Production allocation determining apparatus and production allocation determining method

Abstract

A production allocation determining apparatus is configured to calculate a total supply function model representing a relationship between a total supply quantity and a marginal cost; calculate, based on current supply quantities, change rate constraints, and on capacity upper and lower limits, supply quantity upper and lower limits of the respective producers at a time s; calculate an optimum price based on the total supply function model, a predicted value of a demanded quantity at the time s, and on the supply quantity upper and lower limits; and calculate, based on the supply quantity upper and lower limits, the supply function models, and on the optimum price, optimum supply quantities. Calculation of the supply quantity upper and lower limits, calculation of the optimum price, and calculation of the optimum supply quantities are repeatedly executed from the time s=t to the time s=1.

What is claimed is: 
     
         1 . A production allocation determining apparatus for determining optimum allocations of supply quantities to be produced and supplied by a plurality of producers at each time s (s=1, 2, . . . , T), the production allocation determining apparatus comprising:
 a total supply function calculation unit configured to calculate, from supply function models representing relationships between supply quantities and marginal costs of the respective producers, a total supply function model representing a relationship between a total supply quantity and a marginal cost of the plurality of producers;   an upper and lower limit calculation unit configured to calculate, based on current supply quantities of the respective producers, based on change rate constraints of the supply quantities of the respective producers, and based on capacity upper limits and capacity lower limits indicating upper limits and lower limits of supply capacities of the respective producers, supply quantity upper limits and supply quantity lower limits indicating upper limits and lower limits of the supply quantities of the respective producers at a time s;   an optimum price calculation unit configured to calculate an optimum price indicating a marginal cost at the time s based on the total supply function model, based on a predicted value of a demanded quantity at the time s, and based on the supply quantity upper limits and the supply quantity lower limits; and   a supply quantity calculation unit configured to calculate, based on the supply quantity upper limits and the supply quantity lower limits of the respective producers at the time s, based on the supply function models of the respective producers, and based on the optimum price at the time s, optimum supply quantities indicating allocations of the supply quantities of the respective producers at the time s,   wherein calculation of the supply quantity upper limits and the supply quantity lower limits by the upper and lower limit calculation unit, calculation of the optimum price by the optimum price calculation unit, and calculation of the optimum supply quantities by the supply quantity calculation unit are repeatedly executed from the time s=t to the time s=1.   
     
     
         2 . The production allocation determining apparatus according to  claim 1 ,
 wherein, when the time s=T, for each of the respective producers, the upper and lower limit calculation unit sets, as the supply quantity upper limit at the time s, a smaller one of a first upper limit quantity, calculated based on the current supply quantity and the change rate constraint, and the capacity upper limit,   wherein, when the time s=T, for each of the respective producers, the upper and lower limit calculation unit sets, as the supply quantity lower limit at the time s, a larger one of a first lower limit quantity, calculated based on the current supply quantity and the change rate constraint, and the capacity lower limit,   wherein, when the time s<T, for each of the respective producers, the upper and lower limit calculation unit sets, as the supply quantity upper limit at the time s, a smallest one of a first upper limit quantity, calculated based on the current supply quantity and the change rate constraint, a second upper limit quantity, calculated based on the optimum supply quantity at the time s+1 calculated by the supply quantity calculation unit and based on the change rate constraint, and the capacity upper limit, and   wherein, when the time s<T, for each of the respective producers, the upper and lower limit calculation unit sets, as the supply quantity lower limit at the time s, a largest one of a first lower limit quantity, calculated based on the current supply quantity and the change rate constraint, a second lower limit quantity, calculated based on the optimum supply quantity at the time s+1 calculated by the supply quantity calculation unit and based on the change rate constraint, and the capacity lower limit.   
     
     
         3 . The production allocation determining apparatus according to  claim 1 ,
 wherein the supply quantity calculation unit compares, for each of the respective producers, a marginal cost lower limit and a marginal cost upper limit calculated from a supply quantity upper limit, a supply quantity lower limit, and a supply function model at the time s, with the optimum price at the time s,   wherein when the optimum price is less than the marginal cost lower limit, the supply quantity calculation unit sets, as an optimum supply quantity of a corresponding producer at the time s, the supply quantity lower limit of the corresponding producer,   wherein when the optimum price is greater than or equal to the marginal cost lower limit and less than or equal to the marginal cost upper limit, the supply quantity calculation unit sets, as an optimum supply quantity of a corresponding producer at the time s, a supply quantity corresponding to the optimum price in the supply function model of the corresponding producer, and   wherein when the optimum price exceeds the marginal cost upper limit, the supply quantity calculation unit sets, as an optimum supply quantity of a corresponding producer at the time s, the supply quantity upper limit of the corresponding producer.   
     
     
         4 . The production allocation determining apparatus according to  claim 1 , wherein by applying a quantifier elimination method to a first-order predicate formula obtained by using a variable indicating the total supply quantity, a variable indicating the marginal cost, variables indicating the supply quantities of the respective producers, variables indicating the supply upper limits of the respective producers, variables indicating the supply lower limits of the respective producers, and logic symbols, the total supply function model calculation unit calculates the total supply function model representing a relationship between the variable indicating the total supply quantity, the variable indicating the marginal cost, the variables indicating the supply upper limits of the respective producers, and the variables indicating the supply lower limits of the respective producers. 
     
     
         5 . The production allocation determining apparatus according to  claim 1 , further comprising:
 an output unit configured to output the optimum supply quantities calculated by the supply quantity calculation unit.   
     
     
         6 . The production allocation determining apparatus according to  claim 5 , further comprising:
 an input unit to which the current values of the supply quantities of the respective producers and a predicted value of the demanded quantity at each time s for the respective producers are input for each predetermined control cycle t,   wherein, upon the current values of the supply quantities of the respective producers and the predicted value of the demanded quantity at each time s for the respective producers being input through the input unit, the calculation of the supply quantity upper limits and the supply quantity lower limits by the upper and lower limit calculation unit, the calculation of the optimum price by the optimum price calculation unit, and the calculation of the optimum supply quantities by the supply quantity calculation unit are repeatedly executed from the time s=t to the time s=1, and   wherein the output unit outputs, for each predetermined control cycle t, the optimum supply quantities at the time s=1.   
     
     
         7 . A production allocation determining method for determining optimum allocations of supply quantities to be produced and supplied by a plurality of producers at each time s (s=1, 2, . . . , T), the method comprising:
 a total supply function calculation step of calculating, from supply function models representing relationships between supply quantities and marginal costs of the respective producers, a total supply function model representing a relationship between a total supply quantity and a marginal cost of the plurality of producers;   an upper and lower limit calculation step of calculating, based on current supply quantities of the respective producers, based on change rate constraints of the supply quantities of the respective producers, and based on capacity upper limits and capacity lower limits indicating upper limits and lower limits of supply capacities of the respective producers, supply quantity upper limits and supply quantity lower limits indicating upper limits and lower limits of the supply quantities of the respective producers at a time s;   an optimum price calculation unit step of calculating an optimum price indicating a marginal cost at the time s based on the total supply function model, based on a predicted value of a demanded quantity at the time s, and based on the supply quantity upper limits and the supply quantity lower limits; and   a supply quantity calculation step of calculating, based on the supply quantity upper limits and the supply quantity lower limits of the respective producers at the time s, based on the supply function models of the respective producers, and based on the optimum price at the time s, optimum supply quantities indicating allocations of the supply quantities of the respective producers at the time s,   wherein calculation of the supply quantity upper limits and the supply quantity lower limits by the upper and lower limit calculation step, calculation of the optimum price by the optimum price calculation step, and calculation of the optimum supply quantities by the supply quantity calculation step are repeatedly executed from the time s=t to the time s=1.