F. W Harris - EOQ MODEL & Life History is included in slides. His major contributions towards the field of management and engineering is also listed here. His life achievements and memberships are also included.

1. Abstract - Inventory is a stock of items kept by an organization to meet internal and external customer demand. Inventory is the subject of interest of inventory management. The main objective of inventory management has been to keep enough inventory to meet customer demand and also be cost-effective. The paper reviews the oldest inventory model introduced by F. W. Harris. Harris´s formula, computing EOQ and discussed here, is usually a part of decision support systems or advanced planning modules of an enterprise resource planning. Inventory plays a key role in the logistics behavior of manufacturing systems, but inventory modeling is a very poor field of enterprise practices.
Index Terms - Economic Order Quantity; Setup Cost; Lot Size; Economic lot sizes for inventory control; Sensitivity Analysis; Continuous Inventory System.
I. INTRODUCTION
A. F. W. Harris
Ford Whitman Harris was a well known man. Ford Whitman Harris was born in Deering, Maine on August 8, 1877, the son of Fred Ford and Harriet Whitney (Fox) Harris. His father was an accountant. Harris is an engineer, management scientist and a patent attorney holder. Out of these, his major contribution as a management scientist is admirable.
Fig. 1 F.W. Harris(1877-1962)
Ford Whitman Harris (FWH) thoroughly enjoyed life in Los Angeles and the American West. He was an enthusiastic and lifelong golfer, although only an average player. He also loved trout fishing and took many pack trips into what was then a very inaccessible British Columbia. FWH was a photography nut who developed his pictures in his own darkroom. Purely social activities bored him, so Eugenia, his gregarious wife, went out and about in the daytime and they stayed home nights.
Fig. 2 FWH and his wife Eugenia, enjoying the California outdoors
As the family pictures show, the Harris dressed in what today would be considered a rather formal style even on their outdoor excursions. Fig. 2 shows them on one of these outings, enjoying sitting by a stream near a large grove of trees.
Fig. 3 FWH and his wife Eugenia and FWH Jr. in the car
FORD WHITMAN HARRIS - EOQ MODEL
Shah Rukh Zafar Suri, Hafiz Kashif Bashir, Muhammad Imtiaz, Inzamam Ashraf, Malik Asad and Sajid Mehmood Department of Electrical Engineering The University of Lahore Lahore, Pakistan shahrukhzafarsuri@gmail.com

2. In the Fig. 3, they are about to leave on an excursion, with their son, FWH, Jr., in the car. This picture was taken in about 1915, around the time the EOQ model appeared.
Fig. 4 FWH with his daughter, Jean
Their daughter Jean was born in 1916 and is shown in the Fig. 4. Both children graduated from Stanford University, and after graduating from law school FWH, Jr., joined his father’s law firm. Ford Whitman Harris died in Los Angeles on October 27, 1962 at the age of 85; his widow Eugenia died there on April 30, 1979 at the age of 97.
II. BRIEF HISTORY
Certainly there is nothing in Harris’s early life that would lead one to expect that he might produce such an original and fundamental result. He was born in 1877 and grew up in the Portland, Maine area, where he received a high school education. After high school he worked for four years as an engineering apprentice and draftsman for two Portland employers, the Belknap Motor Company and the Maine Electric Company. Tutoring and self-study had educated him in Electrical Engineering, and he had patented a number of inventions in the Electrical field. However, these patents had all been assigned to Westinghouse as his employer. Patents continued to be granted in his name and assigned to Westinghouse as late as 1916. In 1900 he moved to Pittsburgh, Pennsylvania where he became a draftsman and engineer for Heyl and Patterson. During the period from 1904 to 1912 Harris was employed as an engineer for the Westinghouse Electric and Manufacturing Company in East Pittsburgh.
At the age of 35, Harris was faced with the need to retool his career. His daughter believed that he had an agreement with Westinghouse that barred competitive employment, and this blocked him from further inventions of an electrical nature. He had little in the way of formal educational credentials. But he did have an engineering background and experience in a major industrial corporation. It appears, then, that he began writing and publishing work on industrial management topics in 1913 to help establish his credentials in this broader field.
In 1912, Harris left Westinghouse and moved to Los Angeles, California. Family sources suggest several reasons for this move. He may have wanted to expand his horizons beyond the confines of Westinghouse. . In 1912 he became a consulting engineer in Los Angeles, and there he entered the field of patent law. He was admitted to practice before the U.S. Patent Office in 1914 and became a member of the California Bar in 1916. His admission to practice before the U.S. Supreme Court was in 1922. In Los Angeles, Harris was initially associated with the firm of Townsend, Graham and Harris and later with the firm of Graham and Harris before opening his own office in 1923. In addition to his legal practice, he had various business interests, including positions as President of Big Rock Ranch Co. and Vice President of Wulff Process Co. and Patco, Inc. He died in Los Angeles on October 27, 1962 at the age of 85. The law firm that Harris founded still continues, and is now under the name of Harris, Kern, Wallen and Tinsley. Ford W. Harris was a fellow and life member of the American Institute of Electrical Engineers, and a member of the American Society of Mechanical Engineers and the American Chemical Society. He was one of the founders and, in 1934, the first president of the Los Angeles Patent Law Association. Up to the time of his death he was a member of the American Bar Association and the American Patent Law Association. Harris also was a member of the California Club and, for many years, of the Wilshire Country Club.
III. CONTRIBUTIONS
A. Major Contributions
He had patented a number of inventions in the Electrical field. However, these patents had all been assigned to Westinghouse as his employer. Patents continued to be granted in his name and assigned to Westinghouse as late as 1916.
1) Harris's activities as an inventor spanned more than 50 years. His first (joint) patent, issued in 1904 and assigned to Heyl and Patterson, was for a speed controller.

3. 2) His last, issued in 1958 when he was 80 years old, was for components of a regenerative heat exchanger.
3) Most of his early patents, up through 1916, were for electrical devices—circuit breakers and switches, fuses, and controllers for electric motors—and were assigned to Westinghouse. Many of the later ones were associated with petroleum extraction—devices for pumping oil, dehydrators and separators for oil emulsions, and apparatus for reaming wells. But scattered among these were other items such as a disc harrow, two automatic water heaters, and a "side-loading hearse with a fixed turntable."
4) As an electrical engineer, Harris contributed frequently to the discussions of technical papers in the Transactions of AIEE during the period 1910-1915. He also served on AIEE's Protective Apparatus Committee in 1915 and 1916.
5) The first paper was the one on the EOQ formula (Harris, 1913), which appeared in Factory, The Magazine of Management in its February 1913 issue. Factory, which was published by the A. W. Shaw Company of Chicago, had an intended audience of “the manager in manufacturing,” with 10,000 readers in 1913. What better media outlet could there have been for Harris’s writings in this area? A dozen more of his articles were published in Factory over the next five years.
Given his skills and experiences as an inventor, the exposure to the world of patent law evidently suggested an attractive opportunity.
6) In the field of patent law. Ford Harris authored or coauthored two books and more than a score of articles, comments, and reviews. His writings in this area began in 1914 with a series on practical patent issues that was published in Machinery, and continued through 1954, when he was 76 years old. An earlypiece, pubUshed in 1921, is perhaps the most interesting to management scientists, because it is an elementary operations research analysis of the U.S. Patent Office. In it, he identified the Patent Office as a degenerate queue, with an arrival rate of 90,000 and
a processing rate of 71,000 applications per year. After discussing the near-term consequences of this for the average waiting time per application.
B. Contributions towards Management
Ford Harris's writings on management topics must have begun soon after he left Westinghouse, for they were published in rapid succession beginning in 1913.
1) His first full paper, "How Many Parts to Make at Once," in which he develops the EOQ model, appeared in Factory, The Magazine of Management
in February 1913 and undoubtedly was written in 1912..Harris´s Economic Order Quantity (EOQ) model has been widely studied and is staple of virtually every management science or inventory management textbook.
2) The A. W. Shaw Company’s flagship publication was System, The Magazine of Business, which was renamed Business Week after it was acquired by McGraw-Hill in 1928. Harris contributed an article on the “make or buy” problem to System in 1914.
3) Another paper, "How Much Stock to Keep on Hand," published in the following month, takes more of a systems view of the inventory function, and shows considerable understanding of the need for coordination between marketing, engineering, and production.
4) In addition to systems topics, Harris wrote quite broadly about problems of organization and personnel in a style that is engagingly anecdotal. Many of these papers also appeared in Factory, an A. W. Shaw Company publication with an intended audience of "the manager in manufacturing" and 10,000 readers in 1913.
5) In 1915 Shaw published The Library of Factory Management in six volumes, which presented a remarkable view of the field of factory management at the time of the First World War. An edited version of Harris's EOQ paper was included as a chapter under the title "What Quantity to Make at Once." For many years this chapter was believed to have been the original presentation of the EOQ model. The Library was drawn mainly from the two Shaw periodicals Factory and System, and three chapters were based on articles by Harris.
Although distributed widely. Ford Harris's original 1913 paper on the EOQ model was forgotten until its rediscovery in 1988. His chapter on the EOQ model in The Library of Factory Management was erroneously cited and apparently unread for many years. At various times, others have been credited with the development of the EOQ formula. It does not appear that Harris sought, received, or expected any recognition for this contribution during his lifetime. Even his own family was unaware that he had made such a contribution.
IV. EOQ - MODEL (Economic lot sizes for inventory control)
The EOQ model was Harris´s systematic approach to striking a balance between ordering cost and inventory carrying cost.
A. Inventory
Inventory generally refers to the materials in stock. It is also called the idle resource of an enterprise. Inventories represent those items which are either stocked for sale or they

4. are in the process of manufacturing or they are in the form of materials, which are yet to be utilized. It is, therefore, necessary to hold inventories of various kinds to act as a buffer between supply and demand for efficient operation of the system. Thus, an effective control on inventory is a must for smooth and efficient running of the production cycle with least interruptions.
Keeping adequate inventory is beneficial in several ways.
1) To stabilize production: The demand for an item fluctuates because of the number of factors, e.g., seasonality, production schedule etc. The inventories (raw materials and components) should be made available to the production as per the demand failing which results in stock out and the production stoppage takes place for want of materials. Hence, the inventory is kept to take care of this fluctuation so that the production is smooth.
2) To take advantage of price discounts: Usually the manufacturers offer discount for bulk buying and to gain this price advantage the materials are bought in bulk even though it is not required immediately. Thus, inventory is maintained to gain economy in purchasing.
3) To meet the demand during the replenishment period: The lead time for procurement of materials depends upon many factors like location of the source, demand supply condition, etc. So inventory is maintained to meet the demand during the procurement (replenishment) period.
4) To prevent loss of orders (sales): In this competitive scenario, one has to meet the delivery schedules at 100 per cent service level, means they cannot afford to miss the delivery schedule which may result in loss of sales. To avoid the organizations have to maintain inventory.
5) To keep pace with changing market conditions: The organizations have to anticipate the changing market sentiments and they have to stock materials in anticipation of non-availability of materials or sudden increase in prices.
6) Sometimes the organizations have to stock materials due to other reasons like suppliers minimum quantity condition, seasonal availability of materials or sudden increase in prices.
B. Inventory Control
Inventory control is a planned approach of determining what to order, when to order and how much to order and how much to stock so that costs associated with buying and storing are optimal without interrupting production and sales. Inventory control basically deals with two problems:
(i) When should an order be placed? (Order level)
(ii) How much should be ordered? (Order quantity)
Scientific inventory control aims at maintaining optimum level of stock of goods required by the company at minimum cost to the company.
Objectives of inventory control are:
1) To ensure adequate supply of products to customer and avoid shortages as far as possible.
2) To make sure that the financial investment in inventories is minimum (i.e., to see that the working capital is blocked to the minimum possible extent).
3) Efficient purchasing, storing, consumption and accounting for materials is an important objective.
4) To maintain timely record of inventories of all the items and to maintain the stock within the desired limits.
5) To ensure timely action for replenishment.
6) To provide a reserve stock for variations in lead times of delivery of materials.
7) To provide a scientific base for both short- term and long-term planning of materials.
It is an established fact that through the practice of scientific inventory control, following are the benefits of inventory control:
1) Improvement in customer’s relationship because of the timely delivery of goods and service.
2) Smooth and uninterrupted production and, hence, no stock out.
3) Efficient utilization of working capital. Helps in minimizing loss due to deterioration, obsolescence damage and pilferage.
4) Economy in purchasing.
5) Eliminates the possibility of duplicate ordering.
C. Economic Order Quantity (EOQ)
Inventory models deal with idle resources like men, machines, money and materials. These models are concerned with two decisions: how much to order (purchase or produce) and when to order so as to minimize the total cost. For the first decision—how much to order, there are two basic costs are considered namely, inventory carrying costs and the ordering or acquisition costs. As the quantity ordered is increased, the inventory carrying cost increases while the ordering cost decreases. The ‘order quantity’ means the quantity produced or procured during one production cycle. Economic order quantity is calculated by balancing the two costs. Economic Order Quantity (EOQ) is that size of order which minimizes total costs of carrying and cost of ordering. i.e., Minimum Total Cost occurs when Inventory Carrying Cost = Ordering Cost
Economic order quantity can be determined by two methods:
1) Tabulation method.
2) Algebraic method.

5. a) Tabulation Method
This method involves the following steps:
1) Select the number of possible lot sizes to purchase.
2) Determine average inventory carrying cost for the lot purchased.
3) Determine the total ordering cost for the orders placed.
4) Determine the total cost for each lot size chosen which is the summation of inventory carrying cost and ordering cost.
5) Select the ordering quantity, which minimizes the total cost.
The data calculated in a tabular column can plotted showing the nature of total cost, inventory cost and ordering cost curve against the quantity ordered as in Fig. 5.
Fig. 5 Inventory cost curve
b) Analytical Method
In order to derive an economic lot size formula following assumptions are made:
1) Demand is known and uniform.
2) Let D denotes the total number of units purchase/produced and Q denotes the lot size in each production run.
3) Shortages are not permitted, i.e., as soon as the level of the inventory reaches zero, the inventory is replenished.
4) Production or supply of commodity is instantaneous.
5) Lead-time is zero.
6) Set-up cost per production run or procurement cost is C3.
7) Inventory carrying cost is C1 = CI, where C is the unit cost and I is called inventory carrying cost expressed as a percentage of the value of the average inventory.
Fig. 6 EOQ Analytical Model
This fundamental situation can be shown on an inventory- time diagram in Fig. 6, with Q on the vertical axis and the time on the horizontal axis. The total time period (one year) is divided into n parts.
The most economic point in terms of total inventory cost exists where,
Inventory carrying cost=Annual ordering cost (set-up cost)
Average inventory=1/2 (maximum level + minimum level) = (Q + 0)/2 = Q/2
Total inventory carrying cost=Average inventory × Inventory carrying cost perunit
Total inventory carrying cost=Q/2 × C1 = QC1/2
Total annual ordering costs=Number of orders per year × Ordering cost per order
Total annual ordering costs=(D/Q) × C3 = (D/Q)C3
Now, summing up the total inventory cost and the total ordering cost, we get the total inventory cost C(Q)
Total cost of production run=Total inventory carrying cost + Total annual ordering costs
C(Q)=QC1/2 + (D/Q)C3 (cost equation)
But, the total cost is minimum when the inventory carrying costs becomes equal to the total annual ordering costs.
Therefore,
QC1/2=(D/Q)C3
or QC1 =(2D/Q)C3 or Q2 = 2C3D/C1

6. ACKNOWLEGEMENT
Shah Rukh Zafar and his group thank Dr. Tanzeela Siddiqui for her kind guidance during the entire course of this research paper. We also thank The University of Lahore for supporting us during this entire research work.