The document discusses a chemical company that manufactures three chemicals through three processes. It aims to determine the optimal production quantity of each chemical to maximize total daily profit. The processes have limited daily capacities. Each chemical requires different processing times and contributes different profits per kg. An optimization model is formulated to maximize the total contribution subject to the capacity constraints of each process.

1. © 2013 OptiRisk India (P) Ltd, All rights reserved
Bala. Padmakumar
Director & CEO
OptiRisk India
Ph: +91 98406 18472/ +91 44 4501 8472
Web: http://www.optiriskindia.com
Email : optimize@optiriskindia.com

2. 2© 2013 OptiRisk India (P) Ltd, All rights reserved
XYZ Chemical Ltd manufactures three chemicals, namely CH-A, CH-B, and CH-C. All
three chemicals have to go through three processes namely MIXING, CONVERSION,
and BAGGING. Each process has finite daily capacity, which are given in the below
table. Each chemical requires different processing time, which are also given in the below
table.
Process
Production minutes per Kg of
product
Capacity of
production in
minutes per dayCH-A CH-B CH-C
MIXING
CONVERSION
BAGGING
2
3
1
2
1
4
1
1
0
400
450
390
Contribution /Kg Rs. 30 Rs. 55 Rs. 23
The company can sell whatever it produces (there is no constraint on demand). The
company’s management wants to find out how much of each chemical it should produce
to maximize the contribution (profit).

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Decision Variables:
= Number of Kgs of chemical p produced each day. p = 1, …, P
= Number of minutes per day available at process s.
ConstraintsConstraints
px
Constraints:
sC
= Number of minutes required by product p at production stage s. s = 1, …, S
= Profit per unit of product p
Parameters:
psa ,
pv
Objective Function:
z = Maximize total daily profit

4. 4© 2013 OptiRisk India (P) Ltd, All rights reserved
∑=
P
p
pp xv
1
∑=
≤
P
p
spps Cxa
1
,
0≥px for p = 1, …, P=Max num of products
for s = 1, …, S=Max num of processes
Subject to:
Maximize z =
Objective function
Maximize total contribution (profit)
Constraint
Process Capacity
Constraints
Non negativity
Constraint
Production quantity
must be non negative

5. 5© 2013 OptiRisk India (P) Ltd, All rights reserved
Subject to:
Maximize z =
Objective function
Maximize total contribution(profit)
Constraint
Process Capacity
Constraints
Non negativity
Constraint
Production quantity
must be non negative
321 22 xxx ++
3213 xxx ++
21 4xx +
0,0,0 321 ≥≥≥ xxx
321 235530 xxx ++
≤ 400
≤ 450
≤ 390

6. Objective function
Maximize Contribution
6© 2013 OptiRisk India (P) Ltd, All rights reserved
/*********************************************
* OPL 12.5 Model
* Author: OptiRisk
* Creation Date: 27-Aug-2013 at 10:02:32 AM
*********************************************/
// Input - indices
{string} Chemicals = ...;
{string} Processes = ...;
// Input parameters
float Capacity[Processes] = ...;
float ProcessTime[Chemicals][Processes] = ...;
float Contribution[Chemicals] = ...;
// Decision Variable
// Production Quantity of each Chemical
dvar float+ ChemicalQty[Chemicals];
// Objective Function
// Maximize total contribution
maximize
sum( p in Chemicals )
Contribution[p] * ChemicalQty[p];
Input Parameters
Decision Variables

7. Post Processing
Print Results
Constraint
Capacity Constraint
// Constraints
// 1. Capacity Constraints
subject to {
forall( s in Processes )
ctCapacity:
sum( p in Chemicals )
ProcessTime[p][s] * ChemicalQty[p] <= Capacity[s];
}
// Post processing to print results.
execute {
writeln("Maximum Contribution Possible = Rs. ",
cplex.getObjValue());
writeln("n----- RESULT: Optimal Product Mix---------");
// Print the optimal product quantities.
for( var p in Chemicals){
writeln(p, " ---> ", ChemicalQty[p], " Kgs");
}
writeln("n---- END: Optimal Product Mix-------------");
}
7© 2013 OptiRisk India (P) Ltd, All rights reserved

8. Input Data
Parameters
Index
/*********************************************
* OPL 12.5 Data
* Author: OptiRisk
* Creation Date: 27-Aug-2013 at 10:02:32 AM
*********************************************/
Chemicals = {"CH-A","CH-B","CH-C"};
Processes = {"MIXING", "CONVERSION", "BAGGING"};
// Capacity in minutes of each process
Capacity = [400, 450, 390];
// Processing time for each chemical, for every process
ProcessTime = [[2,3,1],[2,1,4],[1,1,0]];
// Contribution (profit) for each chemical
Contribution = [30, 55, 23];
8© 2013 OptiRisk India (P) Ltd, All rights reserved

9. 9© 2013 OptiRisk India (P) Ltd, All rights reserved
// solution (optimal) with objective 10077.5
Maximum Contribution Possible = Rs. 10077.5
----------- RESULT: Optimal Product Mix---------
CH-A ---> 0 Kgs
CH-B ---> 97.5 Kgs
CH-C ---> 205 Kgs
----------- END: Optimal Product Mix-------------
// solution (optimal) with objective 10077.5
Maximum Contribution Possible = Rs. 10077.5
----------- RESULT: Optimal Product Mix---------
CH-A ---> 0 Kgs
CH-B ---> 97.5 Kgs
CH-C ---> 205 Kgs
----------- END: Optimal Product Mix-------------

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Model Code
ResultsDebug
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Email: optimize@optiriskindia.com
Web: http://www.optiriskindia.com/
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