wargner-whitin方法 的matlab代码

外国人写的，matlab官方网站下载的。程序里面计算成本矩阵用到的矩阵变换很亮，虽然一下子很难看明白。不过知道方法的原理后，直接调用函数计算就可以了

function [z , x , J , arg_J , C] = wargner_whitin(d , K , c , h);

%
% Wagner-Whitin Algorithm  
%
% Build production plans versus time cycles k =1,...,N responding production queries dk 
% and miniming the sum of following production costs  
% 
%   i) Fix production cost K_k 
%  ii) Unitary production cost c_k
% iii) Stockage unitary cost h_k
%
% Assumption : initial and final stocks are null.
%
%
% Inputs
% ------
%
% d            Queries of production througth time cycles (1 x N)
% K            Fix production cost (1 x N) 
% c            Unitary production cost (1 x N)
% h            Stockage unitary cost (1 x N)
%
%
% Outputs
% ------
%
%
% z           Optimal cost at the end of the N cycles
% x           Quantities to product (1 x N)
% J           Partial politics (1 x N)
% arg_J       Arguments of the partial politics (1 x N) 
% C           Cost transition matrix (N x N)
%
%
%
% Example1
% -------
%
%clear,close all hidden
%d = [8 10 7 9 6];
%K = [50 40 50 70 60];
%c = [5 5 6 4 5];
%h = [4 2 3 4 NaN];
%[z , x , J , arg_J , C] = wargner_whitin(d , K , c , h);
%
%
% Example2
% --------
%
%
%clear,close all hidden
%N = 100;
%d = ceil(N*rand(1 , N));
%K = ceil(N*rand(1 , N));
%c = ceil(N*rand(1 , N));
%h = ceil(N*rand(1 , N));
%[z , x , J , arg_J , C] = wargner_whitin(d , K , c , h);
%ind_x = find(x);
%figure(1)
%subplot(211)
%stem((1:N),J)
%xlabel('Period N','fontname','times','fontsize',12)
%ylabel('Production costs','fontname','times','fontsize',12)
%title(['N = ' num2str(N) ],'fontname','times','fontsize',13)
%subplot(212)
%stem(ind_x , x(ind_x) , 'ro')
%xlabel('P-N','fontname','times','fontsize',12)
%ylabel('Quantities to product','fontname','times','fontsize',12)
%figure(2)
%imagesc(C)
%colorbar
%title('Transition cost production matrix ','fontname','times','fontsize',13)
%
%
% Author : Sebastien PARIS (sebastien.paris@lsis.org) 08/30/2001.
% ------
%

N      = length(d);

%------------------- Initialization ----------------------%

C      = zeros(N);

FF     = C;

J      = zeros(1 , N + 1);

arg_J  = J ;

ZN     = zeros(1 , N);

ON     = ones(1 , N);

vect_N = (1:N);


%------- Cost matrix C = {c(k,l)}, k,l = 1,...,N -----%

mat_tp        = triu(vect_N(ON , :));

K1            = K(:);

c1            = c(:);

h1            = h(:);

h1            = h1(1:end - 1);

KK            = triu(K1(: , ON));

CC            = triu(c1(: , ON));

indice        = (mat_tp ~= 0);

FF(indice)    = d(mat_tp(indice));

YY            = cumsum(FF , 2);

SS            = YY(2:end , 1:end);

HH1           = triu(h1(: , ON));

EE            = HH1.*SS;

ZZ            = cumsum(EE(end : -1 : 1 , :) , 1);

ZZ            = ZZ(end : -1 : 1 , :);

C             = KK + (CC.*YY) + ([ZZ ; ZN]);


%------------------------   Dynamic Programming --------------------%

J(end)        = 0;

arg_J(end)    = 0;

for k = N : -1 : 1
    
    tp               = ZN;
    
    tp(:)            = NaN;
    
    tp(k :end)       = C(k , k:end ) + J(k + 1 : end);
    
    [J(k) arg_J(k) ] = min(tp); 
    
end

z = J(1);

%------------------------  Back-Tracking  --------------------%

k = 1;

x = ZN;

while(k <= N)
    
    x(k) = sum(d(k : arg_J(k)));
    
    k    = arg_J(k) + 1;
    
end   

J = J(1:end - 1);