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T h e P u r p o s e o f T h i s C h a p t e r

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Order Essay

After reading this chapter, you should be able to:

• Calculate the correct order quantities and order times using the par stock, Levinson, and theoretical methods.

• Determine the optimal inventory level.

• Explain the benefits and problems of using only the theoretical method for determining inventory levels.

9C H A P T E RThe Optimal

Amount

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CHAPTER 9 The Optimal Amount156

INTRODUCTION

The correct order size and its counterpart, the correct order time, are prob-ably the most important keys to inventory management. Without a reasonableidea of the optimal order size and time, you cannot maintain an ideal inven-tory level of food, beverages, and nonfood supplies.

OPTIMAL INVENTORY LEVEL

Years ago, few hospitality operators concerned themselves with inventorymanagement concepts. When the industry was smaller, was less complex andcompetitive, and inventory costs were minor, the occasional overbuy or stock-out was a forgivable offense. Today, such a casual attitude is rare. Ordering is nolonger haphazard. The emphasis now is on holding the optimal inventory; thatis, management seeks to determine the amount of inventory that will adequate-ly serve the operation without having to suffer the costs of excess inventory.

A principal objective of inventory management is to maintain only the necessary amount offood, beverages, and nonfood supplies to serve guests without running out of anything, but notto have so much inventory that occasional spoilage and other storage costs result.1 We also need

to develop a cost-effective ordering procedure; for example, a buyer does notwant to spend an excessive amount of time, money, and effort to order mer-chandise because this will increase the hospitality operation’s cost of doingbusiness.

These objectives are more easily recited than achieved. Quite commonly,an individual manager may not know the exact value of inventory that shouldbe on hand.

Over the years, hospitality operators have tried to devise ways of computing as accurately aspossible the ideal amount of inventory that should be maintained to conduct business effective-ly and efficiently. Nonetheless, a major portion of the inventory management efforts that are car-ried out in our industry still rely heavily on rules of thumb. For instance, as mentioned inChapter 7, many practitioners rely on a percentage of sales to guide their inventory managementdecisions. Recall that this percentage-of-sales concept suggests, for instance, that a full-servicerestaurant operation requires an inventory of food, beverage, and nonfood supplies to be equalto about 1 percent of annual sales volume.

A buyer can use other rules of thumb to determine the amount of inventory needed toservice guests adequately. As mentioned in Chapter 7, the typical foodservice operationcould devise an inventory management strategy to ensure that the food inventory that iskept on hand at all times does not exceed about one-third of a normal month’s total foodcosts. Also, in a fast-food restaurant, the general feeling is that the food inventory shouldturn over about three times per week, or about 156 times per year. Consequently, the buyer’s

correct order size Theorder size that minimizesthe ordering costs, invento-ry storage costs, and stock-out costs.

correct order time Theorder time that minimizesthe ordering costs, invento-ry storage costs, and stock-out costs.

optimal inventory levelThe amount of inventorythat will adequately serve ahospitality operation’sneeds without having toincur the costs associatedwith excess inventory.

ordering proceduresStandardized process usedby the buyer to ensure thatthe correct amounts ofneeded products areordered at the appropriatetime.

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Correct Order Size and Order Time: A Common Approach 157

inventory management strategy should include an ordering procedure thatmaintains this approximate inventory turnover target.

Most industry practitioners view inventory as an investment. Like anyother investment, this one must offer a return. Unfortunately, an inventoryinvestment does not lend itself to a precise calculation of return, as does, say,a certificate of deposit, whereby an investor can depend on an exact percent-age of return each year.

CORRECT ORDER SIZE AND ORDER TIME:

A COMMON APPROACH

Most part-time and full-time buyers use a relatively simple approach to calcu-late the best order size and order time. This approach is sometimes referred toas the par stock approach. The buyer usually accepts the supplier’s deliveryschedule—for example, twice a week. The buyer then determines a par stock,that is, a level of inventory items that he or she feels must be on hand to main-tain a continuing supply of each item from one delivery date to the next.

The buyer accepts the supplier’s delivery schedule because he or she prob-ably cannot change it without incurring an exorbitant delivery charge. If, how-ever, the buyer’s company represents a very large order size, the supplier mightmake concessions. In addition, the buyer normally accepts the ordering sched-ule the supplier dictates; he or she places the order at a certain time prior tothe actual delivery. For example, a call no later than Monday morning may berequired to ensure a delivery on Tuesday morning.

Assume, for example, that the buyer feels that he or she needs six cases oftomato paste on hand to last between orders. On Monday morning, justbefore placing the order, the buyer counts the number of cases of tomato pasteon hand. Suppose that 11⁄2 cases are left. If it is expected that half a case will beused that day, one case will be left on Tuesday morning. The par stock is six. The buyer then sub-tracts what he or she feels will be on hand Tuesday morning from the par stock (6 minus 1) andorders five cases.

Another way to calculate the order size is for the buyer to subtract what is on hand—in thissituation, 11⁄2 cases—from the par stock of six cases and enter an order for 41⁄2 cases. Either way,the emphasis is on setting an acceptable par stock level and then ordering enough product tobring the stock up to that level. (This concept is a bedrock of our industry. For example, mostbars set up a certain par stock level that must be on hand before opening for the afternoon orevening. The bartender on duty is responsible for counting what is on hand, subtracting thisfrom what should be on hand, and then replenishing the overall inventory of beverages, food-stuffs, and nonfood supplies accordingly.)

Par stocks sometimes change. In a restaurant that does a lot of banquet business, the par stockfor tomato paste might fluctuate monthly or even weekly. This fluctuation can complicate mat-ters, but buyers usually can solve the problem just by adding to the par stock the extra amount

inventory turnover Equalto: (actual cost of productsused, or sold, divided bythe average inventory valuekept at the hospitalityoperation).

par stock approach toordering Method used todetermine the appropriateamount to order. Involvessetting par stocks for allitems and subtracting theamount of each item onhand to calculate the ordersizes.

delivery schedulePurveyor’s planned shippingtimes and dates.

par stock The maximumamount of a product youwant to have on hand.When reordering the product you want to buyjust enough to bring youup to par.

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CHAPTER 9 The Optimal Amount158

of tomato paste needed specifically for any emergency or extra business volume, such as a ban-quet next week. So, for instance, buyers might order enough to reach their par stock level, plusadditional product to be their “safety” stock or to use for the banquet.

The buyer, then, normally uses the following procedures when employing the par stockapproach:

1. Accept the suppliers’ stipulated ordering procedures and delivery schedules.2. Decide when it would be desirable to order enough product to bring the stock level of any

particular item up to par. This decision is normally influenced by the amount of storagefacilities the buyer has, how expensive the inventory item is, and the shelf life of the prod-ucts the buyer orders. For example, if a preferred supplier delivers meat twice a week, andif the meats are expensive, perishable items, a buyer would most likely set a par stock tolast about three or four days. For some inexpensive, nonperishable operating supplies,such as paper towels, the buyer might want to order once every three months.Consequently, he or she sets the par stock large enough to last for three months undernormal operating conditions.

3. Set par stocks for all food, beverages, and nonfood items—enough to last between regu-larly scheduled deliveries.

4. When ordering, subtract what is on hand from the par stock. Then include any addition-al amount necessary to cover extra banquets, increased room service, seasonal patronage,a safety stock perhaps, and so forth.

5. Shop around, if necessary, and enter this order size at the time the supplier designates orat some agreed-upon time.

6. Periodically reevaluate the stock levels, and adjust them as needed. For instance, if youchange suppliers and the new purveyor’s delivery schedule is different, you must adjustaccordingly.

No magic formula is associated with the par stock concept. It is a trial-and-error process. Ifsix cases are too many, the number can be adjusted downward. If it is too low, it can be increased.The trial-and-error procedure requires small amounts of management attention on a continuingbasis; in time, however, these can add up to a significant amount. Nevertheless, the work involvedis quite simple and lends itself to volume swings in overall sales, as well as in sales of individualproducts. The par stock concept works quite effectively in the hospitality industry.

The concept works so well for several reasons. Most important, there is only a slight differ-ence in annual storage and ordering costs between a theoretical order size and a more practicalorder size. (An extended discussion of a theoretical calculation of optimal order size and ordertime is included later in this chapter.) Another reason is the relative predictability of deliveries.The third reason is that most hospitality operations undergo major modifications in their cus-tomer offerings only occasionally. For the most part, menus, sleeping accommodations, and barofferings remain unchanged, thereby giving a buyer sufficient time to determine acceptable parstock levels for each inventory item. Finally, if a considerable sum has already been invested in ahospitality operation, an inventory level that is a few hundred dollars more than a theoreticaloptimal amount will tend to generate little concern.

The major drawback to the par stock method is its emphasis on setting only the par stocklevel, to the possible detriment of the broader view of inventory management. Generally, theoptimal amount of inventory on hand is related to annual storage costs, ordering costs, and

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Correct Order Size and Order Time: Another Approach 159

stockout costs. If acceptable par stocks are achieved, these costs will probably be minimized.However, these concepts may not be examined directly, and, as a result, a buyer may be unawareof the complete picture.

This innocence, or ignorance, can cause problems. For instance, buyers often have an oppor-tunity to purchase large amounts of a product at reasonable savings. The problem arises whenbuyers have little conception of the increase in storage costs that will accompany this huge order.(As with the par stock approach, though, some rule-of-thumb methods can be used to evaluatethe economics of large orders, as discussed in Chapter 10.)

Regardless of its potential drawbacks, the par stock approach is common and works fairlywell. It does not, however, represent the only approach to determining correct order size andorder time.

CORRECT ORDER SIZE AND ORDER TIME:

ANOTHER APPROACH

Another approach used in the hospitality industry is just a bit more complicat-ed than the par stock approach. We call this approach the Levinson approach,since Charles Levinson was one of the very first persons to address these ideas for-mally in his book, Food and Beverage Operation: Cost Control and SystemsManagement, 2nd ed. (Englewood Cliffs, NJ: Prentice-Hall, 1989). Much of thematerial in this section of our text is adapted from Levinson’s volume. This bookis now out of print. However, you might be able to find a used copy at Amazon(www.amazon.com) or on eBay (www.ebay.com).

Buyers using the Levinson approach will employ the following procedures:1. Accept the suppliers’ stipulated ordering procedures and delivery schedules.2. Determine the best time to place orders with the suppliers. For instance, fresh dairy prod-

ucts may be ordered daily, fresh meats and produce may be ordered perhaps every thirdday, and other less perishable items may be ordered less frequently. Consequently, the buy-ers’ work follows a reasonably predictable routine, in that they have enough work to keepbusy each week, even though they are not ordering exactly the same items each day oreach week.

3. Before ordering, forecast the amount of merchandise that will beneeded during the period of time between regularly scheduled deliv-eries. The forecasting procedure includes the following steps:a. Forecast the expected total number of customers, based usually on

past history. b. Forecast the expected number of customers who will order each

specific menu offering, also based on past history. One way to dothis is to compute a popularity index for each menu item. Todetermine a menu item’s popularity index, divide the number soldof that particular menu item by the total number of all menu itemssold; this will give you a percentage, which is the menu item’s popu-larity index.

Levinson approach toordering Method ofdetermining the appropri-ate order sizes. Takes intoaccount forecasted sales,portion sizes, and yieldpercentages when calculat-ing the amount of prod-ucts to order.

forecasting An attempt topredict the future. Currentand historical informationis used to estimate whatmight happen over thenear or long term. Referredto as sales forecasting whenattempting to predictfuture sales.

popularity index Anotherterm for menu mix per-centage.

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CHAPTER 9 The Optimal Amount160

For example, if you project that you will serve 2,500 customers next week and youknow that, based on past history, 25 percent of all customers eat T-bone steaks, then youcan estimate that 0.25 × 2500, or 625 customers, will eat a T-bone steak.

c. Determine the number of raw pounds of each ingredient needed to satis-fy your projected sales. To do this, first you must figure out the portionfactor (PF) and the portion divider (PD) for each ingredient that youneed to satisfy your sales forecast. The PF is computed as follows:

PF = 16 oz. / Amount of ingredient needed for one serving (in ounces)

The PD is computed as follows:

PD = PF × (The ingredient’s edible- (i.e., servable-) yield percentage)

The edible yield percentage is computed in one of two ways: (1) youaccept the supplier’s estimate of edible yield, or (2) you conduct your own yieldtests for each and every ingredient; that is, you use the ingredients for a whileand compute an average of unavoidable waste. This will give you a good ideaof the edible yield percentage you can expect to derive from each ingredient.

d. Compute the order sizes for all items. An order size is equal to the num-ber of customers you feel will consume an ingredient divided by the PDfor that ingredient—this will give you the order size in raw pounds.(Essentially, the PD is the expected number of servings per pound.)

4. Adjust this order size, if necessary, to account for stock on hand, extra banquets, increasedroom service, seasonal patronage, perhaps a safety stock, and so forth.

5. Shop around, if necessary, and enter the order size at the time the supplier designates orat some agreed-upon time.

6. Periodically revise the order time if necessary, as well as the PD of each ingredient if, forinstance, you decide to change suppliers and the new supplier’s ingredients have a differ-ent yield percentage than those you are currently purchasing. (In Chapter 10, we discussthe procedures used to determine whether another supplier’s ingredient provides morevalue to you, even though it might appear that it has more waste. We also revisit the con-cept of the EP cost.)

INGREDIENT SERVING SIZE (OZ.) EDIBLE YIELD (%)

Steak 12 80

Beans 4 90

Potatoes 4 75

portion factor (PF) Equalto (16 ounces divided bythe number of ouncesneeded for one serving).Alternately, equal to (1,000milliliters divided by thenumber of milliliters need-ed for one serving).Alternately, equal to (1,000grams divided by the num-ber of grams needed forone serving).

portion divider (PD)Equal to an item’s (portionfactor (PF) multiplied byits edible yield percentage).

edible yield percentageAnother term for yield percentage.

Example I

Given the following data, compute the number of raw (AP) pounds needed of each ingredient for a

banquet for 500 people.

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Correct Order Size and Order Time: Another Approach 161

Example II

Given the following data, compute the number of cases needed to serve 1,575 customers.

Ingredient: Iceberg lettuce

Serving size: 4 ounces

Edible yield: 75 percent

Minimum weight per case: 36 pounds

Solution:

PF = 16 / 4 = 4.00

PD = 4.00 × 0.75 = 3.00

Number of raw (AP) pounds needed = 1575 / 3.00 = 525 lb.

Number of cases needed = 525 lb. / 36 lb. per case = 14.58 (approximately 15 cases)

Example I (continued)

Solution:

Compute each ingredient’s PF:

PF(steak) = 16 / 12 = 1.33

PF(beans) = 16 / 4 = 4.00

PF(potatoes) = 16 / 4 = 4.00

Compute each ingredient’s PD:

PD(steak) = 1.33 × 0.80 = 1.06

PD(beans) = 4.00 × 0.90 = 3.60

PD(potatoes) = 4.00 × 0.75 = 3.00

Compute the order size, in raw (AP) pounds, for each ingredient:

Order size (steak) = 500 / 1.06 = 472 lb.

Order size (beans) = 500 / 3.60 = 139 lb.

Order size (potatoes) = 500 / 3.00 = 167 lb.

Example III

Given the following data, compute the number of gallons needed to serve 2,000 customers.

Ingredient: Prepared mustard

Serving size: 1⁄2 ounce

Edible yield: 95 percent

Solution:

PF = 16 / 0.5 = 32.00

PD = 32.00 × 0.95 = 30.40

Number of raw (AP) pounds needed = 2000 / 30.40 = 65.79 lb.

Number of raw (AP) ounces needed = 65.79 × 16 oz. per lb. = 1052.64

Number of gallons needed = 1052.64 oz. / 128 oz. per gal. = 8.22 (approximately 9 gallons)

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CHAPTER 9 The Optimal Amount162

CORRECT ORDER SIZE AND ORDER TIME:

VARIATIONS OF THE LEVINSON APPROACH

The procedures in the preceding Examples I, II, and III are appropriate for items purchased inpound units. However, the Levinson approach can be adapted for use with any purchase unit.The general formula for the PF needs to be altered to accommodate the specific purchase unit.The unit of purchase is divided by the portion size as depicted in that unit of purchase. Forinstance, if you purchase liter containers of liquor, the numerator for your PF calculation wouldbe 1,000 milliliters, and the denominator would be the portion size of liquor, in milliliters. Thecomputation of the PD remains the same.

Example I

Given the following data, compute the number of liters (l) needed to serve 250 customers.

Ingredient: Gin

Serving size: 55 milliliters

Servable yield: 95 percent

Solution:

PF = 1000 / 55 = 18.18

PD = 18.18 × 0.95 = 17.27

Number of liters needed = 250 / 17.27 = 14.48 (approximately 15 liters)

Example II

Given the following data, compute the number of cases needed to serve 500 customers.

Ingredient: Lobster tail

Serving size: 2 tails

Servable yield: 100 percent

Number of tails per case: 50

Solution:

PF = 50 / 2 = 25

PD = 25 × 1.00 = 25

Number of cases needed = 500 / 25 = 20 cases

Example III

Given the following data, compute the number of kilograms (kg) needed to serve 125 customers.

Ingredient: Fresh spinach

Serving size: 90 grams

Edible yield: 60 percent

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Correct Order Size and Order Time: Combination Approach 163

CORRECT ORDER SIZE AND ORDER TIME:

COMBINATION APPROACH

It is reasonable to expect the typical buyer to use a combination of the procedures just discussedto determine the proper order sizes and order times. For instance, a buyer could use the par stockapproach to maintain sufficient stock for the normal, predictable business needs of the hospital-ity operation. However, when a buyer needs stock for special events, such as banquets and othersimilar functions, he or she could adopt the Levinson approach, or some variation thereof, whendetermining the correct order amount and order time.

Example III (continued)

Solution:

PF = 1000 / 90 = 11.11

PD = 11.11 × 0.60 = 6.67

Number of kilograms needed = 125 / 6.67 = 18.74 (approximately 19 kilograms)

PURCHASING FROM THE CHEF’S PERSPECTIVEJean Hertzman, Ph.D., CCE, Assistant Professor, Department of Food and Beverage Management,

William F. Harrah College of Hotel Administration, University of Nevada Las Vegas

Do all these PF and PD calculations seem a little confusing? Don’t feelalone. They would be a mystery to the average chef. Although executive

chefs spend more and more of their time performing cost control and

human resources functions, most chefs would rather cook and develop new

menu items than spend a lot of time crunching numbers. Therefore, they

want to use as simple a formula as possible to determine the quantity of

food to purchase.

Chefs rely on the formula of AP (As Purchased) = EP (Edible Portion) ÷

Edible Yield Percentage to determine the amount of product to order. They

basically skip one step of the Levinson approach. But before we use the for-

mula, let’s make sure that you know exactly what the Edible Yield Percentage

means.

Let’s use the example of asparagus. If you buy whole asparagus, but use only the tips for service, you

trim off a lot of stems in the process. The amount cut off would be the trim loss, and the amount left would

be the edible portion. If you started with one pound (16 ounces) of asparagus and had 10 ounces of

asparagus tips after cutting, your yield percentage would be 10 ounces divided by 16 ounces per pound

or approximately 63 percent. If you were determining the yield percentage of other products, for example

roasted meat, you might also have to take into account trimming off the fat, shrinkage during cooking, hav-

ing unusable portions after cutting, and other factors.

Chef Jean Hertzman

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CHAPTER 9 The Optimal Amount164

PURCHASING FROM THE CHEF’S PERSPECTIVE (continued)

As discussed in this book, the most accurate method for determining the yield percentage is to

conduct your own yield test. In that way, you know exactly what you have left using your particular

foodservice operation’s specific procedures. However, calculating yield percentages for all the differ-

ent foods you use can be time and labor intensive. A quicker method is to use supplier estimates of

edible yield percentages. However, suppliers may overstate the percentage so that their product

looks like a better buy or understate the percentage so that you buy more of their product. You might

want to consider a third alternative. There are two excellent sources that give yield percentages for

just about every product you can imagine: The Book of Yields: Accuracy in Food Costing and

Purchasing by Francis Lynch (also available on CD-ROM) and Chef’s Book of Formulas, Yields, and

Sizes by Arno Schmidt. These chefs have spent years calculating portion sizes and percentages just

to make your life a little easier.

Now let’s use the yield percentage in the AP formula. Suppose a banquet chef wants to serve 4

ounces of asparagus tips as a side vegetable to 800 people. Therefore, she needs 4 ounces × 800 or

3,200 ounces (200 lbs) EP of asparagus. But she knows that the yield percentage of asparagus is only

63 percent. Therefore, she really needs 3,200 ounces divided by .63 or 5,080 ounces as purchased.

Translate that to pounds and she would order 318 pounds of asparagus. If she only ordered 200 pounds,

she would have to skimp on the portion sizes or lots of guests would not be getting their vegetable that

evening.

Here is another example. A chef serves a great hot roast beef sandwich using top round of beef roast-

ed fresh daily. A 15-pound top round yields 12 pounds of meat after cooking, removing the external fat,

and slicing. Each sandwich uses 6 ounces of cooked beef and the restaurant sells them to 200 hungry

guests daily. How many top rounds does the chef need to buy for each day?

12 lbs EP ÷ 15 lbs. AP = .80 or 80% edible yield percentage

6 ounces × 200 sandwiches = 1,200 ounces EP

1,200 ounces ÷ .80 = 1,500 ounces or 94 lbs AP

If the top rounds weigh 15 pounds each, then the chef has to decide whether to order 6 and run out

of product or whether to order 7 and have some left for sandwiches or soup the next day. Most would play

it safe and order 7 top rounds of beef.

Chefs use this method because the most important thing for them to know is how much food to pur-

chase, regardless of whether they are calling the order in to a supplier themselves or submitting a requisi-

tion to a central purchasing agent. It also gives the chef the ability to accurately calculate the cost of

preparing a recipe and the individual cost per portion. Once you have the current AP amount for each

ingredient you can multiply that amount by that ingredient’s purchase price to determine the total ingredi-

ent cost. Add up the cost of all the ingredients in the recipe and divide it by the number of portions the

recipe makes, and voila! you have the cost per portion. In addition, knowing how to calculate the EP costs

of the food items can help the chef decide whether to buy the raw product or whether to buy a conven-

ience product with some of the trimming and/or cooking already done. This is an example of the “make-

or-buy” analysis discussed in Chapters 5 and 10.

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Correct Order Size: A Theoretical Approach 165

CORRECT ORDER SIZE: A THEORETICAL

APPROACH

In centralized, multiunit purchasing operations, economies of scale make very large purchases real-istic. When inventory value reaches the multimillion-dollar level, more formalized modes of analy-sis are useful in determining order size. This section suggests tools available for use in such cases.

The correct order size is influenced by two costs: the storage cost, whichis sometimes referred to as the carrying cost, and the ordering cost. The stor-age cost is the sum of several little costs associated with holding inventory. Thecost of maintaining storage facilities, inventory insurance, and risk of spoilageor obsolescence are three aspects of the storage cost. However, the most impor-tant part of the storage cost—the largest aspect of the storage cost—is themoney tied up in inventory, that is, the capital cost. Economists refer to thisas an opportunity cost, which is a nice way of saying that if your money istied up in canned goods on a shelf, you lose the opportunity to invest thismoney elsewhere, such as in a bank, in shares of stock, or in gold. You also maylose the opportunity to expand or make improvements to your facility.

Attempts have been made to calculate the storage cost precisely.Unfortunately, no hard figures exist. Annual estimates run from 10 to 25 per-cent of the value of inventory. This means that for every dollar you tie up onthe shelf, you can expect a storage cost of somewhere between 10 and 25 centsper year.

The ordering cost includes primarily the cost of paperwork, telephone,computer, fax, employee wages and salaries, receiving, and invoice processing.

Differences of opinion exist concerning the dollar value of the orderingcost. One company estimates that it costs approximately $20 for each order itmakes, another estimates the cost at $30 per order, and others set the cost aslow as $3 to as high as somewhere between $100 and $130.2 No matter. Whatis important is that you recognize that placing orders is not a cost-free exerciseand that the potential savings of reducing the number of orders can andshould be determined.

A large order size would ensure a large inventory amount and, hence, ahuge annual storage cost. Because you would not order a large amount asoften as a small amount, however, the annual ordering cost would decrease.On the other hand, a small order size would result in a smaller inventory anda correspondingly smaller annual storage cost; however, unfortunately, your annual orderingcost would increase (see Figure 9.1).

The important point is that there is an optimal order size, one that leads to the lowest possi-ble total cost per year (annual storage and ordering costs). Note that a small order size (any one tothe left of the crosshatched area in Figure 9.1) carries a relatively high total cost per year, as doesany order size to the right of the crosshatched area. The optimal range of order sizes is represent-ed by the crosshatched area. Theoretically, there is one optimal order size in that crosshatched areaat the point where the storage cost curve intersects the ordering cost curve.

storage cost Another termfor carrying cost.

carrying cost Expenses,such as insurance, security,and spoilage, associatedwith holding inventory instorage.

ordering cost Theamount of money spent tomake an order, receive it,and store it. Includesthings such as labor neededto perform the work andadministrative costs such asfaxing, photocopying, andcell phone charges.

capital cost The rate ofreturn (e.g., interestincome) that capital couldbe expected to earn in analternative investment ofequivalent risk.

opportunity cost Bychoosing to do something,you give up the option ofdoing something else. Forinstance, if you pay a billtoo early you lose theoption of investing themoney and earning someinterest income. The lossof income in this case isconsidered to be theopportunity cost.

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CHAPTER 9 The Optimal Amount166

When determining the optimal order size, management must take intoaccount the influence of these two costs. Basically, the intersection of the stor-age cost curve and the ordering cost curve represents the best balance betweenthe cost of carrying inventory and the benefits derived from having the inven-tory available for sale to the customer. When calculating this intersection,management has two options. First, a manager could attempt to graph theoperation’s cost curves and then try to “eyeball” the optimal order size. Second,he or she might use a formula to determine the optimal order sizes.

The most common option is summarized in the economic order quantity(EOQ) formula, which several industries have adopted. Relatively few hospi-tality operations use this formula directly. They do find it useful as a reference,however, insofar as the formula tends to identify the relevant costs and putsthem in their proper perspective. Hence, a look at this formula will immedi-ately drive home the concept of optimal order sizes.

You can calculate the EOQ two basic ways, as noted in Figure 9.2. Assumethat an operation currently uses 600 cases of tomato paste per year, the ordering cost per order

EOQ (in dollars) =

2 � Ordering cost (in dollars)per order

� Amount of itemused in one year

(in dollars)

Storage costs, per year, as a percentageof average dollar value of inventory

2 � Ordering cost (in dollars)per order

� Amount of itemused in one year

(in units)

Storage costs, per year, for oneunit of this particular Item (in dollars)

EOQ (in number of units) =

To calculate the EOQ, number of units:

To calculate the EOQ, dollar value:

FIGURE 9.2 Ways of calculating the EOQ.

Order size

Annual orderingcost

Annual storagecost

Total annual storageand ordering

costs

Tota

l annual c

ost

FIGURE 9.1 Annual storage and ordering costs related to order size.

economic order quantity(EOQ) formulas I. TheEOQ in dollars is equal to:the square root of [(2 timesthe ordering cost in dollarstimes the amount of theitem used in one year indollars) divided by theannual storage costexpressed as a percentage ofaverage inventory value].II. The EOQ in units isequal to: the square root of[(2 times the ordering costin dollars times the amountof the item used in oneyear in units) divided bythe annual storage cost perunit in dollars].

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Correct Order Size: A Theoretical Approach 167

is $3, the annual storage cost is 15 percent of the value of the tomato paste, and the cost of thetomato paste is $8 per case. The question is: How many cases should the buyer purchase at onetime? In other words, what is the EOQ?

Applying the formulas noted in Figure 9.2, you determine that the EOQ is about 55 cases,or approximately $440. The calculations follow:

*$4800.00 = 600 × $8.00†440.00 / $8.00 per case = 55 case‡$1.20 = $8.00 × 15% = $8.00 × .15

2 × $3.00 × $4800.00*EOQ (in dollars)

.15≈

$440.00†≈

2 × $3.00 × 600 unitsEOQ (in units)

$1.20‡≈

55 units (or cases)≈

Total cost per year =

Ordering costper order

Order size

Number ofunits usedin one year

(in units)

� �+

Storage cost,per year, of

one unit

Order size(in units)

2

FIGURE 9.3 The calculation of the annual total cost associated with a particularorder size. (This formula is used in calculating the EOQ formula.)

The total cost per year (annual storage and ordering costs) associated with this EOQ of 55cases is calculated by using the formula depicted in Figure 9.3.

Total cost per year = ($3.00 ×× 600 cases) +

($1.20 ×× 55 cases)55 cases 2

= $32.73 + 33.00

= $65.73

If you order fewer than 55 cases, say, 50 cases, the total cost per year is:

Total cost per year = ($3.00 ×× 600 cases) +

($1.20 ×× 50 cases)50 cases 2

= $36.00 + $30.00

= $66.00

If you order more than 55 cases, perhaps 60 cases, the total cost per year is:

Total cost per year = ($3.00 ×× 600 cases) +

($1.20 ×× 60 cases)60 cases 2

= $30.00 + $36.00

= $66.00

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CHAPTER 9 The Optimal Amount168

You have calculated the order size, 55 cases, that yields the least total cost per year. Anorder size of 50 cases results in a lower annual storage cost, but your annual ordering costincreases since you have to order more often during the year. Conversely, a larger order sizeyields a smaller annual ordering cost, but the increase in annual storage cost negates this slightsavings.

As a practical matter, it may be inconvenient or impossible to order 55 cases at a time. Inaddition, some people are disturbed because so many aspects of the formulas are merely esti-mates, not hard-and-fast figures. The question is, then, of what value is this figure of 55 cases? Isit worthwhile to calculate the EOQ if it cannot be used?

Although it may be impractical to order 55 cases at a time, knowing what the optimal ordersize is can help you make decisions about other more practical order sizes. For instance, if youcan order only in blocks of 50 cases, you will have an idea of the annual ordering and storagecosts associated with this order size and be able to plan your expenses accordingly.

We do not wish to leave the impression that this theoretical approach is simple or easy to use.It presents several potential problems, which we point out later. These difficulties notwithstand-ing, however, the concept of EOQ can be used in many productive ways to ensure an optimaloverall level of inventory, which is the result of the optimal order size and the topic we turn tonext, the optimal order time.

CORRECT ORDER TIME: A THEORETICAL

APPROACH

Continuing with the tomato paste example, you should determine when to order your 55 cases,assuming 55 is a practical order size. If you could depend on instant delivery of inventory items,

you might be able to wait until you are completely out of tomato paste beforeyou order the next batch of 55 cases. Unfortunately, a lag invariably existsbetween the time you place an order and when it arrives. In some instances,this time lag is predictable; in others, it is not. As a result, you will want toorder at some level greater than zero if you want to ensure a continuing, unin-terrupted supply.

This level is sometimes referred to as the safety stock. It is also called thereorder point (ROP). You cannot wait until you are out of stock before order-ing another batch; you must maintain a safety stock. But what this safety stockshould be is open to hunches, theories, and educated guesses.

The trick to calculating the ROP is first to gain some idea of the usagepattern of the particular product in question. In the tomato paste example,you might experience the usage pattern outlined in Figure 9.4.

Normally, this type of pattern is not as predictable as Figure 9.4 implies.If you keep track of your usage patterns for six months or so, however, youcan determine how many cases you use, on average, every day. For discus-sion purposes, assume that you have determined that 40 percent of thetime, you use one case of tomato paste or less per day; that 90 percent of

safety stock Extra stockkept on hand to avoid run-ning out and disappointingguests.

reorder point (ROP) Thelowest amount of stock onhand that you feel comfort-able with, the point thatyou will not go belowbefore ordering more stock.

product’s usage patternWhen referring to foodand beverages, it is the rateat which the products areproduced and served tocustomers. When referringto nonfood and nonbever-age supplies, it is the rateat which the products havebeen exhausted and are nolonger available.

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Correct Order Time: A Theoretical Approach 169

the time, you use two cases or less; that 96 percentof the time, you use three cases or less; and that100 percent of the time, you use four cases or less(see Figure 9.5).

Another way of looking at Figure 9.5 is to con-sider the possibility of using, on any given day,between one and two cases of tomato paste. Notethat, in the past, you have used between one andtwo cases of tomato paste per day 50 percent ofthe time; hence, there is a 50 percent probabilityof selling more than one case but less than twocases per day. Similarly, you have sold less thanone case per day 40 percent of the time, betweentwo and three cases of tomato paste per day 6 per-cent of the time, and between three andfour cases of tomato paste per day 4 percentof the time.

A conservative safety stock in this situ-ation would be four cases for every day thatlapses between the time you place yourorder of 55 cases and the time you receivethis order. The interval of days is some-times referred to as the lead time. If youcan safely assume that your lead time isthree days and you do not want to take achance of running out of tomato paste, youwould then place your order of 55 caseswhen your supply of tomato paste reaches12 cases (see Figure 9.6).

If you use all 12 cases during the three-day lead time, you will be out ofstock when your order of 55 cases arrives. If you use only 10 cases, you willhave 2 cases in inventory when the 55 cases are delivered. Your total invento-ry amount at this point would then be 57 cases.

After your order is delivered, you want to be as close as possible to a totalinventory amount of 55 cases. Ideally, you will be at 55 cases exactly, that is, themoment you run out of inventory, the delivery van will be pulling up at theunloading area with the 55-case order.

Hospitality operations that strive for this ideal arrangement practice whatis generally referred to in the industry as just-in-time (JIT) inventory man-agement. While these firms are trying to keep the total ordering and storagecosts as low as possible, they are especially interested in minimizing the stor-age cost. For instance, if, using the figures in the preceding example, they havetwo cases of inventory in stock when the delivery van arrives, they will then

10

20

30

40

50

60

70

1 2 3 4

Time (in weeks)

5 6 7

Inve

nto

ry le

vel (

in c

ase

s)

FIGURE 9.4 A hypothetical usage patternfor tomato paste.

1 2

50%

40%

6%

4%

Number of cases used per day

3 4

Fre

quency

of occ

urr

ence

FIGURE 9.5 The percentage of times one, two,three, or four cases are used per day.

lead time Period of timebetween when you placean order with a vendor andwhen you receive it.

just-in-time (JIT) inven-tory management Systemthat attempts to ensurethat the moment theinventory level of a partic-ular product reaches zero, ashipment of that itemarrives at your back door.The main objective is toreduce carrying charges totheir lowest possible level.

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CHAPTER 9 The Optimal Amount170

have a current inventory level of 57 cases when the van pulls up. If they have57 cases, they will incur an additional storage cost—which they are very eagerto avoid. However, this additional storage cost must be weighed against thepossibility of running out of tomato paste and incurring various stockoutcosts.

Stockout costs are expenses associated with being unable to serve a prod-uct because you do not have it. These costs are particularly irksome in thehospitality business: you cannot tell customers to come back for a steaktomorrow because you do not have any for them today. If you cannot pro-vide a product, a customer usually selects another, the result being no appar-ent loss in profit. But a customer might be irritated when you cannot sup-

ply the product wanted. In essence, you have diminished the customer’s favorable opinion ofyour operation. The cost of goodwill is difficult to determine, and some operators harbor agreater disdain for stockouts than do others. For example, in the tomato paste example, a moreliberal manager might decide that he or she needs only two cases per day for the three-day peri-od, thereby taking a slight chance on not needing more than two cases of tomato paste per day.A liberal manager would be willing to risk a stockout since, according to Figure 9.5, there is a10 percent chance that more than two cases of tomato paste per day will be needed during thelead-time period.

Another problem associated with this safety stock concept is the exactness of the lead time.In most cases, deliveries are reasonably predictable, but the supplier may not have 55 cases oftomato paste. He or she may have only 30 or 40 cases, or perhaps none at all.

The theoretical approach to the optimal order time rests on the assumptions you make aboutusage patterns, lead times, safety stocks, supplier capabilities, and dependability. By keeping his-torical records, you can determine the ROP with which you feel most comfortable. If the numbersare correct, the ROP will be optimal. If they are not, at least you will be closer to the optimalROP than you ever could be by relying on mere hunches.

stockout cost The costincurred when you do nothave a product guestswant. While the cost can-not always be calculated, inthe long run there willusually be a negativeimpact on your bottomline. For example, theguest leaves without buy-ing anything. Or the gueststays and orders somethingelse, but never comes back.

12 cases(reorderpoint)

55 cases

Time (in days)

3 days

Safetystock

Order 55 casesat this point

Inve

nto

ry le

vel (

in c

ase

s)

FIGURE 9.6: The graphical determination of the reorderpoint (ROP).

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Correct Order Size and Order Time 171

Although the formality of the approach we have been discussing would not be appropriatefor a single operation of modest size, clearly, the logic of the approach has general application.This is a good way to think about ROPs, even if formulas and detailed records do not come intothe picture for each hospitality operator.

CORRECT ORDER SIZE AND ORDER TIME: OTHER

PROBLEMS WITH THEORETICAL APPROACHES

The basic overriding problem, which we alluded to earlier, is the need for certain assumptionsand estimates. Any way you look at it, we deal with highly variable phenomena here. Someadditional variables that tend to detract from the usefulness of these approaches are listedbelow:

• Usage rates vary from day to day and do not normally follow a steady pattern, unless theoperation caters to a fairly predictable group of repeat customers. Although usage patternscan be approximated, they probably can never be calculated exactly.

• Storage and ordering costs can vary; in addition, several opinions exist as to the precisemakeup of these costs.

• Stockout costs are extremely difficult to assess. Management philosophy is the best guidein this case; consequently, the concept of correct order time can change according to man-agement’s tolerance of risk of stockouts.

• Lead times are somewhat predictable, but you may qualify for only once-a-week delivery,which hurts any attempt to implement the EOQ and ROP concepts. In fact, the inabili-ty to control delivery times, either because of tradition or by law (e.g., some states havestrict ordering and delivering schedules for alcoholic beverages), has done more to dis-courage the use of these concepts in the hospitality industry than any of the other diffi-culties. With the theoretical approach, the order size stays the same, but the order timevaries. The opposite is true with the par stock and Levinson approaches. As a result, sincethe typical buyer has no control over order times and delivery schedules, he or she cannotimplement the theoretical approach.

• What items should you consider for EOQ and ROP? All of them? This decision is notvery easy when you realize that the average hospitality operation stocks a minimumof 600 to 800 items. Some people suggest considering only those few items thattogether represent about 80 percent of the value of the total inventory. Others feelthat it is possible to construct a few item categories and develop EOQs and ROPs forthem. In any case, monitoring all items is impossible without the help of sophisticat-ed computer technology. As these types of computer applications become increasing-ly feasible and economical, however, it is possible that you will be able to overcomethis difficulty.

• Keep in mind that your supplier normally buys from someone else. Your EOQ maynot be consistent with your supplier’s EOQ. As a result, you could encounter theproblem of receiving an incomplete order. Alternately, you might have to settle for

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CHAPTER 9 The Optimal Amount172

certain substitutions, a situation that may or may not be compatible with your EOQcalculations.

• At times, a supplier may be forced to discontinue an item that you find especially profitablein your hospitality establishment. This problem is often associated with wines, particularlythose of a certain vintage. Because only so much of a certain type of wine is produced in acertain year, the stock must run out sometime. Before reaching this point, you may decideto order as much as you can in order to maintain your supply as long as possible. Needlessto say, this buying decision flies in the face of the EOQ and ROP concepts.

• The EOQ assumes that you have adequate storage facilities. You may calculate an EOQof 55 cases and then discover that you have space for only 30 cases.

• Moreover, the EOQ assumes that the products you order will be used before they spoil orbecome obsolete. Fewer problems concerning obsolescence exist in the hospitality indus-try than in other industries, but spoilage can be an enormous problem. Although you canexpect 55 cases of tomato paste to maintain their quality for two or three months, youcannot assume this storage life for all products.

CORRECT ORDER SIZE AND ORDER TIME: SOME

BENEFITS OF THE THEORETICAL APPROACH

Theories can have shortcomings, of course, but they can also have numerous benefits. The EOQand ROP concepts are cases in point. Some potential benefits associated with these approachesare listed below:

• A theoretical approach substitutes fact for fiction. Even if some of your estimates are off,at least you have been forced to consider these variables. This discipline in itself can easi-ly lead to a more favorable profit performance.

• A range of order sizes seems to exist in which the total cost per year (annual ordering andstorage costs) does not vary dramatically. In the tomato paste example, the total cost peryear for 50 cases was $66; for 55 cases, $65.73; and for 60 cases, $66. Notice that youcould go down to 50 or up to 60 cases and incur an additional cost of only $0.27 peryear. As a result, you gain insight by using the theory, and you will not have to be over-ly concerned if your estimates are a little off. And, as mentioned earlier in this chapter,this range is the major reason that the par stock approach to ordering is acceptable formany operations.

• As technology becomes more ubiquitous, it is now feasible to monitor EOQs and ROPs.This, in turn, enables you to extract maximum benefit from these theoretical approaches,while at the same time minimizing the time and paperwork involved with analyzing usagepatterns, lead times, safety stock, and so on.

• While the use of the EOQ and ROP concepts may not be feasible for a single-unit hos-pitality operation, the multiunit chain organizations, especially those with company-owned commissaries and/or central distribution centers, would be able to adopt these the-ories and use them to significantly improve their purchasing performance.

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Questions and Problems 173

Theoretical approaches may or may not be completely useful in a specific hospitality opera-tion. We believe, however, that all operations can derive more benefit than cost by consideringthese concepts. A thoughtful consideration of these concepts forces an operator to evaluate all thepertinent variables that influence an overall inventory level. By evaluating these variables, thatoperator comes as close as possible to an optimal overall inventory level, which is the ultimateobjective of the EOQ and ROP concepts.

Key Words and Concepts

Capital costCarrying costCorrect order sizeCorrect order timeDelivery scheduleEconomic order quantity (EOQ) formulaEdible yield percentageForecastingInventory turnoverJust-in-time inventory management (JIT

inventory management)Lead timeLevinson approach to orderingOpportunity costs

Optimal inventory levelOrdering costsOrdering proceduresPar stockPar stock approach to orderingPopularity indexPortion divider (PD)Portion factor (PF)Product’s usage patternReorder point (ROP)Safety stockStockout costStorage cost

Questions and Problems

1. Briefly explain how the par stock approach to ordering works. Why does it work so well?What are some of the method’s drawbacks?

2. Fill in the blanks: Ordering the correct_______ at the correct_______ leads to_______.

3. Why would a general manager want to determine an optimal inventory amount?

4. Briefly describe EOQ and ROP. What benefits are there for managements that adoptthese procedures? What drawbacks are there?

5. What are the elements of the ordering cost? Of the storage cost? How can either, or both,of these costs be reduced without harming the overall hospitality operation’s profit per-formance?

6. You are currently using 750 cases of green beans per year. The cost of one purchase orderis $75. Annual storage costs are approximately 25 percent of inventory value. The beans’wholesale price is $24 per case. Each case contains six No. 10 cans. How many casesshould you purchase at one time?

7. Given the following data, determine the cost of one purchase order:

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CHAPTER 9 The Optimal Amount174

Questions and Problems (continued)EOQ: 500 pounds (1-month supply)

Storage cost: 24 percent per year

Price of the product: $6 per pound

8. The typical owner-operator will accept suppliers’ delivery and ordering procedures. Whatis the primary reason he or she would not try to change them?

9. What is the most important part of the storage cost?

10. What is a safety stock? Why might an operator wish to maintain a safety stock?

11. Briefly describe the concept of an “opportunity cost.”

12. Identify one reason the EOQ concept is not particularly useful to the typical hospitalityoperation.

13. What is the objective of using the JIT inventory management procedure?

14. Given the following data, compute the number of raw pounds needed to serve 250 customers:

ingredient: PORK CHOPS

serving size: 14 OUNCES

edible yield: 75 PERCENT

15. Given the following data, compute the number of liters needed to serve 500 customers:ingredient: SCOTCHserving size: 60 MILLILITERSservable yield: 95 PERCENT

16. Given the following data, compute the number of kilograms needed to serve 750 customers:ingredient: BELGIAN ENDIVEserving size: 75 GRAMS (EP)edible yield: 65 PERCENT

17. Given the following data, compute the number of cases needed to serve 1,000 customers:ingredient: HASH BROWN POTATOESserving size: 4 OUNCES (EP)edible yield: 100 PERCENTweight per case: 50 POUNDS

18. Given the following data, compute the number of cases needed to serve 1,250 customers:ingredient: DINNER ROLLSserving size: 4 OUNCES (TWO ROLLS)servable yield: 100 PERCENTnumber of rolls per case: 250 (500 OUNCES)

19. Given the following data, compute the number of gallons needed to serve 1,500 customers:ingredient: ICE CREAMserving size: 4 OUNCESedible yield: 90 PERCENTweight per gallon: 41⁄2 POUNDS

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References 175

Experiential Exercises

1. What are some advantages and disadvantages of utilizing rules of thumb to direct yourinventory management procedures?

a. Write down the advantages and disadvantages of utilizing rules of thumb to direct yourinventory management procedures.

b. Interview at least two restaurant managers and ask them what rules of thumb they use todirect their inventory management procedures (i.e., amount of inventory to have onhand). Prepare a list of all rules of thumb that you identify.

c. Ask each manager to comment on what they think are the advantages and disadvantagesof utilizing rules of thumb.

d. Submit a list of rules of thumb used to direct inventory management procedures. Includea report detailing the advantages and disadvantages of utilizing these rules of thumb.

2. Can the economic order quantity (EOQ) model assist foodservice managers?

a. Go online and research the EOQ model in detail. Prepare a two-page report that you willuse to persuade a manager of a large or multiunit foodservice operation to incorporate theEOQ model into his or her inventory forecasting procedures.

b. Submit the report to a foodservice manager of a large or multiunit foodservice operation.

c. Ask the manager for comments regarding the EOQ model.

d. Submit a report that includes your two-page persuasion and the manager’s comments.

References

1. Aaron Prather, “Inventory Management—The Principles of Effective Implementation.”Retrieved September 2009 from ezinearticles.com/?id=640265. See also David ScottPeters, “How to Manage Your Inventory Properly,” Restaurant Hospitality, February 2008,92(2), p. 28; Donald Waters, Inventory Control and Management (Hoboken, NJ: JohnWiley & Sons, 2003); Stuart Emmett, Excellence in Warehouse Management: How toMinimise Costs and Maximise Value (Chichester, West Sussex, England: Hoboken, NJ:John Wiley & Sons 2005).

2. See, for example, Fred R. Bleakley, “When Corporate Purchasing Goes Plastic,” The WallStreet Journal, June 14, 1995, p. B1; Willem Haneveld and Ruud Teunter, “Effects ofDiscounting and Demand Rate Variability on the EOQ,” International Journal ofProduction Economics, January 29, 1998, 54(2), pp. 173–193; Victor Aguirregabiria,“The Dynamics of Markups and Inventories in Retailing Firms,” Review of EconomicStudies, April 1999, 66(227), p. 275; Miles Feitzmann and Adam Ostazewski, “Hedgingthe Purchase of Direct Inputs in an Inflationary Environment,” Management AccountingResearch, March 1999, 10(1), pp. 61–84.

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