1

Managing Economies of Scalein the Supply Chainwith Cycle Inventory

Planning and Managing Inventories in a Supply Chain

Cycle Inventory 2

The Role of Cycle Inventory in the Supply Chain

o Cycle inventory exists because producing or purchasing in large lots allows a stage of the supply chain to exploit economies of scale.

o The economies of scale are typically associated with:

n Fixed ordering and transportation costs

n Quantity discounts in product pricing

n Short-term discounts or trade promotions.

2

Cycle Inventory 3

Managing Cycle Inventories

o Each of these factors impact upon the lot size and cycle inventory in particular ways.

o There are several managerial levers that can be employed to reduce cycle inventory in a supply chain without raising costs.

Cycle Inventory 4

Cycle Inventory Defined

o Cycle inventory is the average inventory in the supply chain due to either production or purchases in lot sizes that are larger than those demanded by the customer. We may thus use the following notationn Q = Quantity in a lot or batch

n D = Demand per unit time

o We ignore the impact of demand variability because it has marginal impact on lot size and cycle inventory.

3

Cycle Inventory 5

Cycle Inventory Illustrated

o Consider the sale of jeans at a department store. Demand for jeans is considered to be fairly stable at D=100 jeans per day.n If the store manager purchases in lots of

Q = 1,000 jeans, an inventory profile of the jeans at the store can be drawn.

n This develops as a cyclical pattern repeating over time. It can be easily represented by a graph.

Cycle Inventory 6

Cycle Inventory Interrelationships

o Lot sizes and cycle inventory also influence the flow time of material within the supply chain:n Avg. flow time = Avg. inventory / Avg. flow

rate

o For any supply chain, average flow rate equals the demand. Therefore,n Avg. flow time = Avg. inventory / Demand

n Avg. flow time = Q/2D

4

Cycle Inventory 7

Cycle Inventory Adds to the Flow Time

o The larger the cycle inventory, the longer the lag time between when a product is produced and when it is sold.

o All else being equal, a lower level of cycle inventory is always desirable because large time lags leave a firm vulnerable to demand changes in the marketplace.

o A lower cycle inventory is also desirable because it decreases the working capital requirement for a firm.

Cycle Inventory 8

Understanding Costs Relatedto Lot Sizes

o To understand how the supply chain achieves economies of scale by increasing the lot size, we must first identify supply chain costs that are influenced by the lot size. These are:n Average price paid per unit purchased ‘C’

($/unit)

n Fixed ordering cost ‘S’ ($/lot)

n Holding cost ‘H’ ($/unit/year), or h*C, where his a %age or fraction of holding $1 in inventory for one year.

5

Cycle Inventory 9

Lot-Size Costs Inter-relationships

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

25 50 75 100 125 150 175 200 225 250

Set up Cost Holding Cost Total Cost

Cycle Inventory 10

Extended Lot-Size Interrelationships

o A firm may be better served by ordering a convenient lot size close to the EOQ rather than the precise EOQ.

o If demand increases by a factor k, the EOQincreases by a factor of k1/2. The number of orders placed per year should also increase by a factor k1/2. Flow time should decrease by k1/2.

o To reduce the EOQ by a factor k, the fixed order cost S must be reduced by k2.

6

Cycle Inventory 11

Reducing Lot Sizes Without Increasing Costs

o A key to reducing cycle inventory is the reduction of lot size.

o A key to reducing lot size without increasing costs is to reduce the fixed cost associated with each lot.

o An alternate way of reducing the lot size and (or) fixed cost is by aggregating lots across multiple products, customers, or suppliers.n When aggregating lots, tailored aggregation is

best, especially if product specific order costs are large.

Cycle Inventory 12

Best Buy Computers

o Demand for the Desktop computer at Best Buy is 1,000 units per month. Best Buy incurs a fixed order placement, transportation, and receiving cost of $4,000 each time. Each computer costs Best Buy $500 and carries a holding cost of 20%.n The optimal lot size in this case will be 980

units, a cycle inventory of 480, and a total annual inventory cost of $97,980.

n If the lot size were to be reduced to 200, then the corresponding fixed cost will have to be $166.7.

7

Cycle Inventory 13

Aggregating Multiple Productsin a Single Order

o To effectively reduce the lot size, the materials manger needs to understand the source of the fixed cost.

o In several companies the array of products sold is divided into families or groups with each group managed independently by a separate product manager.

Cycle Inventory 14

Best Buy Computers Revisited

o Best Buy also purchases the Litepro, Medpro, and Heavypro Models apart from the Deskpro.

o Currently, a separate product manager is responsible for the inventory and sales of each model. As a result, the ordering and delivery for each model is independent.

n The fixed transportation cost of $4,000 is thus incurred separately for each model.

n This leads to each product manager ordering a large lot size for their product.

8

Cycle Inventory 15

Optimal Lot Sizes for Independent Demand versus Aggregated Demand

o Assume that the demand for each of the four models is 1,000 units per month. In this case, if each product manager orders separately, he would order a lot size of 980 units.

o Across the four models, the total cycle inventory would thus be 1960 units.

Cycle Inventory 16

Optimal Lot Sizes for Independent Demand versus Aggregated Demand

o If Best Buy Computers realize that all four shipments originate from the same source, then the managers may be asked to ensure that all four products arrive on the same truck.

o In this case, the optimal combined lot size across all four models turns out to be 1,960 units. This is equivalent to 480 units for each model. This action significantly reduces the cycle inventory (980 units) as well as cost to Best Buy.

9

Cycle Inventory 17

An Alternate Situation

o Another way to achieve the previous result is to have a single delivery coming up from multiple suppliers.

n Allows fixed transportation cost to be spread across multiple suppliers.

o Or have a single truck delivering to multiple retailers.

n Allows fixed transportation cost to be spread across multiple retailers.

Cycle Inventory 18

Receiving or Handling Costs

o When considering fixed costs, one cannot ignore the receiving or loading costs. As more products are included in a single order, the product variety on a truck (shipment) increases.

o The receiving warehouse now has to update inventory records for more items per truck. In addition, the task of putting inventory into storage now becomes more expensive because each distinct item must be stocked in a separate location.

10

Cycle Inventory 19

Advanced Shipping Notices (ASN)

o When attempting to reduce lot sizes, it is important to focus on reducing the handling costs. Advanced Shipping Notices (ASN) are files sent electronically by the supplier to the customer that contain precise records of the contents of the truck.

o These electronic notices facilitate updating of inventory records as well as the decision regarding storage locations, helping to reduce the fixed cost of receiving. The reduced fixed cost of receiving makes it optimal to reduce the lot size ordered, thus reducing cycle inventory.

Cycle Inventory 20

Optimal Lot Sizing with Multiple Products or Customers

o Our objective is to arrive at lot sizes and an ordering policy that minimizes the total cost. We assume the following input:n Di = Annual demand for product i

n S = Order cost incurred each time an order is placed independently of the variety of products included in the order

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

11

Cycle Inventory 21

Multiple Order Policy for Best Buy

o In the case of Best Buy Computers with multiple products, the materials manager may consider three approaches to the lot sizing decision:

1. Each product manager orders his model independently.

2. The product managers jointly order every product in each lot.

3. Product managers order jointly but not every order contains every product; that is, each lot contains a selected subset of the products. This is also called ‘tailored aggregation.’

Cycle Inventory 22

Relative Merits of Each Approach

o The first approach does not use any aggregation and will result in the highest cost.

o The weakness with the second approach is that low-volume products are aggregated with high-volume products in every order, which results in the product-specific order cost for the low-volume product being incurred with each order.n In such a situation it may be better to order the

low-volume products less frequently than the high-volume products.

n As a result, the third approach is likely to yield the lowest cost.

12

Cycle Inventory 23

The ‘Selected Subset’ Approach

1. Identify the most frequently ordered product, assuming each product is ordered independently.

2. Identify the frequency with which other products are included with the most frequently-ordered product.

3. Having decided the ordering frequency of each product, recalculate the ordering frequency of the most-frequently ordered product.

4. For each product, evaluate an order frequency of ni = n/mi.

Cycle Inventory 24

Economies of Scale to Exploit Quantity Discounts

o There are many instances where the pricing schedule yields economies of scale, with prices decreasing as lot size is increased. This form of pricing is very common in B2B transactions.

o Two commonly used lot-size based discount schemes are:

o All unit quantity discounts

o Marginal unit quantity discount or multi-block tariffs.

13

Cycle Inventory 25

Economies of Scale to Exploit Quantity Discounts cont.

o In assessing the impact of quantity discounts on the supply chain, the following two questions should be answered.

n Given a pricing schedule with quantity discounts, what is the optimal purchasing decision for a buyer seeking to maximize profits? How does this decision impact the supply chain in terms of lot sizes, cycle inventories, and flow times.

n Under what conditions should a supplier offer quantity discounts? What are appropriate pricing schedules that supplier should offer?

Cycle Inventory 26

All Unit Quantity Discounts

o In all unit quantity discounts, the pricing schedule contains specified break points q0, q1,.....,qr where q0= 0. If an order is placed that is at least as large as qi but smaller than qi+1, then each unit is obtained at a cost of Ci.

o In general, the unit cost decreases as the quantity ordered increases; that is, C0≥C1≥ Cr.n The company’s objective is to decide on lot sizes

to maximize profits or equivalently, to minimize the sum of material, order, and holding costs.

14

Cycle Inventory 27

Optimal Lot-Sizing Approach

o The solution procedure evaluates the optimal lot size for each price Ci and then settles on the lot size that minimizes the overall cost.

o There are three possible cases for Qi:

1. qi ≤ Qi.≤ qi+1

2. Qi < qi

3. Qi > qi+1

Cycle Inventory 28

Marginal Unit Quantity Discount

o In this case, the pricing schedule contains specified break points q0, q1,.....,qr where q0= 0. It is not the average cost of a unit but the marginal cost of a unit that decreases at a break point. If an order of size q is placed, the first q1 - q0 units are priced at C0, the next q2 - q1 at C1, and so on.

o The marginal cost per unit varies with the quantity purchased.n The company’s objective is to decide on lot sizes

to maximize profits or equivalently, to minimize the sum of material, order, and holding costs.

15

Cycle Inventory 29

Optimal Lot-Sizing Approach

o For each ‘i’ the optimal lot size and the corresponding costs are evaluated. The solution is to set the lot size to be the one that minimizes total annual cost across all ranges i.n It can be shown that the overall optimal

lot size will always lie within the range qi ≤ Qi.≤ qi+1. Hence, the case where Qi < qi or Qi > qi+1 will not be evaluated any further.

Cycle Inventory 30

Quantity Discount and Coordination in the Supply Chain

o A supply chain is coordinated if the decisions the retailer and supplier make maximize total supply chain profits.

o In reality, each stage has a separate owner and considers its own costs in an effort to maximize its own profits. Such independent actions can result in a lack of coordination in the supply chain.

o With respect to the quantity discounts, two particular situations can be considered:1. Quantity discounts for commodity products.2. Quantity discounts where the firm has market

power.

16

Cycle Inventory 31

A Commodity Product Example

20%20%Holding cost (item value)

If the manufacturer were to price vitamins so that each bottle cost $3 for all orders with lot sizes under 9,165 and $2.9978 for all orders above 9,165, the retailer will have an incentive to order in lots of 9,165.

$2$3Unit price/cost

$250$100Fixed Order Cost

120,000120,000Annual Demand

ManufacturerRetailerVitamin Product

Cycle Inventory 32

A Key Point

o For commodity products where price is set by the market, manufacturers can use lot size based quantity discounts to achieve coordination in the supply chain and decrease supply chain costs.

n Lot size based discounts, however, increase cycle inventory in the supply chain.