topic Re: PROC OPTMODEL problem to be infeasible in Mathematical Optimization, Discrete-Event Simulation, and OR

PROC OPTMODEL problem to be infeasible

Kaushansky — Thu, 24 Aug 2023 18:55:46 GMT

I don't understand why the my CON 7 is causing the problem to be infeasible?

Here's my code LOG:

OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;

73 /*===============================================================================

73 ! ==========================================================*/

74 /* 8. Perform the optimization to allocate the daily budget per campaign line

74 ! item based on the WAMM media allocation and maximize iROAS */

75 /*===============================================================================

75 ! ==========================================================*/

76 proc optmodel;

78 setOBS;

80 /* Define the in character variables from the input dataset to be used in the

80 ! optimization model */

82 strCampaign_Line_Item {OBS};

83 strMedia_Tactics {OBS};

85 set TACTICS = setof {i in OBS} Campaign_Line_Item[i];

86 set TACTICS2 = setof {j in OBS} Media_Tactics[j];

88 /* Define the numeric variables from the input dataset to be used in the

88 ! optimization model */

90 numInput_Budget {OBS};

91 num Cost_Adj_Input_Budget {OBS};

92 numiROAS {OBS};

93 numUnique_Media_Tactics {OBS};

94 numInput_Min_Number_of_Days {OBS};

95 numPct_WAMM_Optimized_Spend {OBS};

96 numAvg_Pct_WAMM_Optimized_Spend {OBS};

97 numPct_WAMM_Optimized_by_Line_Item {OBS};

98 numInput_End_Date {OBS};

99 numInput_Start_Date {OBS};

100 numCost_Per_Imp_Or_Click {OBS};

101 numSaturation_Point {OBS};

102 numInflection_Point {OBS};

103

104 /* Read in the input dataset to be used in the optimization model */

105

106 read data CI_Optimization_Data_2 into OBS=[_N_]

107

108 /* Include the variables from the input dataset to be used in the optimization

108 ! model */

109

110 Campaign_Line_Item

111 Input_Budget

112 Cost_Adj_Input_Budget

113 Media_Tactics

114 iROAS

115 Unique_Media_Tactics

116 Input_Min_Number_of_Days

117 Pct_WAMM_Optimized_Spend

118 Avg_Pct_WAMM_Optimized_Spend

119 Pct_WAMM_Optimized_by_Line_Item

120 Input_End_Date

121 Input_Start_Date

122 Cost_Per_Imp_Or_Click

123 Saturation_Point

124 Inflection_Point;

NOTE: There were 37 observations read from the data set WORK.CI_OPTIMIZATION_DATA_2.

125

126 /* Set the optimization variable to be maximized for the model */

127

128 var Optimized_Budget {OBS} >= 0;

129

130 /* Create additional variables to be used for optimization and/or contraints

130 ! in the model */

131

132 impvar Input_Incremental_Sales {i in OBS}=iROAS[i] * Input_Budget[i];

133 impvar Optimized_Incremental_Sales {i in OBS}=iROAS[i] * Optimized_Budget[i];

134

135 impvar Optimized_iROAS {i in OBS} =if Cost_Adj_Input_Budget[i] >0 and

135 ! Optimized_Incremental_Sales[i]>0

136 then Optimized_Incremental_Sales[i] /

136 ! Cost_Adj_Input_Budget[i]

137 else Input_Incremental_Sales[i]

137 ! / Input_Budget[i];

138

139 impvar Input_Number_of_Days {i in

139 ! OBS}=max(Input_End_Date[i]-Input_Start_Date[i],1);

140 impvar Total_Campaign_Days {i in OBS}=&Total_Campaign_Days;

141 impvarDaily_Spend_Per_Min_Days {i in OBS}=Optimized_Budget[i] /

141 ! Input_Min_Number_of_Days[i];

142

143 /***

144 impvar Offsite_Budget {i in OBS}=if Media_Tactics[i]='Offsite Display

144 ! Walmart Network' then Input_Budget[i] else 0;

145 impvar SP_KWB_Budget {i in OBS}=if Media_Tactics[i]='SP KWB' then

145 ! Input_Budget[i] else 0;

146 impvar Search_Budget {i in OBS}=SP_KWB_Budget[i] + SP_Auto_Budget [i] +

146 ! SBA_Budget [i];

147 ***/

148

149 /*-------------------------------------------------------------------------*/

150 /* Optimization function */

151 /*-------------------------------------------------------------------------*/

152 max Total_iROAS = sum {i in OBS} iROAS[i] * Optimized_Budget[i];

153

154 /* MAXIMUM BUDGET ALLOWED -> Optimized Budget to comply with the maximum WAMM

154 ! budget allowed */

155 con Mycon1 {i in OBS}:

156 sum {j in OBS} Optimized_Budget[j] <= &overall_input_budget *

157 (1+&allowed_budget_inc) *

158 (1-&value_add_pct);

159

160 con Mycon2 {i in OBS}:

161 Optimized_Budget[i] <= Input_Budget[i] *

162 (1+&wamm_deviation_pct) *

163 (1-&value_add_pct);

164

165 /* ONLY WHEN ALL WAMM TACTICS ARE CONSIDERED -> Optimized Budget to comply with

165 ! the WAMM % allocation plus an allowed increase ratio */

166 *con Mycon2 {i in OBS}:

167 Optimized_Budget[i] <= Input_Budget[i] *

168 Pct_WAMM_Optimized_by_Line_Item[i] *

169 (&total_input_ci_allocation) *

170 (1+&wamm_deviation_pct) *

171 (1+&allowed_budget_inc) *

172 (1-&value_add_pct);

173

174 /* ONLY WHEN NO INPUT BUDGET GIVEN AND ALL WAMM TACTICS ARE CONSIDERED ->

174 ! Optimized Budget to comply with the overall WAMM budget */

175 *con Mycon2 {i in OBS}:

176 Optimized_Budget[i] <= &overall_input_budget *

177 Pct_WAMM_Optimized_by_Line_Item[i] *

178 (&total_input_ci_allocation) *

179 (1+&wamm_deviation_pct) *

180 (1+&allowed_budget_inc) *

181 (1-&value_add_pct);

182

183 /* SATURATION -> Ensure each tactic does not exceed the Point of Saturation

183 ! based on WAMM */

184 con Mycon3 {i in OBS}:

185 Optimized_Budget[i]<=Saturation_Point[i] *

186 Total_Campaign_Days[i] *

187 (1+&allowed_budget_inc);

188

189 /*-------------------------------------------------------------------------*/

190 /* Tactic Specific Mininum Constraints not to exceed 50000 or greater than */

191 /*-------------------------------------------------------------------------*/

192 /* MINIMUM SPEND BY TACTIC -> Ensure every tactic has at least a certain % of

192 ! the Inout Budget contraint */

193 con Mycon4 {i in OBS}:

194 Optimized_Budget[i]>=if Media_Tactics[i] ne ' ' and Media_Tactics[i]

194 ! ne 'Onsite Display Run-Of-Site'

195 then Input_Budget[i]*&wamm_deviation_pct;

196

197 /* MINIMUM SPEND BY TACTIC -> Ensure every tactic has at least a certain $ of

197 ! the Inout Budget contraint */

198 con Mycon5 {i in OBS}:

199 Optimized_Budget[i]>=if Media_Tactics[i] ne ' ' and Media_Tactics[i]

199 ! ne 'Onsite Display Run-Of-Site'

200 then 10000;

201

202 /* MAXIMUM SPEND BY TACTIC -> Ensure every tactic has at least a certain $ of

202 ! the Inout Budget contraint */

203 *con Mycon6 {i in OBS}:

204 Optimized_Budget[i]<=if Media_Tactics[i] ne ' ' then 20900;

205

206 /* MAXIMUM SPEND BY TACTIC -> Onsite Display Contextual Targeting contraint */

207 con Mycon7 {i in OBS}:

208 Optimized_Budget[i]<=if Media_Tactics[i]='Offsite Display Walmart

208 ! Network' then 2000000;

209

210 /* sum of Search_Budget not to exceed 150000 */

211 *con Mycon10 {i in OBS}:

212 sum {j in OBS} Search_Budget[j] <= 149000;

213

214 solve;

NOTE: Problem generation will use 4 threads.

NOTE: The problem has 37 variables (0 free, 0 fixed).

NOTE: The problem has 222 linear constraints (148 LE, 0 EQ, 74 GE, 0 range).

NOTE: The problem has 1554 linear constraint coefficients.

NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range).

NOTE: The OPTMODEL presolver is disabled for linear problems.

NOTE: The LP presolver value AUTOMATIC is applied.

NOTE: The LP presolver time is 0.00 seconds.

NOTE: Constraint Mycon7[1] causes the problem to be infeasible.

NOTE: The LP presolver found this problem to be infeasible.

NOTE: Infeasible.

NOTE: The IIS= option can be used to help diagnose the cause of infeasibility.

215

216 create data CI_Optimization_Data_3(drop=i) from [i]=OBS

217

218 Media_Tactics

219 Campaign_Line_Item

220 Optimized_Budget

221 Input_Budget

222 Cost_Adj_Input_Budget

223 iROAS

224 Unique_Media_Tactics

225 Pct_WAMM_Optimized_Spend

226 Avg_Pct_WAMM_Optimized_Spend

227 Pct_WAMM_Optimized_by_Line_Item

228 Input_Number_of_Days

229 Input_Min_Number_of_Days

230 Saturation_Point

231 Inflection_Point

232

233 Input_Incremental_Sales

234 Optimized_Incremental_Sales

235 Optimized_iROAS

236

237 Total_Campaign_Days

238 Daily_Spend_Per_Min_Days

239 ;

NOTE: Division by zero at line 137 column 82.

NOTE: The data set WORK.CI_OPTIMIZATION_DATA_3 has 37 observations and 19 variables.

240 quit;

NOTE: PROCEDURE OPTMODEL used (Total process time):

real time 0.20 seconds

cpu time 0.03 seconds

241

242

243 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;

255

User: Michael Kaushansky

Messages: 77

Re: PROC OPTMODEL problem to be infeasible

RobPratt — Thu, 24 Aug 2023 19:13:15 GMT

It is hard to tell for sure from just looking at your log, but here is what I suspect is going on. You declared this constraint:

   con Mycon7 {i in OBS}:
      Optimized_Budget[i]<=if Media_Tactics[i]='Offsite Display Walmart Network' then 2000000;

For the IF-THEN/ELSE expression, there is a default of ELSE 0, so what you declared is equivalent to this:

   con Mycon7 {i in OBS}:
      Optimized_Budget[i]<=if Media_Tactics[i]='Offsite Display Walmart Network' then 2000000 else 0;

Because Optimized_Budget[i] is declared with >= 0 and this constraint forces that variable to be <= 0 if Media_Tactics[i] is not 'Offsite Display Walmart Network', the effect is that Optimized_Budget[i] = 0 in that case.

I think you instead meant for the constraint to be enforced only if the condition is satisfied, which you can do as follows:

   con Mycon7 {i in OBS: Media_Tactics[i]='Offsite Display Walmart Network'}:
      Optimized_Budget[i] <= 2000000;

And for a constraint with only one variable, it is more efficient to instead omit the constraint and just change the variable bounds:

   for {i in OBS: Media_Tactics[i]='Offsite Display Walmart Network'}
      Optimized_Budget[i].ub = 2000000;

If I guessed wrong about your intent, I recommend trying the suggestion in the log to use the IIS= option to help diagnose infeasibility:

   solve with lp / iis=1;
   expand / iis;

Re: PROC OPTMODEL problem to be infeasible

Kaushansky — Fri, 25 Aug 2023 01:33:41 GMT

Thank you for your email. This was very helpful.

How can I set global constraints, for several rows as a group Vs by each
Obs (row from the input dataset).

Re: PROC OPTMODEL problem to be infeasible

RobPratt — Fri, 25 Aug 2023 02:58:14 GMT

Your Mycon1 looks like an attempt to do that:

   con Mycon1 {i in OBS}:
      sum {j in OBS} Optimized_Budget[j] <= &overall_input_budget * (1+&allowed_budget_inc) * (1-&value_add_pct);

This family of constraints is indexed by i, but nothing in the constraint refers to i, so you end up with the exact same constraint over and over again. Instead, I think you intended to declare a single constraint:

   con Mycon1:
      sum {j in OBS} Optimized_Budget[j] <= &overall_input_budget * (1+&allowed_budget_inc) * (1-&value_add_pct);

Re: PROC OPTMODEL problem to be infeasible

Kaushansky — Thu, 31 Aug 2023 17:42:33 GMT

Thank you.

And assuming I can set global constraint (if/then) conditions using this single constraint?

Re: PROC OPTMODEL problem to be infeasible

RobPratt — Thu, 31 Aug 2023 18:36:40 GMT

Not sure I follow. Do you mean that you want to use a logical condition with respect to the input data to determine whether to impose a single constraint?

Re: PROC OPTMODEL problem to be infeasible

Kaushansky — Thu, 31 Aug 2023 18:42:03 GMT

Meaning - could I do this:

con Mycon1 {sum {j in OBS} Optimized_Budget[j]='Offsite Display Walmart Network'}: Optimized_Budget[i]<=200000;

Re: PROC OPTMODEL problem to be infeasible

RobPratt — Thu, 31 Aug 2023 18:56:20 GMT

No, that syntax will yield errors, and the logical condition compares a sum of decision variables to a string, so it would never be true.

Do you maybe want the following?

con Mycon1: sum {i in OBS: Media_Tactics[i]='Offsite Display Walmart Network'} Optimized_Budget[i] <= 200000;

If not, what is the business rule that you are trying to enforce?

Re: PROC OPTMODEL problem to be infeasible

Kaushansky — Thu, 31 Aug 2023 19:01:52 GMT

Here's the example of data I am trying to model:

I would like to set a global constraint for Media_Tactics Offsite Display Walmart Network to be less than $350K, but also additional sub-constraints Campaign_Line_Item criteria.

Media_Tactics	Campaign_Line_Item	Input_Budget
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Standard Audience\|In Market Ornaments\|47490\|7974158	$ 25,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Custom Audience\|Ornaments Heavy Spenders\|47490\|7974159	$ 30,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Propensity Audience\|Ornaments\|47490\|7974160	$ 30,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Standard Audience\|Persona Gifters\|47490\|7974165	$ 25,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Custom Audience\|Ornaments Previous Purchasers\|47490\|7974169	$ 25,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Custom Audience\|Collectibles Heavy Spenders\|47490\|7974171	$ 25,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Custom Audience\|Families with Kids+Previous Ornaments Purchasers\|47490\|7974174	$ 25,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Propensity Audience\|Gifting Supplies\|47490\|7974175	$ 25,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Custom Audience\|Nov&DecShoppers\|47490\|7974178	$ 25,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Custom Audience\|GenZMillenial&PopCulture\|47490\|7974179	$ 20,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Custom Audience\|Heavy Spenders Home Decor\|47490\|8003807	$ 20,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Propensity Audience\|Holiday Decor\|47490\|8005360	$ 25,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Standard Audience\|In Market Christmas\|47490\|7974163	$ 25,000.00
Offsite Display Walmart Network	Walmart DSP\|Display\|Cross Device\|Custom Audience\|Contextual Holidays and Celebrations\|47490\|7974199	$ 20,000.00
Offsite Display Walmart Network	Walmart DSP\|Pre-roll\|Cross Device\|Standard Audience\|In Market Ornaments\|47490\|7974313	$ 20,000.00
Offsite Display Walmart Network	Walmart DSP\|Pre-roll\|Cross Device\|Propensity Audience\| Ornaments\|47490\|7974314	$ 20,000.00
Offsite Display Walmart Network	Walmart DSP\|Pre-roll\|Cross Device\|Custom Audience\|Ornaments Heavy Spenders\|47490\|7974315	$ 20,000.00

Re: PROC OPTMODEL problem to be infeasible

RobPratt — Thu, 31 Aug 2023 20:16:52 GMT

OK, I think you want the following:

con Mycon1: sum {i in OBS: Media_Tactics[i]='Offsite Display Walmart Network'} Optimized_Budget[i] <= 350000;

con Mycon2 {j in CAMPAIGNS}: sum {i in OBS: Campaign_Line_Item[i]=j} Optimized_Budget[i] <= Input_Budget[j];

Re: PROC OPTMODEL problem to be infeasible

Kaushansky — Thu, 31 Aug 2023 20:26:20 GMT

Got it.

So this will ensure that:

1. Overall Offsite Display Walmart Network will be less/eq $350K

2. Campaign_Line_Item = to something can be > $50K if needed?

Re: PROC OPTMODEL problem to be infeasible

RobPratt — Thu, 31 Aug 2023 21:27:49 GMT

Yes, as long as 50000 is <= Input_Budget[j] for campaign j.

Re: PROC OPTMODEL problem to be infeasible

Kaushansky — Fri, 01 Sep 2023 19:43:58 GMT

This is giving me an error? Do you know why?

con Mycon9: sum {i in OBS: Campaign_Line_Item[i] in

187 ('Walmart DSP|Display|Cross Device|Standard Audience|In Market

187 ! Christmas|47490|7974163'

188 ,'Walmart DSP|Display|Cross Device|Custom Audience|Heavy Spenders Home

188 ! Decor|47490|8003807'

ERROR 22-322: Syntax error, expecting one of the following: !, !!, &, ), *, **, +, -, .., /,

<, <=, <>, =, >, ><, >=, AND, BY, CROSS, DIFF, ELSE, IN, INTER, NOT, OR,

SYMDIFF, TO, UNION, WITHIN, ^, ^=, |, ||, ~, ~=.

ERROR 76-322: Syntax error, statement will be ignored.

189 ,'Walmart DSP|Display|Cross Device|Propensity Audience|Holiday

189 ! Decor|47490|8005360'

190 ,'Walmart DSP|Display|Cross Device|Propensity

190 ! Audience|Ornaments|47490|7974160'

191 ,'Walmart DSP|Display|Cross Device|Custom

191 ! Audience|Nov&DecShoppers|47490|7974178'

192 ,'Walmart|Display|Cross Device|Contextual Targeting|Holiday

192 ! Decor|CY23|47490|7974064')} Optimized_Budget[i] <= 140000;

193

194 /*-------------------------------------------------------------------------*/

195 /* CONDITIONAL CONSTRAINTS BY Tactic Specific Mininums and Maximums */

196 /*-------------------------------------------------------------------------*/

197

198 /* OVERALL MAXIMUM SPEND BY TACTIC -> Ensure every tactic has at LEAST a certain %

198 ! of the Input Budget contraint */

199 con Mycon2: sum {i in OBS: Media_Tactics[i]='Offsite Display Walmart Network'}

199 ! Optimized_Budget[i] <= 450000;

200 con Mycon3: sum {i in OBS: Media_Tactics[i]='Offsite Display Social Media'}

200 ! Optimized_Budget[i] <= 60000;

201 con Mycon4: sum {i in OBS: find(Campaign_Line_Item[i],'Pre-roll')<=0}

201 ! Optimized_Budget[i] >= 100000;

202

203 *con Mycon8: sum {i in OBS: find(Media_Tactics[i],'In Market

203 ! Christmas|47490|7974163')>0 or

204 find(Media_Tactics[i],'Standard Audience|In Market

204 ! Christmas|47490|7974163')>0 or

205 find(Media_Tactics[i],'Audience|Heavy Spenders Home Decor|47490|8003807')>0

205 ! or

206 find(Media_Tactics[i],'Audience|Holiday Decor|47490|8005360')>0 or

207 find(Media_Tactics[i],'Audience|Ornaments|47490|7974160')>0 or

208 find(Media_Tactics[i],'Audience|Nov&DecShoppers|47490|7974178')>0 or

209 find(Media_Tactics[i],'Targeting|Holiday Decor|CY23|47490|7974064')>0}

209 ! Optimized_Budget[i] <= 140000;

Re: PROC OPTMODEL problem to be infeasible

RobPratt — Fri, 01 Sep 2023 20:16:39 GMT

You have parentheses where you should instead use curly braces. Here is correct syntax:

con Mycon9: sum {i in OBS: Campaign_Line_Item[i] in
{'Walmart DSP|Display|Cross Device|Standard Audience|In Market Christmas|47490|7974163'
,'Walmart DSP|Display|Cross Device|Custom Audience|Heavy Spenders Home Decor|47490|8003807'
,'Walmart DSP|Display|Cross Device|Propensity Audience|Holiday Decor|47490|8005360'
,'Walmart DSP|Display|Cross Device|Propensity Audience|Ornaments|47490|7974160'
,'Walmart DSP|Display|Cross Device|Custom Audience|Nov&DecShoppers|47490|7974178'
,'Walmart|Display|Cross Device|Contextual Targeting|Holiday Decor|CY23|47490|7974064'}} Optimized_Budget[i] <= 140000;

I recommend instead defining the set separately to make the code easier for human consumption:

set CAMPAIGNS = {'Walmart DSP|Display|Cross Device|Standard Audience|In Market Christmas|47490|7974163'
,'Walmart DSP|Display|Cross Device|Custom Audience|Heavy Spenders Home Decor|47490|8003807'
,'Walmart DSP|Display|Cross Device|Propensity Audience|Holiday Decor|47490|8005360'
,'Walmart DSP|Display|Cross Device|Propensity Audience|Ornaments|47490|7974160'
,'Walmart DSP|Display|Cross Device|Custom Audience|Nov&DecShoppers|47490|7974178'
,'Walmart|Display|Cross Device|Contextual Targeting|Holiday Decor|CY23|47490|7974064'};

con Mycon9: sum {i in OBS: Campaign_Line_Item[i] in CAMPAIGNS} Optimized_Budget[i] <= 140000;