一个多阶段库存订货问题的 +Leapms 求解要点

问题来自微信公众号“运筹分享交流”——“互助·运筹擂台3 多阶段库存订货问题”。

数学概念模型

求解结果

+Leapms>mip
relexed_solution=416; number_of_nodes_branched=0; memindex=(2,2)
The Problem is solved to optimal as an MIP.
找到整数规划的最优解.非零变量值和最优目标值如下：
  .........
    s2* =30
    x1_4* =1
    x2_5* =1
    x4_4* =1
  .........
    Objective*=442
  .........
+Leapms>

附：+Leapms求解过程

+Leapms>load
 Current directory is "ROOT".
 .........
        wwp.leap
 .........
please input the filename:wwp
================================================================
1:  min sum{i=1,...,m;k=1,...,n}x[i][k]F[k]+sum{i=1,...,m}s[i]*C
2:  subject to
3:      s[i]=s[i-1]+sum{k=1,...,n}x[i][k]B[k]-D[i]|i=1,...,m
4:      s[0]=0
5:      s[4]=0
6:      s[i]<=40|i=1,...,3
7:  where
8:      m,n are integers
9:      B,F,D are sets
10:     S,C are numbers
11:     s[i] is a variable of nonnegative number|i=0,...,m
12:     x[i][k] is a variable of nonnegative integer|i=1,...,m;k=1,...,n
13:  data_relation
14:     m=_$(D)
15:     n=_$(B)
16:  data
17:     B={10,20, 30, 40, 50}
18:     F={48,86,118,138,160}
19:     S=40
20:     C=0.2
21:     D={40 20 30 40}
22:
23:
================================================================
>>end of the file.
Parsing model:
1D
2R
3V
4O
5C
6S
7End.
..................................
number of variables=25
number of constraints=9
..................................
+Leapms>mip
relexed_solution=416; number_of_nodes_branched=0; memindex=(2,2)
The Problem is solved to optimal as an MIP.
找到整数规划的最优解.非零变量值和最优目标值如下：
  .........
    s2* =30
    x1_4* =1
    x2_5* =1
    x4_4* =1
  .........
    Objective*=442
  .........
+Leapms>