Week 5 Individual Problem


Numerous techniques are available for effectively managing the firm’s inventory. Here we briefly consider four commonly used techniques.

ABC System

A firm using the ABC inventory system divides its inventory into three groups: A, B, and C. The A group includes those items with the largest dollar investment. Typically, this group consists of 20 percent of the firm’s inventory items but 80 percent of its investment in inventory. The B group consists of items that account for the next largest investment in inventory. The C group consists of a large number of items that require a relatively small investment.

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ABC inventory system

Inventory management technique that divides inventory into three groups—A, B, and C, in descending order of importance and level of monitoring—on the basis of the dollar investment in each.

The inventory group of each item determines the item’s level of monitoring. The A group items receive the most intense monitoring because of the high dollar investment. Typically, A group items are tracked on a perpetual inventory system that allows daily verification of each item’s inventory level. B group items are frequently controlled through periodic, perhaps weekly, checking of their levels. C group items are monitored with unsophisticated techniques, such as the two-bin method. With the two-bin method, the item is stored in two bins. As an item is needed, inventory is removed from the first bin. When that bin is empty, an order is placed to refill the first bin while inventory is drawn from the second bin. The second bin is used until empty, and so on.

two-bin method

Unsophisticated inventory-monitoring technique that is typically applied to C group items and involves reordering inventory when one of two bins is empty.

The large dollar investment in A and B group items suggests the need for a better method of inventory management than the ABC system. The EOQ model, discussed next, is an appropriate model for the management of A and B group items.

Economic Order Quantity (EOQ) Model

One of the most common techniques for determining the optimal order size for inventory items is the economic order quantity (EOQ) model. The EOQ model considers various costs of inventory and then determines what order size minimizes total inventory cost.

economic order quantity (EOQ) model

Inventory management technique for determining an item’s optimal order size, which is the size that minimizes the total of its order costs and carrying costs.

EOQ assumes that the relevant costs of inventory can be divided into order costs and carrying costs. (The model excludes the actual cost of the inventory item.) Each of them has certain key components and characteristics. Order costs include the fixed clerical costs of placing and receiving orders: the cost of writing a purchase order, of processing the resulting paperwork, and of receiving an order and checking it against the invoice. Order costs are stated in dollars per order. Carrying costs are the variable costs per unit of holding an item of inventory for a specific period of time. Carrying costs include storage costs, insurance costs, the costs of deterioration and obsolescence, and the opportunity or financial cost of having funds invested in inventory. These costs are stated in dollars per unit per period.

order costs

The fixed clerical costs of placing and receiving an inventory order.

carrying costs

The variable costs per unit of holding an item in inventory for a specific period of time.

Order costs decrease as the size of the order increases. Carrying costs, however, increase with increases in the order size. The EOQ model analyzes the tradeoff between order costs and carrying costs to determine the order quantity that minimizes the total inventory cost.

Mathematical Development of EOQ A formula can be developed for determining the firm’s EOQ for a given inventory item, where

S ; equals ; usage in units per period ; O ; equals ; order cost per order ; C ; equals ; carrying cost per unit per period ; Q ; equals ; order quantity in units ;

The first step is to derive the cost functions for order cost and carrying cost. The order cost can be expressed as the product of the cost per order and the number of orders. Because the number of orders equals the usage during the period divided by the order quantity (S/Q), the order cost can be expressed as follows:

Order cost = O × (S ÷ Q)(15.4)

The carrying cost is defined as the cost of carrying a unit of inventory per period multiplied by the firm’s average inventory. The average inventory is the order quantity divided by 2 (Q/2), because inventory is assumed to be depleted at a constant rate. Thus, carrying cost can be expressed as

Carrying cost = C × (Q ÷ 2)(15.5)

The firm’s total cost of inventory is found by summing the order cost and the carrying cost. Thus, the total cost function is

total cost of inventory

The sum of order costs and carrying costs of inventory.

Total cost = [O × (S ÷ Q)] + [C × (Q ÷ 2)](15.6)

Because the EOQ is defined as the order quantity that minimizes the total cost function, we must solve the total cost function for the EOQ.2 The resulting equation is

EOQ equals the square root of 2 × S × O over C(15.7)

Although the EOQ model has weaknesses, it is certainly better than subjective decision making. Even though the use of the EOQ model is outside the control of the financial manager, the financial manager must be aware of its utility and must provide certain inputs, specifically with respect to inventory carrying costs.

2. In this simple model, the EOQ occurs at the point where the order cost [O × (S ÷ Q)] just equals the carrying cost [C × (Q ÷ 2)]. To demonstrate, we set the two costs equal and solve for Q:

[O × (S ÷ Q)] = [C × (Q ÷ 2)]

Then cross-multiplying, we get

2 × O × S = C × Q2

Dividing both sides by C, we get

Q2 = (2 × O × S) ÷ C


Q equals the square root of open parenthesis 2 × O × S close parenthesis ÷ C

Personal Finance Example 15.4

Individuals sometimes are confronted with personal finance decisions involving cost trade-offs similar to the trade-off between the fixed order costs and variable carrying costs of inventory that corporations face. Take the case of the von Dammes, who are trying to decide whether a conventional car (uses gas) or a hybrid car (uses gas and electric battery) would be more cost effective.

The von Dammes plan to keep whichever car they choose for 3 years and expect to drive it 12,000 miles in each of those years. They will use the same dollar amount of financing repaid under the same terms for either car, and they expect the cars to have identical repair costs over the 3-year ownership period. They also assume that the trade-in value of the two cars at the end of 3 years will be identical. Both cars use regular unleaded gas, which they estimate will cost, on average, $3.20 per gallon over the 3 years. The key data for each car are as follows:

Total cost$24,500$27,300
Average miles per gallon     27     42

We can begin by calculating the total fuel cost for each car over the 3-year ownership period:

Conventional: [(3 years × 12,000 miles per year) ÷ 27 miles per gallon]

× $3.20 per gallon

= 1,333.33 gallons × $3.20 per gallon = $4,267

Hybrid:       [(3 years × 12,000 miles per year) ÷ 42 miles per gallon]

× $3.20 per gallon

= 857.14 gallons × $3.20 per gallon = $2,743

To buy the hybrid car, the von Dammes will have to pay $2,800 more ($27,300 − $24,500) than the cost of the conventional car, but they will save about $1,524 ($4,267 − $2,743) in fuel costs over the 3-year ownership period. Ignoring differences in timing, on a strict economic basis they should buy the conventional car because the $2,800 marginal cost of the hybrid results in a marginal fuel cost savings of only $1,524. Clearly, other factors such as environmental concerns and the reasonableness of the assumptions could affect their decision.

Reorder Point Once the firm has determined its economic order quantity, it must determine when to place an order. The reorder point reflects the number of days of lead time the firm needs to place and receive an order and the firm’s daily usage of the inventory item. Assuming that inventory is used at a constant rate, the formula for the reorder point is

reorder point

The point at which to reorder inventory, expressed as days of lead time × daily usage.

Reorder point = Days of lead time × Daily usage(15.8)

For example, if a firm knows it takes 3 days to place and receive an order and if it uses 15 units per day of the inventory item, the reorder point is 45 units of inventory (3 days × 15 units/day). Thus, as soon as the item’s inventory level falls to the reorder point (45 units, in this case), an order will be placed at the item’s EOQ. If the estimates of lead time and usage are correct, the order will arrive exactly as the inventory level reaches zero. However, lead times and usage rates are not precise, so most firms hold safety stock (extra inventory) to prevent stockouts of important items.

safety stock

Extra inventory that is held to prevent stockouts of important items.

Example 15.5

MAX Company, a producer of dinnerware, has an A group inventory item that is vital to the production process. This item costs $1,500, and MAX uses 1,100 units of the item per year. MAX wants to determine its optimal order strategy for the item. To calculate the EOQ, we need the following inputs:

Order cost per order ; equals ; $150 ; Carrying cost per unit per year ; equals ; $200 ;

Substituting into Equation 15.7, we get

The reorder point for MAX depends on the number of days MAX operates per year. Assuming that MAX operates 250 days per year and uses 1,100 units of this item, its daily usage is 4.4 units (1,100 ÷ 250). If its lead time is 2 days and MAX wants to maintain a safety stock of 4 units, the reorder point for this item is [(2 × 4.4) + 4], or 12.8 units. However, orders are made only in whole units, so the order is placed when the inventory falls to 13 units.

The firm’s goal for inventory is to turn it over as quickly as possible without stockouts. Inventory turnover is best calculated by dividing cost of goods sold by average inventory. The EOQ model determines the optimal order size and, indirectly, through the assumption of constant usage, the average inventory. Thus, the EOQ model determines the firm’s optimal inventory turnover rate, given the firm’s specific costs of inventory.

Just-in-Time (JIT) System

The just-in-time (JIT) system is used to minimize inventory investment. The philosophy is that materials should arrive at exactly the time they are needed for production. Ideally, the firm would have only work-in-process inventory. Because its objective is to minimize inventory investment, a JIT system uses no (or very little) safety stock. Extensive coordination among the firm’s employees, its suppliers, and shipping companies must exist to ensure that material inputs arrive on time. Failure of materials to arrive on time results in a shutdown of the production line until the materials arrive. Likewise, a JIT system requires high-quality parts from suppliers. When quality problems arise, production must be stopped until the problems are resolved.

just-in-time (JIT) system

Inventory management technique that minimizes inventory investment by having materials arrive at exactly the time they are needed for production.

The goal of the JIT system is manufacturing efficiency. It uses inventory as a tool for attaining efficiency by emphasizing quality of the materials used and their timely delivery. When JIT is working properly, it forces process inefficiencies to surface.

Knowing the level of inventory is, of course, an important part of any inventory management system. As described in the Focus on Practice box, radio frequency identification technology may be the “next new thing” in improving inventory and supply chain management.

in practice focus on PRACTICE: RFID: The Wave of the Future?

Wal-Mart Stores, Inc., the world’s number one retailer, operates almost 11,000 retail units under 55 different banners in 27 countries and employs more than two million people around the world. What’s more, Wal-Mart came in third place among general merchandisers in Fortune magazine’s 2013 Most Admired Companies survey. With fiscal 2013 sales of $469 billion, Wal-Mart is able to exert tremendous pressure on its suppliers. When Wal-Mart announced in April 2004 that it was beginning a pilot program to test radio frequency identification (RFID) technology to improve its inventory and supply chain management, suppliers and competitors took notice.

One of the first companies to introduce bar codes in the early 1980s, Wal-Mart required its top 100 suppliers to put RFID tags on shipping crates and pallets by January 2005, with the next 200 largest suppliers using the technology by January 2006. Wal-Mart officials believed that RFID tags would allow the company to wring out inefficiencies from its inventory and supply chain operations, thereby lowering expenses and working capital investments. As of February 2007, Wal-Mart officials said that 600 of its suppliers were RFID-enabled. Nevertheless, Wal-Mart’s ultimate goal to have all its 100,000-plus suppliers on board using electronic product codes (EPC) with RFID technology began to stall. The company failed to show dramatic reductions in inventory (in fact, inventories went up, not down, after the RFID program was put in place), and some suppliers resisted the change.

The major issue with RFID tags is per-chip cost. In 2004, when Wal-Mart announced its intent to use RFID tags, the tags sold for 30 to 50 cents each. Wal-Mart requested a price of 5 cents per tag, expecting increased demand and economies of scale to push the price down to make them more competitive with inexpensive barcodes. Increased demand has brought the price of current-generation RFID tags to about 15 cents apiece, but barcodes cost only a fraction of a cent. Barcodes help track inventory and can match a product to a price, but they lack the electronic tags’ ability to store more detailed information, such as the serial number of a product, the location of the factory that made it, when it was made, and when it was sold.

Wal-Mart expects the RFID technology to improve its inventory management, and it remains committed to advancing its use of RFID. During the 2010 National Retail Federation’s Big Show convention, Wal-Mart’s chief information officer (CIO), Rollin Ford, said, “We’re still bullish on RFID.” He also indicated that Wal-Mart ran some apparel pilots last year that showed good results and that the retailer plans to “eat what we cook.” Wal-Mart manufactures some apparel items and controls its own supply chain, and Ford indicated that Wal-Mart plans to use RFID technology in its apparel supply chain. Wal-Mart will then share the benefits and best practices with its suppliers, which might want to achieve the same benefits from the technology.

 What problem might occur with the full implementation of RFID technology in retail industries? Specifically, consider the amount of data that might be collected.

Computerized Systems for Resource Control

Today, a number of systems are available for controlling inventory and other resources. One of the most basic is the materials requirement planning (MRP) system. It is used to determine what materials to order and when to order them. MRP applies EOQ concepts to determine how much to order. Using a computer, MRP simulates each product’s bill of materials, inventory status, and manufacturing process. The bill of materials is simply a list of all parts and materials that go into making the finished product. For a given production plan, the computer simulates material requirements by comparing production needs to available inventory balances. On the basis of the time it takes for a product that is in process to move through the various production stages and the lead time to get materials, the MRP system determines when orders should be placed for various items on the bill of materials. The objective of this system is to lower the firm’s inventory investment without impairing production. If the firm’s pretax opportunity cost of capital for investments of equal risk is 20 percent, every dollar of investment released from inventory will increase before-tax profits by $0.20.

materials requirement planning (MRP) system

Inventory management technique that applies EOQ concepts and a computer to compare production needs to available inventory balances and determine when orders should be placed for various items on a product’s bill of materials.

A popular extension of MRP is manufacturing resource planning II (MRP II), which integrates data from numerous areas such as finance, accounting, marketing, engineering, and manufacturing using a sophisticated computer system. This system generates production plans as well as numerous financial and management reports. In essence, it models the firm’s processes so that the effects of changes in one area of operations on other areas can be assessed and monitored. For example, the MRP II system would allow the firm to assess the effect of an increase in labor costs on sales and profits.

manufacturing resource planning II (MRP II)

A sophisticated computerized system that integrates data from numerous areas such as finance, accounting, marketing, engineering, and manufacturing and generates production plans as well as numerous financial and management reports.

Whereas MRP and MRP II tend to focus on internal operations, enterprise resource planning (ERP) systems expand the focus to the external environment by including information about suppliers and customers. ERP electronically integrates all a firm’s departments so that, for example, production can call up sales information and immediately know how much must be produced to fill customer orders. Because all available resources—human and material—are known, the system can eliminate production delays and control costs. ERP systems automatically note changes, such as a supplier’s inability to meet a scheduled delivery date, so that necessary adjustments can be made.

enterprise resource planning (ERP)

A computerized system that electronically integrates external information about the firm’s suppliers and customers with the firm’s departmental data so that information on all available resources—human and material—can be instantly obtained in a fashion that eliminates production delays and controls costs.


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