SAS Proc Optmodel 约束语法

Question

我正在尝试进行优化练习，但又被语法困住了。下面是我的尝试，除了解决方案代码之外，我真的很想对语法进行彻底的解释。我认为这是我遇到问题的特定索引部分。

问题： 我有一件物品希望在十周内售罄。我有一个历史趋势，并希望通过降低价格来改变这一趋势。我想要最大的保证金美元。下面的作品，但我想添加两个约束，无法理清语法。我在代码中为这两个约束留出了空间，并简要解释了我认为它们可能是什么样子。这是我需要每个约束做什么的更详细的解释。

inv_cap=每个地点的可用库存有限。我想全部卖掉。位置 1 为 800，位置 2 为 1200。FRC_UNITS 列的总和应等于该数量，但不能超过。

price_down_or_same=价格不能反弹，因此它需要始终小于或大于前一周。所以，price(i)

这是我的尝试。提前感谢您的帮助。

*read in data;
data opt_test_mkdown_raw;
    input 
        ITM_NBR
        ITM_DES_TXT $
        LCT_NBR
        WEEK
        LY_UNITS
        ELAST 
        COST
        PRICE
        TOTAL_INV;
cards;
1 stuff 1 1 300 1.2 6 10 800
1 stuff 1 2 150 1.2 6 10 800
1 stuff 1 3 100 1.2 6 10 800
1 stuff 1 4 60 1.2 6 10 800
1 stuff 1 5 40 1.2 6 10 800
1 stuff 1 6 20 1.2 6 10 800
1 stuff 1 7 10 1.2 6 10 800
1 stuff 1 8 10 1.2 6 10 800
1 stuff 1 9 5 1.2 6 10 800
1 stuff 1 10 1 1.2 6 10 800
1 stuff 2 1 400 1.1 6 9 1200
1 stuff 2 2 200 1.1 6 9 1200
1 stuff 2 3 100 1.1 6 9 1200
1 stuff 2 4 100 1.1 6 9 1200
1 stuff 2 5 100 1.1 6 9 1200
1 stuff 2 6 50 1.1 6 9 1200
1 stuff 2 7 20 1.1 6 9 1200
1 stuff 2 8 20 1.1 6 9 1200
1 stuff 2 9 5 1.1 6 9 1200
1 stuff 2 10 3 1.1 6 9 1200
;
run;

data opt_test_mkdown_raw;
    set opt_test_mkdown_raw;
    ITM_LCT_WK=cats(ITM_NBR, LCT_NBR, WEEK);
    ITM_LCT=cats(ITM_NBR, LCT_NBR);
run;

proc optmodel;

*set variables and inputs;

set<string> ITM_LCT_WK;
number ITM_NBR{ITM_LCT_WK};
string ITM_DES_TXT{ITM_LCT_WK};
string ITM_LCT{ITM_LCT_WK};
number LCT_NBR{ITM_LCT_WK};
number WEEK{ITM_LCT_WK}; 
number LY_UNITS{ITM_LCT_WK}; 
number ELAST{ITM_LCT_WK}; 
number COST{ITM_LCT_WK}; 
number PRICE{ITM_LCT_WK};
number TOTAL_INV{ITM_LCT_WK}; 

*read data into procedure;
read data opt_test_mkdown_raw into
    ITM_LCT_WK=[ITM_LCT_WK]
    ITM_NBR
    ITM_DES_TXT
    ITM_LCT
    LCT_NBR
    WEEK
    LY_UNITS
    ELAST
    COST
    PRICE
    TOTAL_INV; 

var NEW_PRICE{i in ITM_LCT_WK};
impvar FRC_UNITS{i in ITM_LCT_WK}=(1-(NEW_PRICE[i]-PRICE[i])*ELAST[i]/PRICE[i])*LY_UNITS[i];

con ceiling_price {i in ITM_LCT_WK}: NEW_PRICE[i]<=PRICE[i];
/*con inv_cap {j in ITM_LCT}: sum{i in ITM_LCT_WK}=I want this to be 800 for location 1 and 1200 for location 2;*/
con supply_last {i in ITM_LCT_WK}: FRC_UNITS[i]>=LY_UNITS[i];
/*con price_down_or_same {j in ITM_LCT} : NEW_PRICE[week]<=NEW_PRICE[week-1];*/

*state function to optimize;
max  margin=sum{i in ITM_LCT_WK}
    (NEW_PRICE[i]-COST[i])*(1-(NEW_PRICE[i]-PRICE[i])*ELAST[i]/PRICE[i])*LY_UNITS[i];

/*expand;*/
solve;

*write output dataset;
create data results_MKD_maxmargin
    from 
    [ITM_LCT_WK]={ITM_LCT_WK} 
    ITM_NBR
    ITM_DES_TXT
    LCT_NBR
    WEEK
    LY_UNITS
    FRC_UNITS
    ELAST
    COST
    PRICE
    NEW_PRICE
    TOTAL_INV; 

*write results to window;
print 
/*NEW_PRICE */
margin;
quit;

Answer 1

主要困难在于，在您的应用程序中，决策由 (Item,Location) 对和周数索引，但在您的代码中，您合并了 (Item,Location,Week) 三元组。我更喜欢使用数据步骤，但在此示例中的结果是您的代码无法引用特定周和特定对。

更改代码最少的解决方法是使用 OPTMODEL 可以为您计算的已定义集合和输入来添加这些关系。然后你会知道哪些三元组指的是 (Item,Location) 对和周的每个组合：

/* This code creates a set version of the Item x Location pairs 
   that you already have as strings */ 
set ITM_LCTS = setof{ilw in ITM_LCT_WK} itm_lct[ilw];
/* For each Item x Location pair, define a set of which 
   Item x Location x Week entries refer to that Item x Location */
set ILWperIL{il in ITM_LCTS} = {ilw in ITM_LCT_WK: itm_lct[ilw] = il};

通过这种关系，您可以添加其他两个约束。

我保留了您的代码原样，但对新代码应用了我认为有用的约定，尤其是当存在类似的名称时，例如 itm_lct 和 ITM_LCTS：

• 设置为全部大写；
• 输入参数以小写开头；
• 输出（vars、impvars 和约束）以大写 */ 开头

这是新的 OPTMODEL 代码：

proc optmodel;

*set variables and inputs;

set<string> ITM_LCT_WK;
number ITM_NBR{ITM_LCT_WK};
string ITM_DES_TXT{ITM_LCT_WK};
string ITM_LCT{ITM_LCT_WK};
number LCT_NBR{ITM_LCT_WK};
number WEEK{ITM_LCT_WK}; 
number LY_UNITS{ITM_LCT_WK}; 
number ELAST{ITM_LCT_WK}; 
number COST{ITM_LCT_WK}; 
number PRICE{ITM_LCT_WK};
number TOTAL_INV{ITM_LCT_WK}; 

*read data into procedure;
read data opt_test_mkdown_raw into
    ITM_LCT_WK=[ITM_LCT_WK]
    ITM_NBR
    ITM_DES_TXT
    ITM_LCT
    LCT_NBR
    WEEK
    LY_UNITS
    ELAST
    COST
    PRICE
    TOTAL_INV; 

var    NEW_PRICE{i in ITM_LCT_WK} <= price[i];
impvar FRC_UNITS{i in ITM_LCT_WK} = 
       (1-(NEW_PRICE[i]-PRICE[i])*ELAST[i]/PRICE[i]) * LY_UNITS[i];

* Moved to bound
con ceiling_price {i in ITM_LCT_WK}: NEW_PRICE[i] <= PRICE[i];

con supply_last{i in ITM_LCT_WK}: FRC_UNITS[i] >= LY_UNITS[i];

/* This code creates a set version of the Item x Location pairs 
   that you already have as strings */ 
set ITM_LCTS = setof{ilw in ITM_LCT_WK} itm_lct[ilw];
/* For each Item x Location pair, define a set of which 
   Item x Location x Week entries refer to that Item x Location */
set ILWperIL{il in ITM_LCTS} = {ilw in ITM_LCT_WK: itm_lct[ilw] = il};
/* I assume that for each item and location 
   the inventory is the same for all weeks for convenience,
   i.e., that is not a coincidence */
num inventory{il in ITM_LCTS} = max{ilw in ILWperIL[il]} total_inv[ilw];
con inv_cap {il in ITM_LCTS}: 
    sum{ilw in ILWperIL[il]} Frc_Units[ilw] = inventory[il]; 

num lastWeek = max{ilw in ITM_LCT_WK} week[ilw];
/* Concatenating indexes is not the prettiest, but gets the job done here*/
con Price_down_or_same {il in ITM_LCTS, w in 2 .. lastWeek}: 
    New_Price[il || w] <= New_Price[il || w - 1];*/

*state function to optimize;
max  margin=sum{i in ITM_LCT_WK}
    (NEW_PRICE[i]-COST[i])*(1-(NEW_PRICE[i]-PRICE[i])*ELAST[i]/PRICE[i])*LY_UNITS[i];

expand;
solve;

*write output dataset;
create data results_MKD_maxmargin
    from 
    [ITM_LCT_WK]={ITM_LCT_WK} 
    ITM_NBR
    ITM_DES_TXT
    LCT_NBR
    WEEK
    LY_UNITS
    FRC_UNITS
    ELAST
    COST
    PRICE
    NEW_PRICE
    TOTAL_INV; 

*write results to window;
print 
    NEW_PRICE FRC_UNITS
    margin
;

quit;