Determining a possible lot size

Abstract

The invention provides methods and apparatus, including computer program products, for of determining a possible lot size of units with respect to a fixed date for a chain of at least two process steps, each process step requiring a respective assigned resource, and consuming a respective time per unit for being performed by the respective assigned resource, where the process steps are sequentially dependent on each other. This is achieved by the following: (a) determining, for each resource, a respective time interval of availability during which the respective resource is continuously available, each time interval being limited by the fixed date, (b) calculating, for each determined time interval of availability, a respective largest possible number of times the respective process step can be performed by the respective resource, and (c) selecting the lot size of units to the minimum of the largest possible numbers.

1 . A method of determining a possible lot size of units with respect to a fixed date for a chain of at least two process steps, each process step requiring a respective assigned resource, and consuming a respective time per unit for being performed by the respective assigned resource, where the process steps are sequentially dependent on each other, the method including:
 (a) determining, for each resource, a respective time interval of availability during which the respective resource is continuously available, each time interval being limited by the fixed date,   (b) calculating, for each determined time interval of availability, a respective largest possible number of times the respective process step can be performed by the respective resource, and   (c) selecting, by a computer, the lot size of units to the minimum of the largest possible numbers.   
     
     
         2 . The method according to  claim 1 ,
 wherein the fixed date is a date of delivery, defining the end of the time intervals of availability.   
     
     
         3 . The method according to  claim 1 ,
 wherein the fixed date is a process start, defining the beginning of the time intervals of availability.   
     
     
         4 . The method according to  claim 1 ,
 wherein each number is calculated as truncated quotient of the length of the respective determined time interval, and the sum of the unit times of the respective step and each subsequent step.   
     
     
         5 . The method according to  claim 1 ,
 wherein each determined time interval is corrected by subtracting a respective lot size-independent time, whereby each lot size-independent time is the sum of the lot size-independent time of the process step of the assigned resource and the lot size-independent times of the subsequent process steps of the assigned resources.   
     
     
         6 . The method according to  claim 1 ,
 wherein, after selecting the lot size, in an iterable replacement step a current bottleneck resource is identified as the one of the resources corresponding to the minimum largest possible number, and if the corresponding interval of availability is limited by a break period, the time interval of availability is extended beyond the break period until the next limit, and wherein the calculation and selection steps (b) and (c) are repeated with the extended bottleneck time interval of availability as the corresponding time interval of availability to recalculate the lot size.   
     
     
         7 . The method according to  claim 6 ,
 wherein the replacement step is iterated up to at least one of the following break conditions:
 the replacement step does not modify the lot size; 
 the replacement step does not modify the lot size by at least a predefined minimum amount; 
 no break limiting any interval of availability can be localized. 
   
     
     
         8 . The method according to  claim 6 ,
 wherein, whenever a break is included into the modified bottleneck interval of availability, all resources are assumed to be not available during the break, and the calculation and selection steps (b) and (c) are repeated for all resources with their intervals of availability modified by the break.   
     
     
         9 . The method according to  claim 6 ,
 wherein, when a break is included into the modified bottleneck interval of availability, a fixed time span is subtracted from the modified bottleneck interval compensating for delays introduced by the break.   
     
     
         10 . The method according to  claim 9 ,
 wherein the fixed time span depends on the resource and/or on the break.   
     
     
         11 . The method according to  claims 1 ,
 wherein, whenever one of the resources is not available, the other resource(s) are assumed to also not be available in step (a).   
     
     
         12 . An apparatus capable of determining a possible lot size of units with respect to a fixed date for a chain of at least two process steps, each process step requiring a respective assigned resource, and consuming a respective time per unit for being performed by the respective assigned resource, where the process steps are sequentially dependent on each other, the apparatus including
 (a) determining means that, for each resource, determine a respective time interval of availability during which the respective resource is continuously available, each time interval being limited by the fixed date,   (b) calculating means that, for each determined time interval of availability, calculate a respective largest possible number of times the respective process step can be performed by the respective resource, and   (c) selecting means that select the lot size of units to the minimum of the largest possible numbers, wherein the selecting means is a computer.   
     
     
         13 . The apparatus according to  claim 12 ,
 wherein the determination means are adapted to define the fixed date as a date of delivery, defining the end of the time intervals of availability.   
     
     
         14 . The apparatus according to  claim 12 ,
 wherein the determination means are adapted to define the fixed date as a process start, defining the beginning of the time intervals of availability.   
     
     
         15 . The apparatus according to  claim 12 ,
 wherein the calculating means are adapted to calculate each number as truncated quotient of the length of the respective determined time interval, and the sum of the unit times of the respective step and each subsequent step.   
     
     
         16 . The apparatus according to  claim 12 ,
 wherein the determination means are adapted to correct each determined time interval by subtracting a respective lot size-independent time, whereby each lot size-independent time is the sum of the lot size-independent time of the process step of the assigned resource and the lot size-independent times of the subsequent process steps of the assigned resources.   
     
     
         17 . The apparatus according to  claim 12 , further comprising:
 replacement means that, after the selection means have selected the lot size, perform an iterable replacement step to identify a current bottleneck resource as the one of the resources corresponding to the minimum largest possible number, and to extend the time interval of availability beyond the break period until the next limit if the corresponding interval of availability is limited by a break period; and iteration means that address the calculation means and the selection means to repeat the calculation and selection (b) and (c) with the extended bottleneck time interval of availability as the corresponding time interval of availability to recalculate the lot size.   
     
     
         18 . The apparatus according to  claim 17 ,
 wherein the iteration means iterate the replacement and repetition of calculation up to at least one of the following break conditions:
 the replacement does not modify the lot size; 
 the replacement does not modify the lot size by at least a predefined minimum amount; 
 no replacement means can localize any break limiting any interval of availability. 
   
     
     
         19 . The apparatus according to  claim 17 ,
 wherein the replacement means are adapted to assume all resources to be not available during the break whenever a break is included into the modified bottleneck interval of availability, and wherein the calculation (b) and selection (c) are repeated for all resources with their intervals of availability modified by the break.   
     
     
         20 . The apparatus according to  claim 17 ,
 wherein subtraction means are provided that, when a break is included into the modified bottleneck interval of availability, subtract a fixed time span from the modified bottleneck interval compensating for delays introduced by the break.   
     
     
         21 . The apparatus according to  claim 20 ,
 wherein the subtraction means are adapted to determine the fixed time span depending on the resource and/or on the break.   
     
     
         22 . The apparatus according of  claims 12 ,
 wherein the determination means are adapted to determine the intervals of availability such that, whenever one of the resources is not available, the other resources are assumed to also not be available.   
     
     
         23 . A computer readable medium having program code stored therein that when executed by a processor cause the processor to:
 determine a possible lot size of units with respect to a fixed date for a chain of at least two sequentially dependent process steps, each process step requiring a respective assigned resource by:   (a) determining, for each resource, a respective time interval of availability during which the respective resource is continuously available, each time interval being limited by the fixed date,   (b) calculating, for each determined time interval of availability, a respective largest possible number of times the respective process step can be performed by the respective resource, and   (c) selecting the lot size of units as the minimum of the largest possible numbers.