Determining values for characteristic value combinations

Abstract

Methods and apparatus, including computer program products, implementing and using techniques for determining a quantity to be produced for each of two or more product types, where each product type is specified by one or more characteristics. An input specifying a desired distribution of the total quantity among the one or more characteristics is received. If the desired quantity to be produced of a product type is a non-integer value, the desired quantity is rounded to an integer to generate a final quantity to be produced for each product type. The final quantity preserves both a total quantity and the desired distribution of the total quantity among the one or more characteristics.

1 . A method comprising:
 receiving a total quantity value;   receiving a plurality of distribution rules for distributing the total quantity value to a plurality of product types, each distribution rule to govern a separate characteristic of the plurality of product types;   applying the plurality of distribution rules to the total quantity value to derive a desired quantity value for each of the plurality of product types;   rounding in a computer processor the desired quantity value for each of the plurality of product types to an integer when the desired quantity value is a non-integer, the rounding includes:
 maintaining the sum of the desired quantity values as equal to the total quantity value; and 
 approximating the plurality of distribution rules for each value of each separate characteristic as applied to the desired quantity values, taking into account, for the desired quantity value of a product type of the plurality of product types being rounded, rounding errors of desired quantity values rounded prior to the desired quantity value of the product type being rounded; and 
   applying the rounded desired quantity values to a production of products.   
     
     
         2 . The method of  claim 1 , the total quantity value specifying a total quantity of products to be produced. 
     
     
         3 . The method of  claim 1 , wherein rounding comprises:
 using a previously rounded quantity of a first product type for a desired quantity value of a second product type.   
     
     
         4 . The method of  claim 3 , wherein p characteristics of the plurality of product types span a p-dimensional space and each of the plurality of product types is defined as a point in the p-dimensional space, the point being determined by a combination of values for each of the p characteristics. 
     
     
         5 . The method of  claim 4 , wherein including previously rounded quantities comprises:
 calculating a difference function ƒor each dimension, the difference function using previously rounded quantities; and   using the calculated difference functions when rounding the desired quantity value to an integer.   
     
     
         6 . The method of  claim 5 , wherein rounding comprises:
 using an integer function ƒ[x, y]=int[x+y], wherein x is the desired quantity and y is the sum of the calculated difference functions, the integer function keeping the integer part of the sum of x and y and discarding the fractional part of the sum x+y.   
     
     
         7 . The method of  claim 5 , wherein rounding comprises:
 using a rounding function ƒ[x, y]=r[x+y]=int [(x+y)+0.5], wherein x is the desired quantity value and y is the sum of the calculated difference functions, the rounding function rounding the sum of x and y up or down to a nearest integer value.   
     
     
         8 . The method of  claim 5 , wherein rounding comprises:
 using a bounded rounding function ƒ[x, y]=b_r[x, y]=r[x+max[−0.5, 0.5−ε; y]], wherein x is the desired quantity value and y is the sum of the calculated difference functions and ε is a small non-zero value depending on the precision of the number x, the maximum function max [x1, x2; y] having the value of −0.5 when y is smaller than −0.5, the value y when y is between −0.5 and +0.5, and the value +0.5 when y is larger than +0.5.   
     
     
         9 . The method of  claim 1 , wherein the plurality of distribution rules are defined by a ratio, a percentage, or a specific value associated with the separate characteristic of the product type. 
     
     
         10 . The method of  claim 1 , wherein the separate characteristic is any one of a time, a color, a model, or a size. 
     
     
         11 . A computer program product, tangibly stored on a machine-readable medium, comprising instructions operable to cause a programmable processor to:
 receive a total quantity value;   receive a plurality of distribution rules for distributing the total quantity value to a plurality of product types, each distribution rule to govern a separate characteristic of the plurality of product types;   apply the plurality of distribution rules to the total quantity value to derive a desired quantity value for each of the plurality of product types; and   round the desired quantity value for each of the plurality of product types to an integer when the desired quantity value is a non-integer, the rounding includes:
 maintaining the sum of the desired quantity values as equal to the total quantity value; and 
 approximating the plurality of distribution rules for each value of each separate characteristic as applied to the desired quantity values, taking into account, for the desired quantity value of a product type of the plurality of product types being rounded, rounding errors of desired quantity values rounded prior to the desired quantity value of the product type being rounded. 
   
     
     
         12 . The computer program product of  claim 11 , the total quantity value specifying a total quantity of products to be produced. 
     
     
         13 . The computer program product of  claim 11 , wherein the instructions to round comprise instructions to use a previously rounded quantity of a first product type for a desired quantity value of a second product type. 
     
     
         14 . The computer program product of  claim 13 , wherein p characteristics of the plurality of product types span a p-dimensional space and each of the plurality of product types is defined as a point in the p-dimensional space, the point being determined by a combination of values for reach of the p characteristics. 
     
     
         15 . The computer program product of  claim 14 , wherein the instructions to include previously rounded quantities comprise instructions to:
 calculate a difference function ƒor each dimension, the difference function using previously rounded quantities; and   use the calculated difference functions when rounding the desired quantity value to an integer.   
     
     
         16 . The computer program product of  claim 15 , wherein the instructions to round comprise instructions to use an integer function ƒ[x, y]=int[x+y], wherein x is the desired quantity and y is the sum of the calculated difference functions, the integer function keeping the integer part of the sum of x and y and discarding the fractional part of the sum x+y. 
     
     
         17 . The computer program product of  claim 15 , wherein the instructions to round comprise instructions to use a rounding function ƒ[x, y]=r[x+y]=int [(x+y)+0.5], wherein x is the desired quantity value and y is the sum of the calculated difference functions, the rounding function rounding the sum of x and y up or down to a nearest integer value. 
     
     
         18 . The computer program product of  claim 15 , wherein the instructions to round comprise instructions to use a bounded rounding function ƒ[x, y]=b_r[x, y]=r[x+max[−0.5, 0.5−ε; y]], wherein x is the desired quantity value and y is the sum of the calculated difference functions and ε is a small non-zero value depending on the precision of the number x, the maximum function max [x1, x2; y] having the value −0.5 when y is smaller than −0.5, the value y when y is between −0.5 and +0.5, and the value +0.5 when y is larger than +0.5.