LINE Solver
MATLAB API documentation
Loading...
Searching...
No Matches
qrf_bas_mem.m
1function [UN,QN,p2opt]=qrf_bas_mem(f,M,MR,MM,MM1,ZZ,ZM,BB,K,F,N,mu,v,rt)
2%%% PARAMETERS %%%
3% f; % finite capacity queue
4% M, integer, > 0; % number of queues
5% MR, integer, > 0; % number of independent blocking configurations
6% MM {m in 1:MR, i in 1:M} >=0; % blocking order
7% MM1 {m in 1:MR, i in 1:M}; % blocking order
8% ZZ {m in 1:MR} >=0; % nonzeros in independent blocking configurations
9% ZM, integer, >=0; % max of ZZ
10% BB {m in 1:MR, i in 1:M} >=0; % blocking state
11% K {i in 1:M}, integer, > 0; % number of phases for each queue
12% F {i in 1:M}, integer, > 0; % capacity
13% N, integer, >0; % population
14% mu {i in 1:M, k in 1:K(i), h in 1:K(i)} >=0; % completion transition rates
15% v {i in 1:M, k in 1:K(i), h in 1:K(i)} >=0; % background transition rates
16% r {i in 1:M, j in 1:M} >=0; % routing probabilities
17
18%%% VARIABLES %%%
19%var p2 {j = 1:M, nj = 1+(0:N), k = 1:K(j), i = 1:M, ni = 1+(0:N), h = 1:K(i), m = 1:MR} >= 0;
20%var e {i = 1:M, k = 1:K(i)} >=0;
21
22MR=size(MM,1);
23
24q = zeros(M,M,max(K),max(K));
25for i = 1:M
26 for j = 1:M
27 for k = 1:K(i)
28 for h = 1:K(i)
29 if j ~= i
30 q(i,j,k,h) = rt(i,j)*mu(i,k,h);
31 else
32 q(i,j,k,h) = v(i,k,h)+rt(i,i)*mu(i,k,h);
33 end
34 end
35 end
36 end
37end
38
39x = [zeros(M*(N+1)*max(K)*M*(N+1)*max(K)*MR,1); zeros(M*max(K),1)];
40
41options = optimset('fmincon');
42options.Display = 'iter';
43options.LargeScale = 'off';
44options.MaxIter = 100;
45options.MaxFunEvals = 1e10;
46options.MaxSQPIter = 500;
47%options.TolCon = 1e-8;
48options.Algorithm = 'sqp';
49%options.OutputFcn = @outfun;
50
51%[p2opt, fopt] = fmincon(@(x) umin(x, ti),x,[],[],[],[],x*0,x*0+1,@(x) sub_qrfcon(x,q,f,M,MR,MM,MM1,ZZ,ZM,BB,F,N),options);
52[xopt, fopt] = fmincon(@(x) mem(x),x,[],[],[],[],x*0,x*0+1,@(x) sub_qrfcon(x,q,f,M,MR,MM,MM1,ZZ,ZM,BB,F,N),options);
53%[xopt, fopt] = fmincon(@(x) mmi(x),x,[],[],[],[],x*0,x*0+1,@(x) sub_qrfcon(x,q,f,M,MR,MM,MM1,ZZ,ZM,BB,F,N),options);
54[p2opt,~] = sub_qrfvar(xopt);
55
56for ti=1:M
57 UN(ti) = 0;
58 QN(ti) = 0;
59 for m=1:MR
60 for ni=1+(1:F(ti))
61 for ki=1:K(ti)
62 UN(ti) = UN(ti) + p2opt(ti,ni,ki,ti,ni,ki, m);
63 QN(ti) = QN(ti) + ni*p2opt(ti,ni,ki,ti,ni,ki, m);
64 end
65 end
66 end
67end
68
69% add LB>=0 to both p2 and e
70% LINEAR PROGRAMMING: UTILIZATION UPPER BOUND AT QUEUE 1
71%minimize U1min: sum {m in 1..MR} sum {k in 1..K[1]} sum {n1 in 1..F[1]} p2[1,n1,k,1,n1,k,m];
72
73
74 function fobj = mmi(x)
75 % MMI
76 %minimize MI: sum {m in 1..MR} sum {i in 1..M, j in 1..M, ki in 1..K[i], kj in 1..K[j]: i<>j} sum {nj in 0..F[j]} sum {ni in 0..F[j]} p2[i,ni,ki,j,nj,kj,m]*(log(1e-6+p2[i,ni,ki,j,nj,kj,m])-log(1e-6+p2[i,ni,ki,i,ni,ki,m])-log(1e-6+p2[j,nj,kj,j,nj,kj,m]));
77 [p2,~] = sub_qrfvar(x);
78 fobj = 0;
79 for m = 1:MR
80 for i = 1:M
81 for ki = 1:K(i)
82 for j = 1:M
83 if i~=j
84 for kj = 1:K(j)
85 for ni = 1+(1:F(i))
86 for nj = 1+(1:F(j))
87 fobj = fobj + p2(i,ni,ki,j,nj,kj,m)*(log(1e-6+p2(i,ni,ki,j,nj,kj,m))-log(1e-6+p2(i,ni,ki,i,ni,ki,m))-log(1e-6+p2(j,nj,kj,j,nj,kj,m)));
88 end
89 end
90 end
91 end
92 end
93 end
94 end
95 end
96 end
97
98 function fobj = mem(x)
99 % MEM
100 %maximize H: -sum {m in 1..MR} sum {i in 1..M} sum {k in 1..K[i]} sum {ni in 1..F[i]} p2[i,ni,k,i,ni,k,m]*log(1e-6+p2[i,ni,k,i,ni,k,m]);
101 [p2,~] = sub_qrfvar(x);
102 fobj = 0;
103 for m = 1:MR
104 for i = 1:M
105 for k = 1:K(i)
106 for ni = 1+(1:F(i))
107 fobj = fobj - p2(i,ni,k,i,ni,k,m)*log(1e-6 + p2(i,ni,k,i,ni,k,m));
108 end
109 end
110 end
111 end
112 end
113
114 function [p2,e] = sub_qrfvar(x)
115 ctr = 1;
116 p2 = zeros(M,N+1,max(K),M,N+1,max(K),MR);
117 for j = 1:M
118 for nj = 1+(0:N)
119 for k = 1:K(j)
120 for i = 1:M
121 for ni = 1+(0:N)
122 for h = 1:K(i)
123 for m = 1:MR
124 p2(j,nj,k,i,ni,h,m) = x(ctr);
125 ctr = ctr + 1;
126 end
127 end
128 end
129 end
130 end
131 end
132 end
133 e = zeros(M,max(K));
134 for i=1:M
135 for k=1:K(i)
136 e(i,k) = x(ctr);
137 ctr = ctr + 1;
138 end
139 end
140 end
141
142 function [c,ceq] = sub_qrfcon(x,q,f,M,MR,MM,MM1,ZZ,ZM,BB,F,N)
143 c=zeros(0,1);
144 ceq=zeros(0,1);
145
146 %%% VARIABLES %%%
147 [p2,e] = sub_qrfvar(x);
148
149 %% DEFINITIONS
150 % subject to ONE {j in 1..M}: sum {nj in 0..N, k in 1..K[j], m in 1..MR} p2[j,nj,k,j,nj,k,m]=1;
151 for j = 1:M
152 % LHS
153 ceq(end+1) = 0;
154 for nj = 1+(0:N), for k = 1:K(j), for m = 1:MR
155 ceq(end) = ceq(end) + p2(j,nj,k,j,nj,k,m);
156 end, end, end
157 % RHS
158 ceq(end) = ceq(end) -1;
159 end
160
161 % subject to ZERO1 {j in 1..M, k in 1..K[j], nj in 0..N, i in 1..M, h in 1..K[i], ni in 0..N, m in 1..MR: i==j and nj==ni and h<>k}: p2[j,nj,k,i,ni,h,m]=0;
162 for j = 1:M, for k =1:K(j), for nj = 1+(0:N), for i = 1:M, for h = 1:K(i), for ni = 1+(0:N), for m = 1:MR
163 if i==j && (nj-1)==(ni-1) && h~=k % rescaled back nj and ni
164 ceq(end+1) = p2(j,nj,k,i,ni,h,m); %=0
165 end
166 end, end, end, end, end, end, end
167
168 % subject to ZERO2 {j in 1..M, k in 1..K[j], nj in 0..N, i in 1..M, h in 1..K[i], ni in 0..N, m in 1..MR: i==j and nj<>ni}: p2[j,nj,k,i,ni,h,m]=0;
169 for j = 1:M, for k =1:K(j), for nj = 1+(0:N), for i = 1:M, for h = 1:K(i), for ni = 1+(0:N), for m = 1:MR
170 if i==j && (nj-1)~=(ni-1) % rescaled back nj and ni
171 ceq(end+1) = p2(j,nj,k,i,ni,h,m); %=0
172 end
173 end, end, end, end, end, end, end
174
175 % subject to ZERO3 {j in 1..M, k in 1..K[j], nj in 0..N, i in 1..M, h in 1..K[i], ni in 0..N, m in 1..MR: i<>j and nj+ni>N}: p2[j,nj,k,i,ni,h,m]=0;
176 for j = 1:M, for k =1:K(j), for nj = 1+(0:N), for i = 1:M, for h = 1:K(i), for ni = 1+(0:N), for m = 1:MR
177 if i~=j && (nj-1)+(ni-1)>N % rescaled back nj and ni
178 ceq(end+1) = p2(j,nj,k,i,ni,h,m);
179 end
180 end, end, end, end, end, end, end
181
182 % subject to ZERO4 {j in 1..M, k in 1..K[j], nj in 0..N, m in 2..MR: f<>j}: sum {nf in 0..F[f]-1, h in 1..K[f]} p2[j,nj,k,f,nf,h,m]=0;
183 for j = 1:M, for k =1:K(j), for nj = 1+(0:N), for m = 2:MR
184 if f~=j
185 ceq(end+1) = 0;
186 for nf =1+ (0:(F(f)-1)), for h = 1:K(f)
187 ceq(end) = ceq(end) + p2(j,nj,k,f,nf,h,m);
188 end, end
189 end
190 end, end, end, end
191
192 % subject to ZERO5 {j in 1..M, k in 1..K[j], i in 1..M, h in 1..K[i], ni in 0..F[i], m in 2..MR: BB[m,j]==1}: p2[j,0,k,i,ni,h,m]=0;
193 for j = 1:M, for k =1:K(j), for i = 1:M, for h = 1:K(i), for ni = 1+(0:F(i)), for m = 2:MR
194 if BB(m,j)==1
195 ceq(end+1) = p2(j,1+0,k,i,ni,h,m);
196 end
197 end, end, end, end, end, end
198
199 % subject to ZERO6 {j in 1..M, k in 1..K[j], nj in F[j]+1..N, i in 1..M, h in 1..K[i], ni in 0..N, m in 1..MR}: p2[j,nj,k,i,ni,h,m]=0;
200 for j = 1:M, for k =1:K(j), for nj = 1+((F(j)+1):N), for i = 1:M, for h = 1:K(i), for ni = 1+(0:N), for m = 1:MR
201 ceq(end+1) = p2(j,nj,k,i,ni,h,m);
202 end, end, end, end, end, end, end
203
204 % subject to ZERO7 {j in 1..M, k in 1..K[j], nj in 1..F[j], i in 1..M, h in 1..K[i], ni in 0..N, m in 2..MR: BB[m,j]==1 and i<>j and i<>f and ni+nj+F[f]>N}: p2[j,nj,k,i,ni,h,m]=0;
205 for j = 1:M, for k =1:K(j), for nj = 1+(1:F(j)), for i = 1:M, for h = 1:K(i), for ni = 1+(0:N), for m = 2:MR
206 if BB(m,j)==1 && i~=j && i~=f && (ni-1)+(nj-1)+F(f)>N % rescaled back ni and nj
207 ceq(end+1) = p2(j,nj,k,i,ni,h,m);
208 end
209 end, end, end, end, end, end, end
210
211 % subject to ZERO8 {nf in 1..F[f]-1, k in 1..K[f], i in 1..M, h in 1..K[i], ni in 0..N, m in 2..MR}: p2[f,nf,k,i,ni,h,m]=0;
212 for nf = 1+(1:(F(f)-1)), for k =1:K(f), for i = 1:M, for h = 1:K(i), for ni = 1+(0:N), for m = 2:MR
213 ceq(end+1) = p2(f,nf,k,i,ni,h,m);
214 end, end, end, end, end, end
215
216 % subject to SIMMETRY {j in 1..M, nj in 0..N, k in 1..K[j], i in 1..M, ni in 0..N, h in 1..K[i], m in 1..MR}: p2[i,ni,h,j,nj,k,m] = p2[j,nj,k,i,ni,h,m];
217 for j = 1:M, for nj = 1+(0:N), for k =1:K(j), for i = 1:M, for ni = 1+(0:N), for h = 1:K(i), for m = 1:MR
218 ceq(end+1) = p2(i,ni,h,j,nj,k,m) - p2(j,nj,k,i,ni,h,m);
219 end, end, end, end, end, end, end
220
221 % subject to MARGINALS {j in 1..M, k in 1..K[j], nj in 0..N, i in 1..M, m in 1..MR: i<>j}: p2[j,nj,k,j,nj,k,m]= sum {ni in 0..N-nj} sum {h in 1..K[i]} p2[j,nj,k,i,ni,h,m];
222 for j = 1:M, for k =1:K(j), for nj = 1+(0:N), for i = 1:M, for m = 1:MR
223 if i~=j
224 % LHS
225 ceq(end+1) = p2(j,nj,k,j,nj,k,m);
226 % RHS
227 for ni = 1+(0:(N-nj)) %% added +1
228 for h = 1:K(i)
229 ceq(end) = ceq(end) - p2(j,nj,k,i,ni,h,m);
230 end
231 end
232 end
233 end, end, end, end, end
234
235 %subject to UEFF {j in 1..M, i in 1..M, ki in 1..K[i]}: e[i,ki] = sum {nj in 0..N, kj in 1..K[j], m in 1..MR, ni in 1..N: BB[m,i]==0} p2[j,nj,kj,i,ni,ki,m];
236 for j = 1:M, for i = 1:M, for ki = 1:K(i)
237 % LHS
238 ceq(end+1) = e(i,ki);
239 % RHS
240 for nj = 1+(0:N), for kj = 1:K(j), for m = 1:MR, for ni = 1+(1:N)
241 if BB(m,i)==0
242 ceq(end) = ceq(end) - p2(j,nj,kj,i,ni,ki,m);
243 end
244 end, end, end, end
245 end, end, end
246
247 %subject to THM1old {i in 1..M, k in 1..K[i]}: sum {j in 1..M, h in 1..K[i]: h<>k and j==i} q[i,j,k,h]*e[i,k] =sum {j in 1..M, h in 1..K[i]:h<>k and j==i} q[i,j,h,k]*e[i,h];
248% for i = 1:M, for k =1:K(i)
249% ceq(end+1) = 0;
250% % LHS
251% for j = 1:M, for h = 1:K(i)
252% if h~=k && j==i
253% ceq(end) = ceq(end) + q(i,j,k,h)*e(i,k);
254% end
255% end, end
256% % RHS
257% for j = 1:M, for h = 1:K(i)
258% if h~=k && j==i
259% ceq(end) = ceq(end) - q(i,j,h,k)*e(i,h);
260% end
261% end, end
262% end, end
263
264 %subject to THM1 {i in 1..M, k in 1..K[i]}: sum {j in 1..M, h in 1..K[i]} q[i,j,k,h]*e[i,k] =sum {j in 1..M, h in 1..K[i]} q[i,j,h,k]*e[i,h];
265 for i = 1:M, for k =1:K(i)
266 ceq(end+1) = 0;
267 % LHS
268 for j = 1:M, for h = 1:K(i)
269 ceq(end) = ceq(end) + q(i,j,k,h)*e(i,k);
270 end, end
271 % RHS
272 for j = 1:M, for h = 1:K(i)
273 ceq(end) = ceq(end) - q(i,j,h,k)*e(i,h);
274 end, end
275 end, end
276
277 %subject to THM2 {j in 1..M, k in 1..K[j], nj in 0..F[j], m in 1..MR}: sum {i in 1..M, ni in 1..F[i], ki in 1..K[i]} ni*p2[j,nj,k,i,ni,ki,m]= N*p2[j,nj,k,j,nj,k,m];
278 for j = 1:M, for k =1:K(j), for nj = 1+(0:F(j)), for m = 1:MR
279 ceq(end+1) = 0;
280 % LHS
281 for i = 1:M, for ni = 1+(1:F(i)), for ki = 1:K(i)
282 ceq(end) = ceq(end) + (ni-1)*p2(j,nj,k,i,ni,ki,m); % recaled back ni
283 end, end, end
284 % RHS
285 ceq(end) = ceq(end) - N*p2(j,nj,k,j,nj,k,m);
286 end, end, end, end
287
288 %subject to COR1 : sum {m in 1..MR, i in 1..M, j in 1..M, nj in 1..F[j], ni in 1..F[i], ki in 1..K[i], kj in 1..K[j]} ni*nj*p2[j,nj,kj,i,ni,ki,m]= N^2;
289 ceq(end+1) = 0;
290 % LHS
291 for m = 1:MR, for i = 1:M, for j = 1:M, for nj = 1+(1:F(j)), for ni = 1+(1:F(i)), for ki = 1:K(i), for kj = 1:K(j)
292 ceq(end) = ceq(end) + (ni-1)*(nj-1)*p2(j,nj,kj,i,ni,ki,m); % rescaled back ni and nj
293 end, end, end, end, end, end, end
294 % RHS
295 ceq(end) = ceq(end) - N^2;
296
297 %subject to THM30 {i in 1..M, u in 1..K[i]: i<>f}: sum {j in 1..M, nj in 1..F[j], k in 1..K[j], h in 1..K[j], m in 1..MR: j<>i and j<>f and BB[m,j]==0}
298 % q[j,i,k,h]*p2[j,nj,k, i,0,u, m] + sum {j in 1..M, nj in 1..F[j], k in 1..K[j], h in 1..K[j], m in 1..MR: j<>i and j==f and MM[m,1]<>i} q[j,i,k,h]*p2[j,nj,k, i,0,u, m]
299 % = sum {j in 1..M, nj in 0..F[j], k in 1..K[i], h in 1..K[j], m in 1..MR: j<>i and j<>f and BB[m,i]==0} q[i,j,k,u]*p2[j,nj,h, i,0+1,k, m]
300 % + sum {j in 1..M, nj in 0..F[j], k in 1..K[i], h in 1..K[j], m in 1..MR: j<>i and j==f and BB[m,i]==0 and nj<F[j]} q[i,j,k,u]*p2[j,nj,h, i,1,k, m]
301 % + sum {j in 1..M, nj in 0..F[j], y in 1..K[j], m in 1..MR: j<>i and j==f and BB[m,i]==1 and nj==F[j] and MM[m,1]==i} sum {p in 1..K[f], w in 1..M: w<>f and w<>i} q[f,w,y,p]*p2[f,nj,y, i,1,u, m] ;
302% for i = 1:M, for u = 1:K(i)
303% if i~=f
304% ceq(end+1)=0;
305% % LHS
306% for j = 1:M, for nj = 1+(1:F(j)), for k = 1:K(j), for h = 1:K(j), for m = 1:MR
307% if j~=i && j~=f && BB(m,j)==0
308% ceq(end)= ceq(end) + q(j,i,k,h)*p2(j,nj,k, i,1+0,u, m);
309% end
310% end, end, end, end, end
311%
312% for j = 1:M, for nj = 1+(1:F(j)), for k = 1:K(j), for h = 1:K(j), for m = 1:MR
313% if j~=i && j==f && MM(m,1)~=i
314% ceq(end)= ceq(end) + q(j,i,k,h)*p2(j,nj,k, i,1+0,u, m);
315% end
316% end, end, end, end, end
317% % RHS
318% for j = 1:M, for nj = 1+(0:F(j)), for k = 1:K(i), for h = 1:K(j), for m = 1:MR
319% if j~=i && j~=f && BB(m,i)==0
320% ceq(end)= ceq(end) - q(i,j,k,u)*p2(j,nj,h, i,1+0,k, m);
321% end
322% end, end, end, end, end
323%
324% for j = 1:M, for nj = 1+(0:F(j)), for k = 1:K(i), for h = 1:K(j), for m = 1:MR
325% if j~=i && j==f && BB(m,i)==0 && (nj-1)<F(j) % rescaled back nj
326% ceq(end)= ceq(end) - q(i,j,k,u)*p2(j,nj,h, i,1+1,k, m);
327% end
328% end, end, end, end, end
329%
330% for j = 1:M, for nj = 1+(0:F(j)), for y = 1:K(j), for m = 1:MR
331% if j~=i && j==f && BB(m,i)==1 && (nj-1)==F(j) && MM(m,1)==i % rescaled back nj
332% for p = 1:K(f), for w = 1:M
333% if w~=f && w~=i
334% ceq(end)= ceq(end) - q(f,w,y,p)*p2(f,nj,y, i,1+1,u, m);
335% end
336% end, end
337% end
338% end, end, end, end
339% end % if
340% end, end
341
342 % subject to THM3 {i in 1..M, ni in 0..(F[i]-1): i<>f}:
343 % sum {j in 1..M, nj in 1..F[j], k in 1..K[j], h in 1..K[j], u in 1..K[i], m in 1..MR: j<>i and j<>f and BB[m,j]==0} q[j,i,k,h]*p2[j,nj,k, i,ni,u, m]
344 % + sum {j in 1..M, nj in 1..F[j], k in 1..K[j], h in 1..K[j], u in 1..K[i], m in 1..MR: j<>i and j==f and MM[m,1]<>i} q[j,i,k,h]*p2[j,nj,k, i,ni,u, m]
345 % = sum {j in 1..M, nj in 0..F[j], k in 1..K[i], u in 1..K[j], m in 1..MR: j<>i and j<>f and BB[m,i]==0} sum {h in 1..K[i]} q[i,j,k,h]*p2[j,nj,u, i,ni+1,k, m]
346 % + sum {j in 1..M, nj in 0..F[j], k in 1..K[i], u in 1..K[j], m in 1..MR: j<>i and j==f and BB[m,i]==0 and nj<F[j]} sum {h in 1..K[i]} q[i,j,k,h]*p2[j,nj,u, i,ni+1,k, m]
347 % + sum {j in 1..M, nj in 0..F[j], k in 1..K[i], u in 1..K[j], m in 1..MR: j<>i and j==f and BB[m,i]==1 and nj==F[j] and MM[m,1]==i} sum {p in 1..K[f], w in 1..M: w<>f and w<>i} q[f,w,u,p]*p2[f,nj,u, i,ni+1,k, m] ;
348% for i = 1:M, for ni = 1+(0:(F(i)-1))
349% if i~=f
350% ceq(end+1)=0;
351% % LHS
352% for j = 1:M, for nj = 1+(1:F(j)), for k = 1:K(j), for h = 1:K(j), for u = 1:K(i), for m = 1:MR
353% if j~=i && j~=f && BB(m,j)==0
354% ceq(end)= ceq(end) + q(j,i,k,h)*p2(j,nj,k, i,ni,u, m);
355% end
356% end, end, end, end, end, end
357% for j = 1:M, for nj = 1+(1:F(j)), for k = 1:K(j), for h = 1:K(j), for u = 1:K(i), for m = 1:MR
358% if j~=i && j==f && MM(m,1)~=i
359% ceq(end)= ceq(end) + q(j,i,k,h)*p2(j,nj,k, i,ni,u, m);
360% end
361% end, end, end, end, end, end
362% % RHS
363% for j = 1:M, for nj = 1+(0:F(j)), for k = 1:K(i), for u = 1:K(j), for m = 1:MR
364% if j~=i && j~=f && BB(m,i)==0
365% for h = 1:K(i)
366% ceq(end)= ceq(end) - q(i,j,k,h)*p2(j,nj,u, i,ni+1,k, m);
367% end
368% end
369% end, end, end, end, end
370% for j = 1:M, for nj = 1+(0:F(j)), for k = 1:K(i), for u = 1:K(j), for m = 1:MR
371% if j~=i && j==f && BB(m,i)==0 && (nj-1)<F(j) % rescaled back nj
372% for h = 1:K(i)
373% ceq(end)= ceq(end) - q(i,j,k,h)*p2(j,nj,u, i,ni+1,k, m);
374% end
375% end
376% end, end, end, end, end
377% for j = 1:M, for nj = 1+(0:F(j)), for k = 1:K(i), for u = 1:K(j), for m = 1:MR
378% if j~=i && j==f && BB(m,i)==1 && (nj-1)==F(j) && MM(m,1)==i % rescaled back nj
379% for p = 1:K(f), for w = 1:M
380% if w~=f && w~=i
381% ceq(end)= ceq(end) - q(f,w,u,p)*p2(f,nj,u, i,ni+1,k, m);
382% end
383% end, end
384% end
385% end, end, end, end, end
386% end
387% end, end
388
389 % subject to THM3f {i in 1..M, ni in 0..(F[i]-1): i==f}: sum {j in 1..M, nj in 1..F[j], k in 1..K[j], h in 1..K[j], u in 1..K[i], m in 1..MR: j<>i and j<>f and BB[m,j]==0 and ni < F[i]} q[j,i,k,h]*p2[j,nj,k, i,ni,u, m]
390 % + sum {j in 1..M, nj in 1..F[j], k in 1..K[j], h in 1..K[j], u in 1..K[i], m in 1..MR: j<>i and j==f and ni==F[i] and MM[m,1]==j} sum {w in 1..M: w<>f} q[j,i,k,h]*p2[j,nj,k, i,ni,u, m]
391 % = sum {j in 1..M, nj in 0..F[j], k in 1..K[i], h in 1..K[i], u in 1..K[j]: j<>i and ni < F[i]} q[i,j,k,h]*p2[j,nj,u, i,ni+1,k, 1];
392% for i = 1:M, for ni = 1+(0:(F(i)-1))
393% if i==f
394% ceq(end+1) = 0;
395% % LHS
396% for j = 1:M, for nj = 1+(1:F(j)), for k = 1:K(j), for h = 1:K(j), for u = 1:K(i), for m = 1:MR
397% if j~=i && j~=f && BB(m,j)==0 && (ni-1) < F(i) % rescaled back ni
398% ceq(end) = ceq(end) + q(j,i,k,h)*p2(j,nj,k, i,ni,u, m);
399% end
400% end, end, end, end, end, end
401% for j = 1:M, for nj = 1+(1:F(j)), for k = 1:K(j), for h = 1:K(j), for u = 1:K(i), for m = 1:MR
402% if j~=i && j==f && (ni-1)==F(i) && MM(m,1)==j % rescaled back ni
403% for w = 1:M
404% if w~=f
405% ceq(end) = ceq(end) + q(j,i,k,h)*p2(j,nj,k, i,ni,u, m);
406% end
407% end
408% end
409% end, end, end, end, end, end
410% % RHS
411% for j = 1:M, for nj = 1+(0:F(j)), for k = 1:K(i), for h = 1:K(i), for u = 1:K(j)
412% if j~=i && (ni-1) < F(i) % rescaled back ni
413% ceq(end) = ceq(end) - q(i,j,k,h)*p2(j,nj,u, i,ni+1,k, 1);
414% end
415% end, end, end, end, end
416% end % if
417% end, end
418
419 % subject to THM3I {i in 1..M, z in 0..(ZM-1): i==f}: sum {j in 1..M, nj in 1..F[j], k in 1..K[j], h in 1..K[j], u in 1..K[f], m in 1..MR: j<>f and BB[m,j]==0 and ZZ[m]==z} q[j,f,k,h]*p2[j,nj,k, f,F[f],u, m]
420 % = sum {j in 1..M, nj in 0..F[j], k in 1..K[f], h in 1..K[f], u in 1..K[j], m in 1..MR: j<>f and ZZ[m]=z+1 } q[f,j,k,h]*p2[j,nj,u, f,F[f],k, m];
421% for i = 1:M, for z = 1+(0:(ZM-1))
422% if i==f
423% ceq(end+1)=0;
424% % LHS
425% for j = 1:M, for nj = 1+(1:F(j)), for k = 1:K(j), for h = 1:K(j), for u = 1:K(f), for m = 1:MR
426% if j~=f && BB(m,j)==0 && ZZ(m)==z
427% ceq(end) = ceq(end) + q(j,f,k,h)*p2(j,nj,k, f,F(f),u, m);
428% end
429% end, end, end, end, end, end
430% % RHS
431% for j = 1:M, for nj = 1+(0:F(j)), for k = 1:K(f), for h = 1:K(f), for u = 1:K(j), for m = 1:MR
432% if j~=f && ZZ(m)==z+1
433% ceq(end) = ceq(end) - q(f,j,k,h)*p2(j,nj,u, f,F(f),k, m);
434% end
435% end, end, end, end, end, end
436% end % if
437% end, end
438
439 % subject to THM3L {m in 1..MR: ZZ[m]==ZM-1}: sum {j in 1..M, k in 1..K[j], u in 1..K[f], nj in 1..F[j], h in 1..K[j]: j<>f and BB[m,j]==0 and MM1[m,j]>0} q[j,f,k,h]*p2[j,nj,k, f,F[f],u, m]
440 % = sum {j in 1..M: j<>f and BB[m,j]==0 and MM1[m,j]>0} sum {w in 1..M, k in 1..K[f], u in 1..K[f]:w<>f} q[f,w,k,u]*p2[f,F[f],k, f,F[f],k, MM1[m,j]];
441% for m = 1:MR
442% if ZZ(m)==ZM-1
443% ceq(end+1)=0;
444% % LHS
445% for j = 1:M, for k = 1:K(j), for u = 1:K(f), for nj = 1+(1:F(j)), for h = 1:K(j)
446% if j~=f && BB(m,j)==0 && MM1(m,j)>0
447% ceq(end) = ceq(end) + q(j,f,k,h)*p2(j,nj,k, f,F(f),u, m);
448% end
449% end, end, end, end, end
450% % RHS
451% for j = 1:M
452% if j~=f && BB(m,j)==0 && MM1(m,j)>0
453% for w = 1:M, for k = 1:K(f), for u = 1:K(f)
454% if w~=f
455% ceq(end) = ceq(end) - q(f,w,k,u)*p2(f,F(f),k, f,F(f),k, MM1(m,j));
456% end
457% end, end, end
458% end
459% end
460% end
461% end
462
463 % subject to THM4 {j in 1..M, k in 1..K[j], i in 1..M, m in 1..MR}: sum{t in 1..M} sum {h in 1..K[t]} sum {nj in 0..N} sum {nt in 0..N} nt*p2[j,nj,k,t,nt,h,m]
464 % >= N*sum {h in 1..K[i]} sum {nj in 0..N} sum {ni in 1..N} (p2[j,nj,k,i,ni,h,m]);
465 for j = 1:M, for k = 1:K(j), for i = 1:M, for m = 1:MR
466 c(end+1) = 0; % <= inequality
467 % LHS with sign swapped since >= in GLPK
468 for t = 1:M, for h = 1:K(t), for nj = 1+(0:N), for nt = 1+(0:N)
469 c(end) = c(end) - (nt-1)*p2(j,nj,k,t,nt,h,m); % rescaled back nt
470 end, end, end, end
471 % RHS with sign swapped since >= in GLPK
472 for h = 1:K(i), for nj = 1+(0:N), for ni = 1+(1:N)
473 c(end) = c(end) + N*(p2(j,nj,k,i,ni,h,m));
474 end, end, end
475 end, end, end, end
476 end
477end
478
Generated by doxygen 1.9.8