Economic Order Quantity model (EOQ) and the Just-In-Time model (JIT)

Custom Student Mr. Teacher ENG 1001-04 19 July 2016

Economic Order Quantity model (EOQ) and the Just-In-Time model (JIT)


It is very important that successful enterprises need efficient stock control management, especially in manufacturing companies and retail distribution. In business practice, we usually use many stock control models such as the Economic Order Quantity model (EOQ) and Just-In-Time model (JIT). The purpose of this report is to indicate the rationale of EOQ and JIT models and detailed to explain the effectiveness in practice of the two models. Moreover, I decided to take the McDonald company as an example, which illustrate JIT model is being applied by McDonald company.

In this report, by serious study and literature review, combined with refer to relevant books, search useful information from internet and my personal idea. I have examined concepts of EOQ and JIT models. Followed by discuss the rationale of them, and illustrate effectiveness of the two models in practice that we may fully understand the importance of EOQ and JIT systems in company’s daily operation. Finally, use JIT system in McDonald Company is presented.


2.1 Definition

2.1.1 Economic Order Quantity model

The Economic Order Quantity stock control model also called the economic lot size or economic production quantity, it affirms that “the optimal quantity of an inventory item to order at any time is that quantity that minimizes total inventory costs over planning period” (Horne and Wachowicz 1995, p.271).

2.1.2 Just-In-Time model

The Just-In-Time stock control model “is an integrated set of activities designed to achieve high-volume production using minimal inventories of raw materials, work-in-process, and finished goods” (Aquilano et al. 2004, p.426).


In 1913, F. W. Harris developed an EOQ model which has been applied widely. This model is being used in planning the purchase raw materials, and suppliers, and in planning purchases for wholesalers and retailers who resell products.

3.1 Assumptions of EOQ Model

It is necessary to the inventory management that EOQ model is one of the most commonly approach. Use this model is relatively simple, however, according to Heizer and Render (2001, p.481), it must based on the following assumptions or conditions:

Rate of demand is constant, known and independent.

Lead time is certainty and constant, therefore, when the stock down to zero, the stock could be added at a precise time.

Quantity discounts are impossible.

The stock is immediate and complete.

If ordered goods are in appropriate time, shortages can be prevent.

Setup cost and holding or carrying cost are belong to variable costs.

3.2 The Objective of EOQ Model

“The objective of the EOQ model is to determine the optimal quantity of inventory to order and the best time to place the order” (Dyclcman et al. 1990, p.630). In fact, the EOQ is balancing two inventory management costs: carrying cost and ordering costs. Dyclcman et al. argue (1990): Carrying costs include out-of-pocket costs such as storage, insurance, taxes and so on. Opportunity costs is related to the cost of investing capital in inventory rather than in other income-producing assets. Ordering costs include out-pf-pocket expenditures incurred every time an order is placed, such as handling, shipping, and so on.

Dyclcman et al. (1990) make a further statement: Carrying costs and ordering costs demonstrate different cost behaviors relative to the level of inventory maintained. Carrying costs increase with the quantity of inventory maintained; ordering costs decrease with the quantity of inventory maintained. The more inventory kept on hand, the more storage, handling, and other such carrying costs are incurred. The larger the amount of inventory, the fewer number of orders needed to replenish the inventory and the smaller the amount of ordering costs.

3.3 Validity of the assumptions and model robustness

Although the assumption of EOQ model shows highly restrictive, one advantage of EOQ model is that it is quite robust. As mentioned onwards, there are some assumptions will be dropped, like no quantity discounts, no shortages, no uncertainty in demand and lead time. On the other hand, “such as a constant demand rate and a constant holding cost per unit, can be violated somewhat without substantially reducing the accuracy of the solution” (Martinich 1997, p. 671). When the demand face seasonal changes, model can be changed to adapt to this situation.

Martinich (1997) stated clearly: The important feature of EOQ model is that the function of total stocking cost is flat around the optimal order quantity. Estimating ordering cost per unit time and holding cost per unit time are very crucial, because they are not often very accurate. Therefore, the value computed for EOQ cannot equal

the true optimal value. “However, because of the flatness of the total stocking cost function, even if the computed EOQ is 20%-30% different from the true optimal, the cost penalty is relatively small”(Martinich 1997, p.671).

Robust is defined as “a model that gives satisfactory answers even with substantial variation in its parameters” (Heizer and Render 2001, p.486). As we mentioned above, it is difficult to decide accurate ordering costs and holding costs for inventory management. Thus, a robust model is very favorable and some errors do not cost us very much. This is because that the EOQ model is most convenient and it can accurately forecast demand, holding cost, and ordering cost is limited.

3.4 Fixed Order Point versus Fixed Order Interval Policy

EOQ model is an approach of the fixed order point policy. According to Ellram et al. (1998, p.128): Throughout the ordering process, as long as the EOQ model was identified, a fixed quantity will be ordered every time. “An order is placed when inventory on hand reaches a predetermined minimum level necessary to satisfy demand during the order cycle.” An order will be generated through the automated inventory management system.

Another reorder policy is the fixed order interval method. Use this method, we may set time interval, maybe every week. Under this method, many projects are bought by the same supplier. “A weekly order may be placed to reduce ordering costs and take advantages of purchase volume discounts and freight consolidation.”


As we all know, the most effective stock management approach is JIT production control system over the past 50 years. The system is currently being used by many industries.

4.1 JIT Logic

For the purpose of JIT system, it intend to use minimum inventories of raw materials, process of production, and finished goods to achieve high output. Need is based on the occurrence of product’s actual demand, otherwise nothing will be produced. Theoretically, if an item is sold, the market will pull a substitute in the system. “This triggers an order to the factory production line, where a worker then pulls another unit from an upstream station in the flow to replace the unit taken” (Aquilano et al. 2004, p.427). Then this upstream station pulls to further upstream and back to release of raw materials. To make this pull process more smoothly, JIT need high quality in every procedure, strong supplier relationships, and a very clearly demand for the final product.

4.2 Feature of JIT production system

In JIT production system, Black et al. (1996, p.842) argue that it include three key features:

1). Operation of production line is based on demand-pull, as a result, each workstation’s activity is subject to the approval of the demand of downstream workstations. There are many approaches to use demand-pull feature, but the most common method is Kanban system which is the Japanese term for a visual record or card.

Under Kanban system, use a kanban card to operate to authorized another operation to produce a given part of the special quantity. Black et al. (1996) provide an example: “suppose the assembly department of a muffler manufacture receives an order for 10 mufflers. The assembly department triggers productions of the 10 metal pipes it needs to make the 10 mufflers by sending a kanban card to the machining department, which then begins producing the pipes. When production is completed, the machining department attaches the kanban card to the box containing the mental pipes and ships the package downstream to the assembly department, which starts the cycle over again when it receives the next customer order.”

2). Each unit including the setup time and manufacturing lead time are minimized. When a product is prepare to begin in production line, then turned into finished products, the process of the elapse of the time is known as manufacturing lead time. Production of demand normally produced relatively small quantities, however, as long as setup times are small, it is cost-effective to produce product in small quantities.

3). If parts have defective and insufficient, the production line will cease operation. Each staff should attach great importance to reducing the occurrence of such problems like defective material parts. Conversely, under the traditional inventory management system, workers can ignore defective parts and continue to work because the inventory parts and work in process are huge.

Hirsch et al. (1989, p.746) take a similar view, they have also added an important argument that total quality control (TQC) is often combined with JIT system. All the staff have become quality control inspection personnel, meanwhile, if products and materials are found to be not meeting quality standard, the production line should suspend operation. As long as this situation happened, it must be resolved as soon as possible. It means that workers have not impetus to ignore the fault in the early of production process stage, they had to stop their work process.

4.3 JIT Costing

The fundamental difference between JIT method and other traditional methods is the treatment of the costs.

According to Hirsch et al. (1989, p.746), under the traditional approach of costing, raw materials or reserves firstly get into an asset account, when they are transported. After these amounts are transferred into a work-in process account, they will be put into operation as raw materials. “Then, as the materials move from process to process they pass through a series of work-in-process accounts for each operation.” Eventually, when the product
inventory through work-in-process account transfer to finished product inventory account.

“With JIT the incoming materials are entered at cost directly into a material and work-in-process inventory account.” There is no series of work-in-process accounts for each process because there is very little work-in-process to account for. The value of material is diverted to finished product inventory account because the product has been completed.

4.4 JIT Purchasing

In JIT purchasing, suppliers use the replacement principle of Kanban by using small, standard-size containers and make several shipments daily to each customer. JIT not only reduces in-process inventories by using Kanban, but also raw materials inventories are reduced by applying the same principles to suppliers as well.

According to Frazier and Gaither (2001): the elements of JIT purchasing are as following:

1). Supplier development and supplier relations undergo fundamental changes. The nature of the relationships between customers and suppliers shifts from being adversarial to being cooperative. The Japanese call these relationships subcontractor networks and refer to suppliers as co-producers.

2). Purchasing departments develop long-term relationships with suppliers. The result is long-term supply contracts with a few suppliers rather than short-term supply contracts with many suppliers.

3). Although price is very important, delivery schedules, product quality, and mutual trust and cooperation become the primary basis of supplier selection.

4). Suppliers are encouraged to extend JIT approach to their own suppliers.

5). Suppliers are ordinarily located near the buying firm’s factory, or if they are some distance from the factory, they are often clustered together. This causes lead times to be shorter and more reliable.

6). Shipments are delivered to the customer’s production line directly. Because suppliers are encouraged to produce and supply parts at a steady rate that matches the use rate of the buying firm, company-owned hauling equipment tends to be preferred.

7). Parts are delivered in small, standard-size containers with a minimum of paperwork and in exact quantities.

8). Delivered material is of near-perfect quality. Because suppliers have a long-term relationship with the buying firms and because parts are delivered in small lot sizes, the quality of purchased materials tends to be higher.


5.1 Examination of EOQ Assumptions

In the practice of business arena, although EOQ model enable to generate many good results, many limitations of EOQ model is combined with its own assumptions. Schroeder (1993, p.592) argued as following:

1). In practice, demand is assumed to be constant, but in many cases demand is shifty.

2). The unit cost is assumed constant, in practice, however, normally if the purchase of large quantities, it will gain quantities discounts. “This case needs a modification of the basic EOQ model and is treated in the chapter supplement.”

3). The material in the lot is assumed to arrive all at once, but in some cases material will be placed in inventory continuously as it is produced. This case is also treated in the supplement.

4). A single product is assumed, however, sometimes several projects were purchased through a single provider. Meanwhile they are being shipped at one time.

5). Suppose the setup cost is static, as a matter of fact, it is always decreased.

These assumptions have been pointed out to illustrate the limitation of the basic EOQ model, nevertheless it is useful approximation in practice. The formula at least “puts you in the ballpark”, provided the assumptions are reasonably accurate. In addition, the total-cost curve is rather flat in the region of the minimum. Therefore the EOQ can be adjusted somewhat to conform to reality without greatly affecting the costs.

The EOQ formula can also offer insight into economic behavior of inventories. For example, traditional turnover arguments suggest that inventory should increase directly with sales if a constant turnover ratio is desired. Since turnover is the ratio of sales to inventory, a doubling of sales will allow a doubling of inventory if the turnover rate is held constant. But the EOQ formula suggests that inventory should increase only with the square root of sales. This indicates that it is net economical to maintain a constant turnover ratio as sales increase; a higher turnover is indeed justified.

It is important for financial manager that fully understand limitations and assumptions of the EOQ model will offer a strong base of making stock management decision.

5.2 EOQ Model Extension

Obviously, through the above discussion, some assumptions of EOQ model are impractical. In order to make this model more useful, it is necessary to extension for EOQ model. Besley and Brigham (2005, pp.602-603) state clearly:

To begin with, if there is a delay between the time inventory is ordered and when it is received, the company have to reorder before it use up inventory. To avoid this, the firm can carry safety stock, which means “additional inventory carried to guard against unexpected changes in sales rates or production/shipping delays.”

The amount of safety stock a company holds generally increase with a) the uncertainty of demand forecasts, b) the costs (in term of lost sales and lost goodwill) that result from stockouts, and c) the chances that delay will occur in receiving shipments. The amounts of safety stock decreases as the cost of carrying this additional inventory increase. Moreover, a company should consider when determining appropriate inventory level is whether its supplier provides discounts to purchase large quantities.

It is unrealistic to suppose that the demand for the inventory is uniform in the year, the EOQ model should not be based on an annual to applying. More appropriate approach should divide the year into the seasons like the spring, the summer, the fall, and the winter which sales are relatively constant; then the EOQ model can be applied separately to each periods.


In practice, we have already found that JIT system have its potential benefits and its problems. It is important to use that fully comprehension the merits and the problems of JIT system.

6.1 Typical Benefits of JIT

Meredith and Shafer (2002, p.351) deem that JIT provide various advantage in real operation:

Cost savings. There are many approaches to save cost. Such as inventory reduction, reduced scrap, fewer defect, less space, fewer changes due to both customers and engineering, decreased labor hours, less rework, reduced rework, and other such effects. Total savings range in the neighborhood of 20 to 25 percent, with significantly higher savings on individual categories such as inventory and defects.

Revenue increases. Through high-quality product and satisfactory service to customers, revenue will be increased. Short lead time and rapidly reply to meet customer’s need lead to better margins and higher sales. The rapid research and development of new products and service will bring more revenues.

Investment savings. Investment is saved through three primary effects. First, less space is needed for the same capacity. Second, inventory is reduced to the point that turns run about 50 to 100 a year. Third, the volume of work produced in the same facility is significantly increased, frequently by as much as 100 percent.

Workforce improvement. JIT company’s employees are more satisfied with their work. They prefer the teamwork it demands, and they like the fact the fewer problems arise. They are also better trained for the flexibility and skills needed with JIT, and they enjoy the growth they experience in their jobs. “All this translates into better, more productive work.”

Uncovering problems. One of the unexpected benefits is the greater visibility to problems that JIT allows, if management is willing to capitalize on the chance to fix these problems. In trying to speed up a process, all types of difficulties are uncovered and most of them are various from of waste so not only is response time but also is usually zero.

6.2 Potential Problems in Implementing JIT

It is important that JIT system has some problems and limitations. According to Meredith and Shafer (2002, p.353), there are some difficulties and problems as following:

First of all, JIT system is do for repetitive production case, including relatively standard products. It does not applicable to custom, continuous flow, or project situation. JIT system is not long-term operations, because it is based on the identical mixed-model plans to operation in every day. Clearly, when setups need to spend a long time, JIT will not able to run continuously. JIT system often has setups, it also has frequent shipments and receipts. Therefore the company must be prepared for this too.

JIT need principle as well. Production will cease, once products are not arrive on schedule, or flaws happen. Moreover, we have no other means or time to make up for mistakes. Production system must be used correctly, workers must fulfill their work seriously, otherwise run of JIT system will fail.

Principle is usually linked with supply chain. The biggest problem to successful operation of JIT system is unrealistic deliveries from suppliers. For example: Suppose X company’s two important suppliers have already gone strike for several days, X company was forced to close 10 of its plants at a cost of almost $500 million in lost profits. When an important supplier their supply, JIT is very danger if there is no backup supplier.

In addition, equally serious problem is when a comprehensive delivery service goes on strike, like UPS and FEDEX strike that idled thousands of business and caused a major disruption in the economy. Although other delivery service can sometimes fill in, they often cannot bring sufficient capacity to the problem to keep JIT operating without disruption.

On the other hand, JIT is based on cooperation and trust among workers, managers, suppliers, customers, and so on. The current environment must be trust and competition is not exist, or else JIT will not run successfully. Trust and cooperation must also be extended to the external such as suppliers and customers. “With suppliers, this means moving to risky, single-source contracts and bringing an outsider into the project team, where there may be proprietary secrets.”

6.3 E-Commerce and JIT Purchasing

Nowadays, JIT system combined with e-commerce, making the JIT purchasing has become better to use in practice. E-commerce has already put up a advantage to JIT purchasing. There are some merits being showed: Reduce waste of time to deal with paper work and reduce the procurement lead time; labor costs are also reduced. “The bottom line is a more efficient and effective purchasing process” (Frazier and Gaither 2001, p.477).

E-commerce can drive the use of Kanban between manufacturer and suppliers. Under method of Internet-based system, a manufacturer can electronically send Kanban to suppliers. E-Kanban and paper Kanban have identical functions, however they can provided to suppliers rapidly.


·What are the benefits for McDonald?

The major benefits for McDonald are better food at a lower cost. McDonald Company has found something that allows them to improve quality and lower costs.

·Improved Quality

The less obvious benefit is the higher quality customer service that arises from the JIT burger assembly. When McDonald waits for you to order the burger, they do a few things to improve customer service. First of all, when you place a special order, it does not send McDonald’s into a panic that causes huge delays.

Now that McDonald company is in the practice of waiting until you order a burger until they make it, they don’t freak out when they have to make a special order fresh just for you. This higher quality customer service is subject to McDonald ability to produce faster. Without this ability, McDonald’s ordering costs would be sky-high because the costs associated with ordering would be the loss of customers tired of ordering fast food that really isn’t fast.

Second, JIT allows McDonald to adapt to demand a little bit better. Seemingly, lower inventory levels would cause McDonald’s bigger problems in a higher demand because they wouldn’t have their safety stock. However, because they can produce burgers in a record time, they don’t have to worry about their pre-made burger inventories running out in the middle of an exceptionally busy shift.

·Lower Costs In McDonald, the holding costs for burger parts (beef, cheese, whatever other garbage they put on their burgers) are fairly high because of their spoilage costs. Frozen ground beef that’s good today might not be so good in a few months. Once cooked, the same ground beef’s spoilage rate shoots through the roof. Instead of having a shelf life of months or weeks, the burger needs to be sold within 15 minutes or so. The holding costs go from roughly 20% per week to 100% per hour.

·Why use JIT?

According to argument of Inventory management review (2005):

·Economic Order Quantity Savings A large benefit of JIT is that it reduces the total cost of ordering and holding inventory. High holding costs is the nature of the fast food industry. JIT system allowed them to exploit the savings that were realized by holding less inventory.

High holding costs and low ordering costs are the factors that drive JIT. Generally, it’s the ability to lower ordering costs that make it a feasible solution. McDonald was slave to the high holding costs. It was just the nature of their industry. The solution for them was that while they couldn’t lower holding costs, they could lower ordering costs.

EOQ determines how much you should order and there are two factors that drive economic order quantities down: low ordering costs and high holding costs. Depending on the product and the industry, one or both of these qualities may exist in your operations. If they do, JIT may be right for you. Without the ability to make ordering costs low as a percentage of holding costs, then there is no need for JIT. In fact, the increased frequency in ordering will result in cost increases.

·Safety Stock Reductions

The other aspect of JIT is the drastic reduction in safety stock. Two reasons result in safety stock exist: variability in demand and variability in lead times from suppliers (for McDonald company, the supplier is the internal production process). If lead time is shorter, which JIT tries to accomplish, then this part of the safety stock is smaller, this lowering safety stock inventory. McDonald company is accomplished this by creating a system that allowed a faster burger production (McDonald’s lead times are internal).

On the other hand, If lead time has no variance or is reduced, then this term can be eliminated or at least reduced. Again, this is what JIT try to accomplish. McDonald company is accomplished by standardizing production.

McDonald Company fully understand that a considerable amount of work needs to be done with suppliers/internal operations in order to accomplish the tasks of shortening lead times and reducing their variances. McDonald company has the resource to implement JIT system successfully.

However, in competitive industries, JIT is not optimal for all the firms. JIT, like most management accounting techniques, is not a universal panacea, and some firms find it profitable like McDonald, Walmart, and so on; some are not.


It should be said that stock management is prominent aspect of working capital management. For the purpose of control stock level, most of companies use EOQ and JIT models in practice. Efficiency gains in inventory management can bring significant improvement to overall company financial performance. However, no model has been fully satisfactory. The two models have advantages and disadvantages respectively. In general, although each model will work well in certain environments, they may not work well in other environments. An inappropriate choice of system can be expensive mistake. Thus, it can be concluded that each company should choose own different stock control model with its own conditions and efficient inventory management can lead to better planning and business control.


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