Method and structure for bid winning probability estimation and pricing model

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention generally relates to developing an expected winning probability distribution in response to a customer request for a price quote. More specifically, only the seller's internal historical win/loss bid data is used as a prediction of competitors' pricing and for development of the expected winning probability distribution.

[0003] 2. Description of the Related Art

[0004] A business-to-business (b2b) direct selling process begins with a customer's request for price quote for the products specified in a high level description. Then, it is the responsibility of a sales representative or pricing agent to come up with a reasonable price range that can be offered. If the price quote is too high, then a high profit will be expected, but the probability that the bid is materialized is very low.

[0005] If the price quote is too low, then there is an expected high probability of obtaining this bid, but the profit level would be very low. For this reason, sales representatives must be equipped with a smart pricing decision support tool, which can provide useful information such as expected winning probability level and expected revenue (or profit) for each price quote.

[0006] In the conventional model, a knowledge of the competitors' win/loss distribution is required, either by obtaining actual data about the competitor or by making assumptions. Although assumptions of competitors' behavior make price modeling easier, models developed from these assumptions inherently lack the realism of models based on actual data. What is missing in the conventional methods is a method that relies only on information readily available to a seller.

SUMMARY OF THE INVENTION

[0007] In view of the foregoing and other problems, drawbacks, and disadvantages of the conventional systems, it is an object of the present invention to provide a method (and structure) in which a winning probability estimate is developed, as based exclusively on the offeror's own historical bid data.

[0008] It is another object of the present invention to provide a method to use internal historical bidding data to develop a normalizing factor which is then used to develop a winning probability estimate.

[0009] In order to achieve the above goals and objects, as a first aspect of the present invention, described herein is a method (and structure) for developing a distribution function for the probability of winning a bid by a seller for a product or service, using the seller's own historical data for won bids and lost bids, including normalizing the data for winning bids and the data for lost bids and merging the normalized data into a single set of data.

[0010] As a second aspect of the present invention, also described herein is a signal-bearing medium tangibly embodying a program of machine-readable instructions executable by a digital processing apparatus to perform the above-described method.

[0011] The present invention provides an advantage over the conventional methods of developing an expected winning probability estimate by providing a method as based exclusively on the offeror's own historical bid data without knowledge of a competitor's win/loss distribution.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The foregoing and other objects, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, in which:

[0013]FIG. 1 shows an exemplary graph using an offeror's internal data for past bids, with the data for the won bids on the left-hand side of the drawing and the bids for the lost bids on the right-hand side of the drawing;

[0014]FIG. 2 shows the exemplary graph of win/loss data after having been normalized and merged;

[0015]FIG. 3 shows an exemplary expected winning probability curves, as resulting from the merged win/loss graph;

[0016]FIG. 4 illustrates an exemplary hardware/information handling system <b>400</b> for incorporating the present invention therein; and

[0017]FIG. 5 illustrates a signal bearing medium <b>500</b> (e.g., storage medium) for storing steps of a program of a method according to the present invention.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION

[0018] Referring now to the drawings, and more particularly to FIG. 1, which shows a distribution of historical bid data relative to competitors, in which the data for the winning bids appears in the left bell-shaped graph <b>10</b> and data for the lost bids appears in the right graph <b>11</b>. This internal data can become the basis of an expected winning probability distribution by reasoning as follows.

[0019] First, the left-hand graph <b>10</b>, by representing the price data that won the bids, is therefore presumed to be at least slightly below the competitor's corresponding bid amounts. Therefore, by increasing slightly the data of this curve, the resultant shifted curve represents a set of midway bids that would be an optimal winning set of bids. This data increase would be a shifting to the right of the left-hand curve.

[0020] Similarly, the right-hand graph <b>11</b> contains the data for bids lost to this competitor and indicates that the data in this curves is at least slightly higher relative to the bid of the competitor. Presumably, decreasing slightly the price data of this curve by shifting the right-hand curve slightly to the left would represent a set of prices that would have won those bids.

[0021] The present invention uses the above described strategy of taking historical internal bidding data and normalizing it appropriately to merge the win bid data with the lost bid data to become an expected winning probability distribution.

[0022] Hybrid Bid Pricing Model

[0023] As shown in FIG. 2, in the modeling technique of the present invention, both statistical analysis <b>21</b> on the historical data and decision maker's inputs <b>22</b> are required to predict the competitor's behavior on bids being requested <b>23</b>. Throughout this model, fine-grained customer segmentation and product-grouping is assumed, which should lead to a reasonable bid price range where the eventual winning price (e.g., price quote <b>24</b>) is expected to settle.

[0024] In FIG. 3 is shown an exemplary embodiment of the present invention. The seller's internal bidding history <b>31</b> is normalized <b>32</b> so that the win data and loss data can be merged <b>33</b> into an estimation <b>34</b> of the competitors' bidding behavior. A winning probability function <b>35</b> is built from this data. The process is described below, and a specific example is provided afterwards.

[0025] Step—1: Bid Offering Price Normalization

[0026] In the present invention, the value-adjusted Market Price (VAMP) is used as a normalizing factor. Also, the Price Function Value (PFV) index is used to calculate the competitor's value-adjusted List Price. PFV is an output of brand specific competitive analysis.

[0027] A novel approach of the present invention is that of using PFV (Price Function Value) index to calculate competitor's value-adjusted list price. This unique interpretation allows this index to be used as a strategic indicator for competitive pricing as well as internal pricing. PFV is used to estimate the list price that competitor would put for the matching configuration.

Price_Ratio=Approved_Price/value-adjusted Market Price

<i>VAMP </i>(value-adjusted Market Price)=<i>SUM</i>(market share*value-adjusted list price)

<i>VALP </i>(value-adjusted List Price)=company (<i>i.e.,IBM</i>)'<i>s </i>list price*competitor'<i>s PFV </i>

[0028] Step—2: Price Range Estimation

[0029] Applying price normalization technique in &lt;STEP—<b>1</b>&gt;, a price range is estimated in terms of Price-Ratio. In most of the cases, Price-Ratio will be between 0 and 1. From historical data for this segment at the expected competition rate, the Price_Ratio range is estimated as follows.

[0030] For the lowest bid Price_Ratio, the Mean of final offering price−K*standard deviation is used. For the highest bid Price_Ratio, the Mean of final offering price+K*standard deviation is used. K is a control variable and can be determined according to a decision maker's utility function.

[0031] Step—3: Winning Probability Estimation Against Price_Ratio

[0032] Suppose there were k competitors in the bidding. From the history of winning and losing bids with final offering prices, estimate f(p,k), the probability that k competitors' bidding Price_Ratio is higher than p.

[0033] Based on the “WIN” history, it is known that other competitors' bidding price was higher than the final win price. That is, it is possible to build f(p+delta_—1, k), the probability that k-competitors' bidding price was higher than p+delta_—1.

[0034] Based on the “LOSS” history, it is then straightforward to develop the function f(p-delta_—2, k), the probability that k-competitors' bidding price was higher than p-delta_—2. Note that delta_—1 is the price difference between the company's win price and the lowest price among competitors, and delta_—2 is the price difference between the company's losing price and the lowest price among competitors.

[0035] Now there are two estimators for the competitors' bidding behavior. To have two estimators with a least statistical difference, delta_—1 and delta_—2 are adjusted to have the same expected mean.

[0036] Without loss of generality, it can be assumed that the company's losing bid lies on the midrange of the losing bids. Then delta_—2 is the distance between the first and median of the bids, while delta_—1 is the distance between the first and the second of the bids. Now following this reasoning, delta_—1 and delta_—2 are adjusted in the ratio of 1 to ((k/2)+1).

[0037] The two data sets are now merged to finalize f(p,k) based on the whole (both WIN and LOSS) data.

[0038] This model also can be extended to make delta_—1 and delta_—2 as random variables. This demonstrates that this model can accommodate the cases where pricing itself is not the primary factor to determine winning status.

[0039] Step—4: Calculate Price Elasticity Factor and Shift Estimate

[0040] The price elasticity factor is now calculated for this segment at this competition rate k. As such, the Winning Probability Estimation is shifted up or down according to the calculated price elasticity factor for this bids.

[0041] Using the winning probability estimation, the pricing agent can use this information to finalize an offering price under their winning probability target.

EXAMPLE

[0042] The following example is provided to clarify details of the present invention. In this example, Customer_A asked for a price quote for 1,000 units of machine_M. To support Pricer's pricing decision, the Pricing Optimization Tool proceeds in the following sequences:

[0043] 1. Price Normalization:

[0044] For Machine_M, three competitors' compatible Machines are identified. <tables id="TABLE-US-00001" num="1"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="1"><colspec colname="1" colwidth="217PT" align="center" /><thead><row><entry namest="1" nameend="1" align="center">TABLE 1</entry></row></thead><tbody valign="top"><row><entry /></row><row><entry namest="1" nameend="1" align="center" rowsep="1" /></row><row><entry>Competitor's compatible machines and PFVs</entry></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="5"><colspec colname="1" colwidth="56PT" align="left" /><colspec colname="2" colwidth="42PT" align="left" /><colspec colname="3" colwidth="49PT" align="center" /><colspec colname="4" colwidth="28PT" align="center" /><colspec colname="5" colwidth="42PT" align="center" /><tbody valign="top"><row><entry>Company</entry><entry>Machine</entry><entry /><entry /><entry>Market</entry></row><row><entry>name</entry><entry>Name</entry><entry>List Pice ($)</entry><entry>PFV</entry><entry>Share (%)</entry></row><row><entry namest="1" nameend="5" align="center" rowsep="1" /></row><row><entry>My_Company</entry><entry>IM</entry><entry>3,349</entry><entry>—</entry><entry>25</entry></row><row><entry>Competitor_1</entry><entry>C1-M</entry><entry>2,316</entry><entry>1.32</entry><entry>30</entry></row><row><entry>Competitor_2</entry><entry>C2-M</entry><entry>2,799</entry><entry>1.09</entry><entry>30</entry></row><row><entry>Competitor_3</entry><entry>C3-M</entry><entry>2,455</entry><entry>1.16</entry><entry>15</entry></row><row><entry namest="1" nameend="5" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>

[0045] Now, PFVs are used to calculate competitor′ offering prices when competitors build their machines with exactly same configuration as My_Company's I-M. For instance, Competitor_l's PFV for machine_M is 1.32. When Competitor_—1 reconfigures C1_M in the exactly same configuration as My_Company's machine I-M, its list price would be 3,349/1.32=($)2,537. <tables id="TABLE-US-00002" num="2"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="1"><colspec colname="1" colwidth="217PT" align="center" /><thead><row><entry namest="1" nameend="1" align="center">TABLE 2</entry></row></thead><tbody valign="top"><row><entry /></row><row><entry namest="1" nameend="1" align="center" rowsep="1" /></row><row><entry>Competitor's price when they manufacture same quality machine as</entry></row><row><entry>My_Company</entry></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="5"><colspec colname="OFFSET" colwidth="14PT" align="left" /><colspec colname="1" colwidth="56PT" align="left" /><colspec colname="2" colwidth="56PT" align="center" /><colspec colname="3" colwidth="35PT" align="center" /><colspec colname="4" colwidth="56PT" align="left" /><tbody valign="top"><row><entry /><entry /><entry /><entry /><entry>Competitor's</entry></row><row><entry /><entry /><entry /><entry /><entry>VALP</entry></row><row><entry /><entry /><entry>my_Company's</entry><entry /><entry>(Value-Adjusted</entry></row><row><entry /><entry>Company name</entry><entry>Price</entry><entry>PVC</entry><entry>List Price)</entry></row><row><entry /><entry namest="OFFSET" nameend="4" align="center" rowsep="1" /></row><row><entry /><entry>Competitor_1</entry><entry>3,349</entry><entry>1.32</entry><entry>3.349/1.32=2,537</entry></row><row><entry /><entry>Competitor_2</entry><entry>3,349</entry><entry>1.09</entry><entry>3,349/1.09=3,251</entry></row><row><entry /><entry>Competitor_3</entry><entry>3,349</entry><entry>1.16</entry><entry>3,349/1.16=2,887</entry></row><row><entry /><entry namest="OFFSET" nameend="4" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>

[0046] To calculate fair market list price of machine_M, the competitor's VALP and its market share is used, as follows: <tables id="TABLE-US-00003" num="3"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="1"><colspec colname="1" colwidth="217PT" align="center" /><tbody valign="top"><row><entry /></row><row><entry namest="1" nameend="1" align="center" rowsep="1" /></row><row><entry>VAMP (Value Adjusted Market Price) = SUM of (market_share*VALP)</entry></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="5"><colspec colname="OFFSET" colwidth="14PT" align="left" /><colspec colname="1" colwidth="49PT" align="left" /><colspec colname="2" colwidth="42PT" align="center" /><colspec colname="3" colwidth="49PT" align="center" /><colspec colname="4" colwidth="63PT" align="center" /><tbody valign="top"><row><entry /><entry /><entry /><entry /><entry>VALP*Market</entry></row><row><entry /><entry>Company name</entry><entry>VALP</entry><entry>Market Share</entry><entry>Share</entry></row><row><entry /><entry namest="OFFSET" nameend="4" align="center" rowsep="1" /></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="5"><colspec colname="OFFSET" colwidth="14PT" align="left" /><colspec colname="1" colwidth="49PT" align="left" /><colspec colname="2" colwidth="42PT" align="center" /><colspec colname="3" colwidth="49PT" align="center" /><colspec colname="4" colwidth="63PT" align="char" char="." /><tbody valign="top"><row><entry /><entry>My_Company</entry><entry>3,349</entry><entry>25</entry><entry>837.25</entry></row><row><entry /><entry>Competitor_1</entry><entry>2,537</entry><entry>30</entry><entry>761.1</entry></row><row><entry /><entry>Competitor_2</entry><entry>3,251</entry><entry>30</entry><entry>975.3</entry></row><row><entry /><entry>Competitor_3</entry><entry>2,887</entry><entry>15</entry><entry>433.05</entry></row><row><entry /><entry namest="OFFSET" nameend="4" align="center" rowsep="1" /></row><row><entry /><entry namest="OFFSET" nameend="4" align="left"><!--footnotes removed--></entry></row></tbody></tgroup></table></tables>

[0047] All the final Approved Prices is now normalized by VAMP, which is $3,006.7 in <b>15</b> this example:

Normalized Price Ratio=(Approved-Price)/<i>VAMP. </i>

[0048] 2. Price Range Estimation

[0049] Based on either the historical bidding data or expert's input, a reasonable price range is determined for this bid. Suppose in history, normalized price ratios for the bids with similar bidding characteristics is:

Price-Ratio for this type of bids in history˜(Mean=0.8 and Standard-Deviation=0.04)

[0050] Then, reasonable price range for the current bid would be:

0.8−(1.97)*0.04≦offering_price_for_this_bid≦0.8+(1.97)*0.04

[0051] This is the step where K can be set, e.g., K=1.97, where K is a control variable which can be adjusted according to pricer's judgment for this deal. In this sense, price range estimation is somewhat strategic decision making for the bid. Price_Range_Estimation now would be the range (0.7212, 0.8788).

[0052] 3. Winning Probability Estimation

[0053] 3-1. Winning bids' price ratio estimation:

[0054] Select only the winning bids from the bidding history and calculate sample MEAN of this Win cluster. In this example,

[0055] Mean (price ratio of winning bids)=0.85

[0056] 3-2. Losing bids' price ratio estimation:

[0057] Select only the losing bids from the bidding history and calculate the sample MEAN of this Loss Cluster.

[0058] Mean(price ratio of losing bids) =<b>0</b>.<b>75</b>

[0059] 3-3. Competitor's bidding behavior construction:

[0060] In this example there are three competitors (Competitor_—1, Competitor_—2, and Competitor_—3) identified in the current bid. Including My-Company, the competition rate in this bid is four. Since δ_winand δ_lossis defined as the distance between (First Lowest and Second Lowest) and (First Lowest and Median=2.5), respectively, the ratio between δ_winand δ_losswould be:

δ_win:δ_loss=distance(first,second):distance(first,median)≃(2−1):(2.5−1)=1:1.5

[0061] Now the Win and Loss prices in the ratio of (1 to 1.5) are moved to have same cluster MEANs. That is, <maths id="MATH-US-00001" num="1"><math overflow="scroll"><mrow><msub><mi>δ</mi><mi>win</mi></msub><mo></mo><mtable><mtr><mtd><mrow><mo>=</mo><mrow><mrow><mi>Difference</mi><mo></mo><mrow><mo>(</mo><mrow><mi>Win</mi><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><mi>and</mi><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><mi>Loss</mi><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><mi>Cluster</mi><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><mi>MEANs</mi></mrow><mo>)</mo></mrow></mrow><mo>×</mo><mrow><mn>1.0</mn><mo>/</mo><mrow><mo>(</mo><mrow><mn>1.0</mn><mo>+</mo><mn>1.5</mn></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mrow><mrow><mrow><mo>(</mo><mrow><mn>0.85</mn><mo>-</mo><mn>0.75</mn></mrow><mo>)</mo></mrow><mo>×</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>/</mo><mn>2.5</mn></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mn>0.04</mn></mrow></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>δ</mi><mi>loss</mi></msub><mo>=</mo><mrow><mrow><mrow><mo>(</mo><mrow><mn>0.85</mn><mo>-</mo><mn>0.75</mn></mrow><mo>)</mo></mrow><mo>×</mo><mrow><mo>(</mo><mrow><mn>1.5</mn><mo>/</mo><mn>2.5</mn></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mn>0.06</mn></mrow></mrow></mtd></mtr></mtable></mrow></math><img file="US20030195832A1-20031016-M00001.TIF" id="EMI-M00001" he="33.1128" wi="216.027" img-format="tif" img-content="mf" /><attachments><attachment idref="MATHEMATICA-00001" attachment-type="nb" file="US20030195832A1-20031016-M00001.NB" /></attachments></maths><tables id="TABLE-US-00004" num="4"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="1"><colspec colname="1" colwidth="217PT" align="center" /><thead><row><entry namest="1" nameend="1" align="center">TABLE 4</entry></row></thead><tbody valign="top"><row><entry /></row><row><entry namest="1" nameend="1" align="center" rowsep="1" /></row><row><entry>Win and Loss Price Ratios are adjusted to induce Competitor's bidding</entry></row><row><entry>price</entry></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="4"><colspec colname="1" colwidth="35PT" align="center" /><colspec colname="2" colwidth="56PT" align="center" /><colspec colname="3" colwidth="63PT" align="center" /><colspec colname="4" colwidth="63PT" align="left" /><tbody valign="top"><row><entry /><entry /><entry>Final Offering Price</entry><entry>Adjusted By</entry></row><row><entry>BID_NO</entry><entry>Win/Loss status</entry><entry>Ratio</entry><entry>δ_winand δ_loss</entry></row><row><entry namest="1" nameend="4" align="center" rowsep="1" /></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="4"><colspec colname="1" colwidth="35PT" align="center" /><colspec colname="2" colwidth="56PT" align="center" /><colspec colname="3" colwidth="63PT" align="char" char="." /><colspec colname="4" colwidth="63PT" align="left" /><tbody valign="top"><row><entry>1</entry><entry>Win</entry><entry>0.85</entry><entry>(0.85 δ_win) =</entry></row><row><entry /><entry /><entry /><entry>0.85 −0.04 = 0.81</entry></row><row><entry>2</entry><entry>Loss</entry><entry>0.78</entry><entry>(0.78 + δ_loss) = 0.78</entry></row><row><entry /><entry /><entry /><entry>+0.06 = 0.84</entry></row><row><entry>3</entry><entry>Loss</entry><entry>0.75</entry><entry>0.75 + 0.06 = 0.81</entry></row><row><entry>4</entry><entry>Win</entry><entry>0.86</entry><entry>0.86 − 0.04 = 0.82</entry></row><row><entry>. . . </entry></row><row><entry>10,000</entry><entry>Loss</entry><entry>0.76</entry><entry>0.76 + 0.06 = 0.82</entry></row><row><entry namest="1" nameend="4" align="center" rowsep="1" /></row><row><entry namest="1" nameend="4" align="left"><!--footnotes removed--></entry></row></tbody></tgroup></table></tables>

[0062] Using the last column of Table 4, the competitor's bidding behavior distribution (i.e., estimate its Mean and standard deviation for this column) is estimated. In this example,

Competitor's Bidding Behavior Distribution <i>f</i>(<i>p</i>)˜Normal (Mean=0.79, STD=0.07).   (1)

[0063] To establish Winning Probability function from this competitor's bidding behavior distribution, the following relationship is noticed between the two:

Probability (Winning at Offering Price=<i>p</i>)=Probability(Competitor's Offering Price&gt;=<i>p</i>).

[0064] Let F(p) be the cumulative distribution of f(p). Then

Winning_Probability(<i>p</i>)=1−<i>F</i>(<i>p</i>)   (2)

Example

[0065] When the offering price is $2,345, its price ratio (=offering_price/Value-Adjusted Market Price) is 0.78(=2,345/3,006.7). To find out Winning Probability at this price point, use (2).

Winning_Probability(0.78)=1<i>−F</i>((0.78-0.79)/0.07)=1−<i>F</i>(−0.143)=0.557

[0066] Note that F(.) can be obtained from the Normal Distribution table. In this example, estimated winning probability at $2,345 is 55.7% for this bid.

[0067] 4. Optimal Pricing (Optional)

[0068] Using the winning probability estimation, pricing agents finalize offering price within his/her winning probability target.

[0069] If the objective of pricing decision is to maximize expected profit from this bid, then the pricer can proceed to the next step with the estimated winning probability function above but this step is irrelevant to the present invention.

[0070] Exemplary Hardware Implementation

[0071]FIG. 4 illustrates a typical hardware configuration of an information handling/computer system in accordance with the invention and which preferably has at least one processor or central processing unit (CPU) <b>411</b>.

[0072] The CPUs <b>411</b> are interconnected via a system bus <b>412</b> to a random access memory (RAM) <b>414</b>, read-only memory (ROM) <b>416</b>, input/output (I/O) adapter <b>418</b> (for connecting peripheral devices such as disk units <b>421</b> and tape drives <b>440</b> to the bus <b>412</b>), user interface adapter <b>422</b> (for connecting a keyboard <b>424</b>, mouse <b>426</b>, speaker <b>428</b>, microphone <b>432</b>, and/or other user interface device to the bus <b>412</b>), a communication adapter <b>434</b> for connecting an information handling system to a data processing network, the Internet, an Intranet, a personal area network (PAN), etc., and a display adapter <b>436</b> for connecting the bus <b>412</b> to a display device <b>438</b> and/or printer <b>439</b> (e.g., a digital printer or the like).

[0073] In addition to the hardware/software environment described above, a different aspect of the invention includes a computer-implemented method for performing the above method. As an example, this method may be implemented in the particular environment discussed above.

[0074] Such a method may be implemented, for example, by operating a computer, as embodied by a digital data processing apparatus, to execute a sequence of machine-readable instructions. These instructions may reside in various types of signal-bearing media.

[0075] Thus, this aspect of the present invention is directed to a programmed product, comprising signal-bearing media tangibly embodying a program of machine-readable instructions executable by a digital data processor incorporating the CPU <b>411</b> and hardware above, to perform the method of the invention.

[0076] This signal-bearing media may include, for example, a RAM contained within the CPU <b>411</b>, as represented by the fast-access storage for example. Alternatively, the instructions may be contained in another signal-bearing media, such as a magnetic data storage diskette <b>500</b> (FIG. 5), directly or indirectly accessible by the CPU <b>411</b>.

[0077] Whether contained in the diskette <b>500</b>, the computer/CPU <b>411</b>, or elsewhere, the instructions may be stored on a variety of machine-readable data storage media, such as DASD storage (e.g., a conventional “hard drive” or a RAID array), magnetic tape, electronic read-only memory (e.g., ROM, EPROM, or EEPROM), an optical storage device (e.g. CD-ROM, WORM, DVD, digital optical tape, etc.), paper “punch” cards, or other suitable signal-bearing media including transmission media such as digital and analog and communication links and wireless. In an illustrative embodiment of the invention, the machine-readable instructions may comprise software object code.

[0078] While the invention has been described in terms of a single preferred embodiment, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the appended claims.