Home > Articles

This chapter is from the book

Inventory Policy in a Fixed-Order Quantity System

A fixed-order quantity system is one of the most important in inventory management. For that reason we need to look at how to compute the two variables that define it: the order quantity Q and the reorder point ROP. Before we do that, however, we need to look at the assumptions this system makes. Most importantly, the system assumes that all the variables occur at a constant rate and their values are known with certainty. For example, the system assumes that the demand, D, occurs at a constant rate and that there is no variability in demand. Also, the lead time, L, is constant, the holding cost, H, is known and fixed, as are stockout cost, S, and unit price, C. Although these assumptions are not realistic the model is highly robust and provides excellent results despite these assumptions.

How Much to Order?

The first decision in the fixed-order quantity model is to select the order quantity Q. Recall that there are a number of inventory costs, most notably inventory holding cost and ordering cost. We want to select the “best” order quantity that minimizes these costs—the EOQ mentioned previously. This is computed by looking at the total annual inventory cost and finding the order quantity that minimizes it. Consider that the total annual cost is comprised of annual purchase cost, annual ordering cost, and annual holding cost, and looks as follows:

  • Total cost = Purchase cost + Ordering cost + Holding cost
  • TC = DC + (D/Q) S + (Q/2) H

where

  • TC = Total cost
  • D = Annual demand
  • C = Unit cost
  • Q = Order quantity
  • S = Ordering cost
  • H = Holding cost

The first term in the equation, DC, is the annual purchase cost for items. It is comprised of annual demand (D) times the unit cost of each item (C). The second term (D/Q) S is the annual ordering cost. It is computed as the number of orders placed per year (D/Q), times the cost of each order, S. Finally, the third term is annual holding cost where (Q/2) is the average inventory held. Remember that our maximum inventory is Q units when the order is received. When inventory is depleted we have zero. Therefore on average we have Q/2 units in inventory. H is the annual holding cost per unit of inventory.

The behavior of the two costs is shown in Figure 1-7. Notice that inventory holding cost increases with the order quantity, Q. The reason is that higher order quantities mean holding more inventory. However, this also means that we are ordering less frequently so ordering cost decreases. The opposite is true as the order quantity Q is decreased. A smaller order quantity results in a lower holding cost, but a higher ordering cost, as we are ordering more frequently.

Figure 1-7

Figure 1-7 Ordering versus holding cost

The objective is to pick an order quantity that minimizes the sum of both the holding and ordering costs, which is the minimum point on the total cost curve. To compute this we use calculus and end up with the following classic computation of the “best” or optimal order quantity, the EOQ:

21equ01.jpg

When to Order?

The EOQ answers the question of how much to order, but we still need to determine when to order. Assume that the demand rate (D) and lead time (L) are constant and known with certainty. In that case the ROP would simply be enough inventory to ensure that demand is covered during the length of the lead time. In this simple case, the ROP would be computed as

  • ROP = demand during lead time
  • ROP = D L

Let’s assume that lead time L for a product is one week and the demand, d, is 250 units per week. The ROP would be

  • Reorder Point = ROP = D x L = 1 week x 250 = 250 units

This means that every time inventory reaches 250 units an order is placed for the economic order quantity Q.

Unfortunately, D and L are rarely fixed, and demand is often higher than expected. As a result we often have to carry a bit more inventory to address this uncertainty. This is called safety stock or buffer stock and is inventory we carry in addition to the demand during lead time. Safety stock is added to the ROP calculation and is computed as follows:

  • ROP = demand during lead time + safety stock
  • ROP = D L + SS

Safety stock is computed based on the service level a company wants to maintain, which is simply the chance that we will not run out of stock. This is set by the company based on the level of service it wants to provide for a particular product and customer base. Higher service levels mean higher levels of inventory. Another factor that is used to compute safety stock is the variability of demand. The higher the variability and the higher the service level the higher the safety stock, or the amount added to the final computation of the ROP.

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Overview


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information


To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information


Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children


This site is not directed to children under the age of 13.

Marketing


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information


If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information


Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020