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Product Mix Optimization Case Study - OPL/ CPLEX Code
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).
3.
3© 2013 OptiRisk
India (P) Ltd, All rights reserved 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-------------
10.
10© 2013 OptiRisk
India (P) Ltd, All rights reserved Model Code ResultsDebug Project Explorer
11.
Asia Pacific, Africa,
Australia & Middle East: Europe & America: No 12, 25th Cross Street Thiruvalluvar Nagar , Thiruvanmiyur, Chennai –600041, India OptiRisk R&D House, One Oxford, Uxbridge, Middlesex, UB9 4DA, United Kingdom Bala. Padmakumar Ph: +91 98406 18472 / +91 44 4501 8472 Email: optimize@optiriskindia.com Web: http://www.optiriskindia.com/ 11© 2013 OptiRisk India (P) Ltd, All rights reserved Development Center: Corporate Head Quarters: No 1/4 , Justice Dwarkanath Road, Kolkata - 700020, India.
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