Inventory Management

FIN 340

Prof. David S. Allen

Northern Arizona University

Types of Inventory• Raw materials inventory:

• Factors of production that will be used in a later stage of production or assembly.

• Work-in-progress inventory: • Partially assembled or completed goods.

• Finished goods inventory: • Items ready for distribution or sale.

Types of Inventory• Independent items: Have demand unrelated to the

requirements for other items, e.g. finished goods.• Independent items lend themselves to analysis by

quantitative techniques.

• Dependent items: Derive their demand from the need for other items or finished products, e.g. raw materials or work-in-progress.• The demand for the end product is used to infer demand for

its components, subcomponents, and raw materials, This is combined with the existing inventory balances to establish a net requirement.

Benefits of Holding Inventory• For finished goods, most marketing analyses suggest

that product availability is the most important factor in customer satisfaction.

• The ability to order in larger lot sizes can create economies of scale in pricing, handling, and setups.

• In manufacturing, inventory decouples supply and demand. It makes possible longer production runs and more flexibility in the manufacturing process.

• Inventory also can enhance firm liquidity. In periods of high cash flows, the firm can invest excess cash in building up inventory. When cash flows are lower, the firm can sell off excess inventory without replacing it in order to generate cash.

Costs of Holding Inventory• Ordering costs: The fixed and variable costs resulting

from the placement and processing of an order.• These include freight, labor, and handling charges. They are

generally assumed to be proportional to the number of orders placed. In a production setting, these correspond to setup costs, i.e. the costs associated with delays and costs in resetting machinery to accommodate a different item.

Costs of Holding Inventory• Carrying costs:

• Cost of capital• Storage costs• Deterioration and obsolescence costs• Insurance costs• Handling costs

• Carrying costs are usually assumed to be proportional to the average inventory level. They are often split into financing costs (the first item above) and holding costs (all others above).

Costs of Holding Inventory

Approx. annual cost as percentage of inventory value

Carrying costs

Cost of capital 12.0%

Storage and handling 0.5%

Insurance 0.5%

Property taxes 1.0%

Depreciation and obsolescence 12.0%

Total 26%

Ordering, shipping, and receiving costs

Cost of placing orders, including production and set-up costs

Varies

Shipping and handling 2.5%

Cost of stock-outs

Loss of sales Varies

Loss of customer goodwill Varies

Disruption of production schedules Varies

Factors Influencing Inventory Management• Effective inventory management is complicated by a

number of factors:• Uncertainty: The inability to perfectly anticipate supply and

demand.• Problems with cost and benefit assessments: Costs and

benefits are difficult to quantify. • Variety in product: Perishability, value, demand, and

interaction with other products are difficult to model.• Constraints: Limitations on financing, storage, and supply

can lead to suboptimal decisions.

Inventory Management Systems• Early inventory management focused on quantitative

approaches to determining optimal order sizes, such of EOQ.

• This was followed by techniques that focused more on order timing, such as materials requirements planning (MRP). These two focuses have had varying degrees of success.

• More recently, the focus has been on "stockless" or just-in-time (JIT) systems, which emphasize minimal inventory levels.

Inventory Management Systems• An important reason for holding inventory is the

inability of the company to synchronize delivery with demand.

• The traditional western inventory system is thus a "just-in-case" type. • Large safety stocks are held to cover the uncertainty of

demand because of long and variable lead time or because of lumpiness in the production process.

• Much of the inventory management revolves around what to do because of this lead time.

Inventory Management Systems• Just-in-time is a philosophy for managing inventory

that seeks to identify and eliminate waste and bottlenecks in the supply chain.

• By holding little or no inventory, problems become apparent, and demand a solution.

Just-in-Time• JIT requires at least eight factors to be effective:

1. short distances between buyer and supplier

2. dependable quality

3. small supplier network

4. dependable transportation

5. manufacturing flexibility

6. small lot sizes

7. effective receiving and materials-handling facilities

8. strong management commitment

The EOQ Inventory Model• Two costs associated with inventory:

• Carrying costs• Ordering costs

• Carrying costs increase as inventory levels increase.• However, ordering costs decline as the inventory level increases.

• The firm attempts to minimize the total cost.• Total inventory cost = carrying cost + ordering cost

The EOQ Inventory Model• Note that the EOQ model applies to individual

inventory items, not aggregate inventory.

The EOQ Inventory Model• S = annual demand for item in units• Q = number of items per order

• So, average inventory = Q/2

• C = carrying cost as proportion of inventory value• P = price (i.e. cost) per unit• The total annual carrying cost is then:

• TCC = (C)(P)(Q/2)

• F = fixed cost to place an order• N = number of orders placed per year• So, total annual ordering cost is:

• TOC = F(S/Q)

The EOQ Inventory Model• Total Inventory Cost

TIC = TCC + TOC = (C)(P)(Q/2) + (F)(S/Q)• So, as the order quantity Q increases, the first term

increases, but the second term decreases.

The EOQ Inventory Model• To find the cost-minimizing order quantity, Q*, we

apply calculus to the TIC equation:• TIC = (C)(P)(Q/2) + (F)(S/Q)

• Solving, we find:• Q* = [2FS/(CP)]1/2

• A consequence of this equation is that Q* increases with the square root of annual sales, S. So, the firm’s inventory turnover is assumed to increase as sales increase.

The EOQ Inventory Model

EOQ With Safety Stocks• Safety stocks are used to:

• Meet demand in the event that it is larger than expected.• Meet demand if new orders take longer to receive than

expected.

EOQ With Safety Stocks

EOQ With Safety Stocks• With safety stocks, the average inventory is higher

than without them:• Avg. inventory = Q*/2 + safety stock

EOQ With Quantity Discounts• If the firm’s suppliers offer a discount for larger orders

(larger than Q*), the firm will need to compare the reduction in purchase price with the additional TIC from holding a larger than optimal quantity:• Reduction in purchase price

+ TIC discount quantity – TIC optimal quantity= net savings from taking the discount

• Let Q’ = discount quantity, D = discount percent• Net savings from taking the discount

= (D)(P)(S)-(Q’ / 2)(C)(P)(1-D) + (F)(S/Q’) +(Q* / 2)(C)(P)+ (F)(S/Q*)