First a clarification about BY-group processing for other users who do have SAS Viya: the BY statement for PROC OPTNETWORK does not apply when there are multiple input tables, as in this use case.  The groupBy parameter for runOptmodel applies for any number of tables.   Regarding the objective being a sum of groups, when you have a bunch of disjoint problems like this, it is mathematically equivalent to solve them individually or together as one big problem.  But it is usually computationally better (both time and memory) to solve them individually, and the decomp=(method=concomp), algorithm=ns, and solve with network approaches all automatically split the big problem into one problem per group.  All the approaches I have illustrated yield the same optimal objective value of 9069.4.   In SAS 9.4, the most memory-efficient approach is to use PROC OPTNET (which for minimum-cost network flow problems calls the same network simplex algorithm): /* node data */ proc sql; create table lib.group_subject as select distinct group, subject, cat(group,'_',subject) as node, 1 as weight from lib.have; quit; data lib.group_area; set lib.have_constraints; node = cat(group,'_',area); weight = -n; run; data NodeSetIn; set lib.group_subject lib.group_area; run; /* link data */ data LinkSetIn; set lib.have; from = cat(group,'_',subject); to = cat(group,'_',area); run; proc optnet direction=directed nodes=NodeSetIn links=LinkSetIn out_links=out_links; links_var weight=distance; mincostflow; run; But for large enough data, you will run out of memory.  So I recommend splitting your 10k groups into smaller batches and calling PROC OPTNET once per batch. ... View more

For the syntax issue, the logical condition must appear last in the index set, and here are two correct approaches: /* sum {i in ISN:T2_ISN[ i]=w,b in BOX} */ sum {i in ISN: T2_ISN[i]=w} sum {b in BOX} sum {i in ISN, b in BOX: T2_ISN[i]=w}   For the second CREATE DATA statement, you want only the w for that i: /* (where=(VolShare>0)) from [ISN=i BoxType=b T2=w]={i in ISN, b in BOX, w in T2: BOXNeeded_CFS[b,w] > 0.5}*/ (where=(VolShare>0)) from [ISN=i BoxType=b T2=w]={i in ISN, b in BOX, w in {T2_ISN[i]}: BOXNeeded_CFS[b,w] > 0.5}   For the remaining modeling issues, I recommend writing out the values of all decision variables and the resulting costs for a toy example, like you did in the spreadsheet before.  It is not clear to me what you want Proportion_CFS[b,w] to be, and I suspect you might instead want Proportion_CFS[i,b], where w = T2_ISN[i]. ... View more

Here are several comments and corrections.   1. You also need new unique_t1, unique_t2, and unique_box tables.   2. The num Is_BoxAvalable_for_a_lane parameter is declared and populated but not used in the optimization model.   3. The following IMPVAR declaration cannot be correct because it does not link i to b or w.  In particular, you want only the i for which T2_ISN[i] = w. impvar VolumeInsideBox_CFS {b in BOX, w in T2} = sum{i in ISN} Volume_ISN[i] * Proportion_CFS[b,w];   4. You do not need to sum over m here: /* impvar PerBox_Based_Costs_CYS {i in ISN} = sum {b in BOX,m in {'CYS'}}*/ impvar PerBox_Based_Costs_CYS {i in ISN} = sum {b in BOX} PerBox_Based_Rate[Org_ISN[i],Des_ISN[i],b,'CYS',T1_ISN[i],T2_ISN[i]] * BOXNeeded_CYS[i,b];   5. You do not need Proportion_CYS or Is_ISN_MOL here, and removing them avoids nonlinearity: /* impvar VolBasedCost_CYS {i in ISN, b in BOX} = VolumeInsideBox_CYS[i,b] * Proportion_CYS[i,b] * */ /* sum {<Org_ISN[i],Des_ISN[i],m,T1_ISN[i],T2_ISN[i]> in PerVol_Based_Rate_NoZeroes} */ /* PerVol_Based_Rate[Org_ISN[i],Des_ISN[i],'CYS',T1_ISN[i],T2_ISN[i]] * Is_ISN_MOL[i,'CYS'];*/ impvar VolBasedCost_CYS {i in ISN, b in BOX} = sum {<Org_ISN[i],Des_ISN[i],m,T1_ISN[i],T2_ISN[i]> in PerVol_Based_Rate_NoZeroes} PerVol_Based_Rate[Org_ISN[i],Des_ISN[i],'CYS',T1_ISN[i],T2_ISN[i]] * VolumeInsideBox_CYS[i,b];   6. Similar comment here, but the VolumeInsideBox[b,w] variable doesn't depend on i, so I suspect you want a different coefficient: /* impvar VolBasedCost_CFS {b in BOX, w in T2} = sum{i in ISN} VolumeInsideBox_CFS[b,w] * Proportion_CFS[b,w] * */ /* sum {<Org_ISN[i],Des_ISN[i],m,T1_ISN[i],T2_ISN[i]> in PerVol_Based_Rate_NoZeroes} */ /* PerVol_Based_Rate[Org_ISN[i],Des_ISN[i],'CFS',T1_ISN[i],T2_ISN[i]] * Is_ISN_MOL[i,'CFS'];*/ impvar VolBasedCost_CFS {b in BOX, w in T2} = sum{i in ISN} sum {<Org_ISN[i],Des_ISN[i],m,T1_ISN[i],T2_ISN[i]> in PerVol_Based_Rate_NoZeroes} PerVol_Based_Rate[Org_ISN[i],Des_ISN[i],'CFS',T1_ISN[i],T2_ISN[i]] * VolumeInsideBox_CFS[b,w];   7. You do not need both Proportion_CYS and Is_ISN_MOL here, but I don't know which one you want because in the toy example each shipment happened to use only one box. impvar ShipmentBasedCost_CYS {i in ISN, b in BOX} = Proportion_CYS[i,b] * sum {<Org_ISN[i],Des_ISN[i],m,T1_ISN[i],T2_ISN[i]> in PerShp_Based_Rate_NoZeroes} PerShp_Based_Rate[Org_ISN[i],Des_ISN[i],'CYS',T1_ISN[i],T2_ISN[i]] * Is_ISN_MOL[i,'CYS'];   8. Similar comment to #3 and #7: impvar ShipmentBasedCost_CFS {b in BOX, w in T2} = sum{i in ISN} Proportion_CFS[b,w] * sum {<Org_ISN[i],Des_ISN[i],m,T1_ISN[i],T2_ISN[i]> in PerShp_Based_Rate_NoZeroes} PerShp_Based_Rate[Org_ISN[i],Des_ISN[i],'CFS',T1_ISN[i],T2_ISN[i]] * Is_ISN_MOL[i,'CFS'];   9. Avoid nonlinearity: con SumProportionToOne_CYS {i in ISN}: /* sum {b in BOX} VolumeInsideBox_CYS[i,b]= sum {b in Box}Volume_ISN[i] * Proportion_CYS[i,b] * IS_ISN_MOL[i,'CYS'];*/ sum {b in BOX} Proportion_CYS[i,b] = IS_ISN_MOL[i,'CYS']; con SumProportionToOne_CFS {w in T2}: /* sum {b in BOX} VolumeInsideBox_CFS[b,w]= sum {i in ISN,b in Box}Volume_ISN[i] * Proportion_CFS[b,w] * IS_ISN_MOL[i,'CFS'];*/ sum {b in BOX} Proportion_CFS[b,w] = 1;   10. This constraint needs to hold for each b, not a sum over b: /* con BoxConCFS {w in T2}:*/ /* sum {b in BOX} Volume_Capacity_CFS[b,w] * BOXNeeded_CFS[b,w] >= sum {b in BOX} TotalVol['CFS',w] * VolumeInsideBox_CFS[b,w];*/ con BoxConCFS {w in T2, b in BOX}: Volume_Capacity_CFS[b,w] * BOXNeeded_CFS[b,w] >= VolumeInsideBox_CFS[b,w];   11. Both CREATE DATA statements refer to parameters that are not defined: /* VolBasedCost=VolBasedCost[i] */ VolBasedCost=VolBasedCost_CYS[i,b] /* VolBasedCost=VolBasedCost[i] */ VolBasedCost=VolBasedCost_CFS[b,w]   I recommend working these issues out with the toy data before attempting to solve with your full data. ... View more

Here is code to replicate the summary info for the toy example: create data SolutionDataCYS from [ISN=i BoxType=b]={i in ISN, b in BOXES: NumBoxesCYS[i,b] > 0.5} MOL='CYS' Org=Org_ISN[i] Des=Des_ISN[i] T1=T1_ISN[i] T2=T2_ISN[i] Volume=Volume_ISN[i] Weight=Weight_ISN[i] BoxNeeded=NumBoxesCYS Vol_InsideBox=Volume_ISN[i] VolShare=1 BoxBasedCost=(boxRate[b]*NumBoxesCYS[i,b]) VolBasedCost=0 ShipmentBasedCost=shipmentRate['CYS'] VolCapacity=(volCapacity[b]*NumBoxesCYS[i,b]); create data SolutionDataCFS(where=(VolShare>0)) from [ISN=i BoxType=b]={i in ISN, b in BOXES: NumBoxesCFS[b] > 0.5} MOL='CFS' Org=Org_ISN[i] Des=Des_ISN[i] T1=T1_ISN[i] T2=T2_ISN[i] Volume=Volume_ISN[i] Weight=Weight_ISN[i] BoxNeeded=(volShareCFS[i]*NumBoxesCFS[b]) Vol_InsideBox=Volume_ISN[i] VolShare=volShareCFS[i] BoxBasedCost=(volShareCFS[i]*boxRate[b]*NumBoxesCFS[b]) VolBasedCost[i] ShipmentBasedCost=0 VolCapacity=(volCapacity[b]*NumBoxesCFS[b]); quit; data SolutionData; set SolutionDataCYS SolutionDataCFS; Total = BoxBasedCost + VolBasedCost + ShipmentBasedCost; Utilization = Volume/VolCapacity; run; proc print data=SolutionData; sum _numeric_; run; Obs ISN BoxType MOL Org Des T1 T2 Volume Weight BoxNeeded Vol_InsideBox VolShare BoxBasedCost VolBasedCost ShipmentBasedCost VolCapacity Total Utilization 1 V1 40H CYS SHA ATL D1 W1 130 304 2.00000 130 1.00000 2400.00 0 50 138 2450.00 0.94203 2 V2 40F CFS SHA ATL D1 W1 42 491 0.97674 42 0.97674 976.74 168 0 60 1144.74 0.70000 3 V8 40F CFS SHA ATL D2 W1 1 2 0.02326 1 0.02326 23.26 4 0 60 27.26 0.01667                 173 797 3.00000 173 2.00000 3400.00 172 50 258 3622.00 1.65870 ... View more

Please supply the tables you are using based on the toy example. ... View more

1.  Please see my response here: https://communities.sas.com/t5/Mathematical-Optimization/AssetOptimization-Contd/m-p/885516/highlight/true#M3957 2. Do you still need to account for capacity and minThreshold for both volume and weight?  Your latest code uses only volume capacity. 3. If the solution uses more than one box type per shipment, do you want multiple rows for that shipment? 4. That syntax error about IMPLIES means that you are not running a version that supports indicator constraints, which are available only in SAS Viya 4. ... View more

I made one more correction to RationalVendor in the toy code, and the new optimal solution has objective value $4304, with both V1 and V2 using CYS.  Note that for the $3622 solution in your spreadsheet, vendor V2 does not behave rationally because the CYS cost is $1050 < $1145, so V2 would instead choose CYS.  On the other hand, $3622 is still the correct optimal objective value if the vendors cooperate.   Regarding your question (c), I think this is what you want: impvar PerBox_Based_Costs_CFS {w in T2} = sum {b in BOX} PerBox_Based_Rate_CFS[b,w] * BoxesNeeded_CFS[b,w]; impvar TotalVol {m in MOL, w in T2} = sum {i in ISN} Volume_ISN[i] * Is_ISN_Mol[i,m,w]; con BoxConCFS {w in T2}: sum {b in BOX} Volume_Capacity_CFS[b,w] * BoxesNeeded_CFS[b,w] >= TotalVol['CFS',w];   ... View more

Sorry for the confusion about the RationalVendor constraint.  I had mistakenly considered only the volume-based costs and neither the box costs nor shipment costs.  I have now updated the code to correctly account for these.  The constraint enforces the rule that, if a vendor uses CFS, the resulting volume-prorated cost for that vendor must be at most the optimal CYS cost for that vendor.  I also imposed explicit upper bounds on the NumBoxesCYS and NumBoxedCFS variables to make the resulting (automatically generated) big-M constraints more numerically stable.   If you instead want to allow the vendors to cooperate to minimize overall cost (even it means that some individual vendor might have been better off with CYS), just omit the FIX/UNFIX statements and the RationalVendor constraint and solve once.   Yes, you will still need Proportion to account for the weight-based restrictions in your full problem. ... View more

Thank you for providing the toy example, which is very helpful for understanding the problem.  If all 3 shipments use CFS, then 3 boxes of 40F (rather than 40H) would be cheaper and still cover the volume (since 180 >= 173), with a total cost of $3692.  But your third solution is still the cheapest, with total cost $3622.   Please clarify whether the vendors cooperate to minimize the overall cost or whether a vendor is able to choose CYS because it reduces that vendor's cost even if it makes the overall cost higher. ... View more

The error in your new CREATE DATA statement is that you used the wrong index set for the logical condition: create data OptMix_RESULTS_Vol(where=(Proportion > 0)) from [ISN=i BOX=b MOL=m T1=d T2=w]={i in ISN, b in BOX,m in MOL,d in T1,w in T2: <Org_ISN[i],Des_ISN[i],b,m,d,w> in PerBox_Based_Rate_NoZeroes} It should instead be: create data OptMix_RESULTS_Vol(where=(Proportion > 0)) from [ISN=i BOX=b MOL=m T1=d T2=w]={i in ISN, b in BOX,m in MOL,d in T1,w in T2: <Org_ISN[i],Des_ISN[i],b,m,d,w> in PerVol_Based_Rate_NoZeroes} Also, with your latest data, I get an objective value of 49,600 rather than 24,800.   But I think these data and syntax issues are distracting from what seems to be your main concern, which is how to mathematically model the problem.  For that purpose, I recommend taking an even smaller instance (maybe one week and two days) and writing out a feasible (not necessarily optimal) plan: how much of what will go where and when, and how much would it cost?  That will help you see what the decision variables, constraints, and objective should be.  After you have constructed the optimization model, converting to PROC OPTMODEL code will be much simpler. ... View more

With the additional data you provided, I am able to run the code now.  The third CREATE DATA statement yields an error because the macro variables CUST and SCNAME are not defined, so I have just commented those two lines out for now.   The log shows several warnings related to the READ DATA for InputData_AssetMix: 0 read data CASUSER.InputData_AssetMix into ISN=[ISN] Org_ISN=ORG Des_ISN=DES 30 ! Volume_ISN=Volume Weight_ISN=Weight T1_ISN=T1 T2_ISN=T2; WARNING: Duplicate key <SHA_ATL_V1_D1_W1> was read at observation 14. WARNING: Duplicate key <SHA_ATL_V2_D1_W1> was read at observation 15. WARNING: Duplicate key <SHA_ATL_V3_D1_W1> was read at observation 16. WARNING: Duplicate key <SHA_ATL_V4_D1_W1> was read at observation 17. WARNING: Duplicate key <SHA_ATL_V5_D1_W1> was read at observation 18. WARNING: Duplicate key <SHA_ATL_V6_D1_W1> was read at observation 19. WARNING: Duplicate key <SHA_ATL_V7_D1_W1> was read at observation 20. WARNING: Duplicate key <SHA_ATL_V8_D1_W1> was read at observation 21. WARNING: Duplicate key <SHA_ATL_V9_D1_W1> was read at observation 22. WARNING: Duplicate key <SHA_ATL_V10_D1_W1> was read at observation 23. WARNING: Duplicate key <SHA_ATL_V11_D1_W1> was read at observation 24. WARNING: Duplicate key <SHA_ATL_V12_D1_W1> was read at observation 25. WARNING: Duplicate key <SHA_ATL_V13_D1_W1> was read at observation 26. NOTE: 13 duplicate keys were read. NOTE: There were 26 observations read from the data set CASUSER.INPUTDATA_ASSETMIX. You are using the ISN column as a key, but the last 13 observations have the same values of ISN as the first 13 observations.  If you add a PUT ISN= statement after this, you can see that only 13 observations are used: ISN={'SHA_ATL_V1_D1_W1','SHA_ATL_V2_D1_W1','SHA_ATL_V3_D1_W1','SHA_ATL_V4_D1_W1', 'SHA_ATL_V5_D1_W1','SHA_ATL_V6_D1_W1','SHA_ATL_V7_D1_W1','SHA_ATL_V8_D1_W1','SHA_ATL_V9_D1_W1', 'SHA_ATL_V10_D1_W1','SHA_ATL_V11_D1_W1','SHA_ATL_V12_D1_W1','SHA_ATL_V13_D1_W1'} If you print T1_ISN and T2_ISN, you can see that it is the last 13 observations (exactly the ones with T2 = W2): [1] T1_ISN T2_ISN SHA_ATL_V10_D1_W1 D6 W2 SHA_ATL_V11_D1_W1 D6 W2 SHA_ATL_V12_D1_W1 D6 W2 SHA_ATL_V13_D1_W1 D6 W2 SHA_ATL_V1_D1_W1 D4 W2 SHA_ATL_V2_D1_W1 D4 W2 SHA_ATL_V3_D1_W1 D5 W2 SHA_ATL_V4_D1_W1 D5 W2 SHA_ATL_V5_D1_W1 D5 W2 SHA_ATL_V6_D1_W1 D5 W2 SHA_ATL_V7_D1_W1 D6 W2 SHA_ATL_V8_D1_W1 D6 W2 SHA_ATL_V9_D1_W1 D6 W2 Furthermore, the values in the T1 and T2 columns in the InputData_AssetMix table do not match the ISN column.  For example, observation 6 has ISN = SHA_ATL_V7_D1_W1 but T1 = D2 rather than D1.  I suspect that the last part of each ISN value should instead match T1 and T2.   Before I investigate any further, please confirm whether this table is correct. ... View more

Thank you for attaching the additional data.  I will not have a chance to look at this again until tomorrow afternoon.  Although you addressed the question to me, anybody in the community is welcome to respond. ... View more