Best Buy

Lot Sizing for a Single Product (3 of 3)

The economic order quantity (E O Q)

Optimal lot size,

The optimal ordering frequency

E O Q Example (1 of 3)

Annual demand,

Order cost per lot, S = $4,000

Unit cost per computer, C = $500

Holding cost per year as a fraction of unit cost, h = 0.2

Notes:

E O Q Example (2 of 3)

Notes:

Key Point (1 of 3)

Total ordering and holding costs are relatively stable around the economic order quantity. A firm is often better served by ordering a convenient lot size close to the E O Q rather than the precise E O Q.

Key Point (2 of 3)

If demand increases by a factor of k, the optimal lot size increases by a factor of

The number of orders placed per year should also increase by a factor of

Flow time attributed to cycle inventory should decrease by a factor of

E O Q Example (3 of 3)

Lot size reduced to Q = 200 units

Notes:

Lot Size and Ordering Cost

If the lot size Q* = 200, how much should the ordering cost be reduced?

Desired lot size, Q* = 200

Annual demand,

Unit cost per computer, C = $500

Holding cost per year as a fraction of inventory value, h = 0.2

Key Point (3 of 3)

To reduce the optimal lot size by a factor of k, the fixed order cost S must be reduced by a factor of

Production Lot Sizing

The entire lot does not arrive at the same time

Production occurs at a specified rate P

Inventory builds up at a rate of P−D

Inventory depleted at a rate of D

Annual setup cost

Annual holding cost

Lot Sizing with Capacity Constraint

If order size is constrained to K units and Q > K,

Compare the cost of ordering K units and the E O Q

Optimal order size is the minimum of E O Q and capacity K

Summary of Learning Objective 2

In deciding on the optimal lot size, the supply chain goal is to minimize the total cost—the order cost, holding cost, and material cost. As lot size increases, so does the annual holding cost. However, the annual order cost and, in some instances, the annual material cost decrease with an increase in lot size. The E O Q balances the three costs to obtain the optimal lot size. The higher the order and transportation cost, the higher the lot size and cycle inventory. The optimal lot size can be decreased if the fixed cost associated with each lot is reduced.

Aggregating Multiple Products in a Single Order

Savings in transportation costs

Reduces fixed cost for each product

Lot size for each product can be reduced

Cycle inventory is reduced

Single delivery from multiple suppliers or single truck delivering to multiple retailers

Reduce receiving and loading costs to reduce cycle inventory

Lot Sizing with Multiple Products or Customers (1 of 2)

Ordering, transportation, and receiving costs grow with the variety of products or pickup points

Lot sizes and ordering policy that minimize total cost

Di: Annual demand for product i

S: Order cost incurred each time an order is placed, independent of the variety of products in the order

si: Additional order cost incurred if product i is included in the order

Lot Sizing with Multiple Products or Customers (2 of 2)

Three approaches

Each product manager orders his or her model independently

The product managers jointly order every product in each lot

Product managers order jointly but not every order contains every product; that is, each lot contains a selected subset of the products

Multiple Products Ordered and Delivered Independently (1 of 2)

Demand

Common order cost

S = $4,000

Product-specific order cost

Holding cost

h = 0.2

Unit cost

Notes:

Multiple Products Ordered and Delivered Independently (2 of 2)

Table 11-1 Lot Sizes and Costs for Independent Ordering

Blank	Litepro	Medpro	Heavypro
Demand per year	12,000	1,200	120
Fixed cost/order	$5,000	$5,000	$5,000
Optimal order size	1,095	346	110
Cycle inventory	548	173	55
Annual holding cost	$54,772	$17,321	$5,477
Order frequency	11.0 per year	3.5 per year	1.1 per year
Annual ordering cost	$54,772	$17,321	$5,477
Average flow time	2.4 weeks	7.5 weeks	23.7 weeks
Annual cost	$109,544	$34,642	$10,954

Total annual cost = $155,140

Notes:

Lots Ordered and Delivered Jointly

Annual order cost = S * n

Products Ordered and Delivered Jointly (1 of 2)

Annual order cost

Annual ordering

and holding cost = $61,512 + $6,151 + $615 + $68,250

= $136,528

Products Ordered and Delivered Jointly (2 of 2)

Table 11-2 Lot Sizes and Costs for Joint Ordering at Best Buy

Blank	Litepro	Medpro	Heavypro
Demand per year (D)	12,000	1,200	120
Order frequency (n∗)	9.75 per year	9.75 per year	9.75 per year
Optimal order size (D/n∗)	1,230	123	12.3
Cycle inventory	615	61.5	6.15
Annual holding cost	$61,512	$6,151	$615
Average flow time	2.67 weeks	2.67 weeks	2.67 weeks

Aggregation with Capacity Constraint (1 of 3)

W . W. Grainger example

Demand per product, Di = 10,000

Holding cost, h = 0.2

Unit cost per product, Ci = $50

Common order cost, S = $500

Supplier-specific order cost, si = $100

Notes:

Aggregation with Capacity Constraint (2 of 3)

Notes:

Aggregation with Capacity Constraint (3 of 3)

Total required capacity per truck

Truck capacity = 2,500 units

Order quantity from each supplier

Order frequency increased to

Annual order cost per supplier increases to $3,600

Annual holding cost per supplier decreases to $3,125

Lots Ordered and Delivered Jointly for a Selected Subset (1 of 3)

Step 1: Identify the most frequently ordered product assuming each product is ordered independently

Step 2: For all products

evaluate the ordering

frequency

Lots Ordered and Delivered Jointly for a Selected Subset (2 of 3)

Step 3: For all

evaluate the frequency of product i

relative to the most frequently ordered product i* to be mi

Step 4: Recalculate the ordering frequency of the most frequently ordered product i* to be n

Lots Ordered and Delivered Jointly for a Selected Subset (3 of 3)

Step 5: Evaluate an order frequency of

and the

total cost of such an ordering policy

Tailored aggregation – higher-demand products ordered more frequently and lower-demand products ordered less frequently

Ordered and Delivered Jointly – Frequency Varies by Order (1 of 4)

Applying Step 1

Thus

Ordered and Delivered Jointly – Frequency Varies by Order (2 of 4)

Applying Step 2

Applying Step 3

Ordered and Delivered Jointly – Frequency Varies by Order (3 of 4)

Applying Step 4

n = 11.47

Applying Step 5

Annual order cost

Total annual cost

$130,767

Ordered and Delivered Jointly – Frequency Varies by Order (4 of 4)

Table 11-3 Lot Sizes and Costs for Ordering Policy Using Heuristic

Blank	Litepro	Medpro	Heavypro
Demand per year (D)	12,000	1,200	120
Order frequency (n∗)	11.47 per year	5.74 per year	2.29 per year
Optimal order size (D/n∗)	1,046	209	52
Cycle inventory	523	104.5	26
Annual holding cost	$52,307	$10,461	$2,615
Average flow time	2.27 weeks	4.53 weeks	11.35 weeks

Summary of Learning Objective 3

A key to reducing lot size without increasing costs is reducing the fixed cost associated with each lot. This may be achieved by aggregating lots across multiple products, customers, or suppliers. Complete aggregation, where all products are included in each order, is very effective when product-specific order costs are small. If product-specific order costs are large, tailored aggregation, where only a subset of products is included in each order, is more effective.

Economies of Scale to Exploit Quantity Discounts

Lot size-based discount – discounts based on quantity ordered in a single lot

Volume based discount – discount is based on total quantity purchased over a given period

Two common schemes

All-unit quantity discounts

Marginal unit quantity discount or multi-block tariffs

Quantity Discounts

Two basic questions

What is the optimal purchasing decision for a buyer seeking to maximize profits? How does this decision affect the supply chain in terms of lot sizes, cycle inventories, and flow times?

Under what conditions should a supplier offer quantity discounts? What are appropriate pricing schedules that a supplier seeking to maximize profits should offer?

All-Unit Quantity Discounts (1 of 6)

Pricing schedule has specified quantity break points

If an order is placed that is at least as large as qi but

smaller than

then each unit has an average unit

cost of Ci

Unit cost generally decreases as the quantity increases,

Objective is to decide on a lot size that will minimize the sum of material, order, and holding costs

All-Unit Quantity Discounts (2 of 6)

Figure 11-3 Average Unit Cost with All Unit Quantity Discounts

All-Unit Quantity Discounts (3 of 6)

Step 1: Evaluate the optimal lot size for each price

as follows

All-Unit Quantity Discounts (4 of 6)

Step 2: We next select the order quantity Q*i for each price Ci

Case 3 can be ignored as it is considered for

For Case 1 if

then a discount is not possible

Set

to qualify for the discounted price of Ci

All-Unit Quantity Discounts (5 of 6)

Step 3: Calculate the total annual cost of ordering

Total annual cost,

All-Unit Quantity Discounts (6 of 6)

Step 4: Select

with the lowest total cost TCi

Cutoff price

All-Unit Quantity Discount Example (1 of 3)

Order Quantity	Unit Price
0–4,999	$3.00
5,000–9,999	$2.96
10,000 or more	$2.92

q0 = 0, q1 = 5,000, q2 = 10,000

C0 = $3.00, C1 = $2.96, C2 = $2.92

All-Unit Quantity Discount Example (2 of 3)

Step 1

Step 2

Ignore i = 0 because Q0 = 6,325 > q1 = 5,000

For i = 1, 2

All-Unit Quantity Discount Example (3 of 3)

Step 3

Lowest total cost is for i = 2

Order

bottles per lot at $2.92 per bottle

Marginal Unit Quantity Discounts (1 of 6)

Multi-block tariffs – the marginal cost of a unit that decreases at a breakpoint

For each value of i,

let Vi be the cost of

ordering qi units

Marginal Unit Quantity Discounts (2 of 6)

Figure 11-4 Marginal Unit Cost with Marginal Unit Quantity Discount

Marginal Unit Quantity Discounts (3 of 6)

Material cost of each order

Marginal Unit Quantity Discounts (4 of 6)

Step 1: Evaluate the optimal lot size for each price Ci

Marginal Unit Quantity Discounts (5 of 6)

Step 2: Select the order quantity

for each price Ci

Marginal Unit Quantity Discounts (6 of 6)

Step 3: Calculate the total annual cost of ordering

Step 4: Select the order size

with the lowest total

cost TCi

Marginal Unit Quantity Discount Example (1 of 3)

Original data now a marginal discount

Order Quantity	Unit Price
0−4,999	$3.00
5,000−9,999	$2.96
10,000 or more	$2.92

q0 = 0, q1 = 5,000, q2 = 10,000

C0 = $3.00, C1 = $2.96, C2 = $2.92

Marginal Unit Quantity Discount Example (2 of 3)

Step 1

Marginal Unit Quantity Discount Example (3 of 3)

Step 2

Step 3

Summary of Learning Objective 4

Lot-size–based quantity discounts increase the lot size and cycle inventory within the supply chain because they encourage buyers to purchase in larger quantities to take advantage of the decrease in price. The relative increase in cycle inventory because of quantity discounts increases as the buyer reduces fixed costs per order.

Why Quantity Discounts?

Quantity discounts can increase the supply chain surplus for the following two main reasons

Improved coordination to increase total supply chain profits

Extraction of surplus through price discrimination

Notes:

Quantity Discounts for Commodity Products

D = 120,000 bottles/year, SR = $100, hR = 0.2, CR = $3 SM = $250, hM = 0.2, CM = $2

Notes:

Locally Optimal Lot Sizes

Notes:

Designing a Suitable Lot Size-Based Quantity Discount

Design a suitable quantity discount that gets D O to order in lots of 9,165 units when its aims to minimize only its own total costs

Manufacturer needs to offer an incentive of at least $264 per year to D O in terms of decreased material cost if D O orders in lots of 9,165 units

Appropriate quantity discount is $3 if D O orders in lots smaller than 9,165 units and $2.9978 for orders of 9,165 or more

Notes:

Quantity Discounts When Firm Has Market Power (1 of 3)

Demand curve = 360,000−60,000p

Production cost = CM = $2 per bottle

Notes:

Quantity Discounts When Firm Has Market Power (2 of 3)

CR = $4 per bottle, p = $5 per bottle

Total market demand = 360,000 − 60,000p = 60,000

Coordinated retail price

Notes:

Quantity Discounts When Firm Has Market Power (3 of 3)

Prices coordinated at p = $4

Market demand = 360,000 − 60,000p = 120,000 bottles

Total supply chain profit

Prices set independently, supply chain loses

$240,000 − $180,000 = $60,000

Double marginalization – supply chain margin divided between two stages

Notes:

Two-Part Tariff

Manufacturer charges its entire profit as an up-front franchise fee ff

Sells to the retailer at cost

Retail pricing decision is based on maximizing its profits

Effectively maximizes the coordinated supply chain profit

Notes:

Volume-Based Quantity Discounts

Design a volume-based discount scheme that gets the retailer to purchase and sell the quantity sold when the two stages coordinate their actions

Notes:

Lessons from Discounting Schemes (1 of 2)

Quantity discounts play a role in supply chain coordination and improved supply chain profits

Discount schemes that are optimal are volume based and not lot size based unless the manufacturer has large fixed costs associated with each lot

Even in the presence of large fixed costs for the manufacturer, a two-part tariff or volume-based discount, with the manufacturer passing on some of the fixed cost to the retailer, optimally coordinates the supply chain and maximizes profits

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