CPLEX solvers

The model was solved using GAMS and the CPLEX solver version 9.1.2. The computational results for case 1 are shown in are shown in Table 3.3. From these results it is clear to see the potential benefits for using the PIS operational philosophy, with a 50% increase in throughput. 

The performance of the presented formulation was tested by applying it to a literature example and an industrial case study. All solutions were obtained using the GAMS/CPLEX solver in a 1.4 GHz Pentium M processor. 

The MILP model had 7500 variables, of which 300 were binary and 7000 constraints. The mathematical model was coded in ILOG and solved using the CPLEX solver (www.ILOG.com). The solver reached optimality in 2 min. 

The basic supply chain model was a multi-period MILP. The binary variables identified whether a certain product was produced at a given plant. The continuous variables represented the annual volume in supply, production, and distribution. The objective function included fixed capital expenditure as well as variable costs for supply, production, and distribution. An example model in the case study had 6 plants, 36 products, and 8 sales regions for a 12 year planning horizon. The MILP model had 60,000 variables (2000 binary) and 145,000 constraints. The model was solved using the ILOG/CPLEX solver on a 1.6GHz processor injust4min ... 

The mathematical formulation was coded in ILOG and solved using a CPLEX solver. The optimization model consisted of approximately 7,500 variables, from which 300 were binary and around 7,000 were constraints. Three persons were involved in coding the models in ILOG and then using the CPLEX software to solve the problems. In general, optimal solutions were obtained very efficiently, taking less than three minutes for each scenario analysis to run. 

Under the profit maximization assumption, a single objective integer programming problem was solved using the ILOG CPLEX Solver. The optimal solution gave the best values of the decision variables (defined in Section 3.3.2)... 

The results for scenario 2 were obtained using GAMS 2.5/DICOPT. The NLP and MILP combination of solvers selected for DICOPT were MINOS5 and CPLEX, respectively. The overall formulation involves 421 constraints, 175 continuous variables and 36 discrete variables. Only 2 nodes were explored in the branch and... 

As in the previous case the solution procedure described in Sect. 4.4 was used to solve the example. The resulting models were formulated in GAMS 22.0, as with the previous case. CPLEX 9.1.2 was used to solve the MILP and the DICOPT2 solution algorithm was used to solve the exact MINLP. In the DICOPT solution algorithm, CLPEX 9.1.2 was the MIP solver and CONOPT3 the NLP solver. The same processor as the previous example was used to find a solution. 

The example was formulated in GAMS 22.0 and solved using the DICOPT2 solution algorithm, with CPLEX 9.1.2 as the MIP solver and CONOPT3 as the NLP solver. The model was solved using a Pentium 4 3.2 GHz processor and required 16.8 CPU seconds to find a solution. DICOPT did 4 major iterations to find the final solution. The optimal number of time points was 8, which resulted in 192 binary variables for the model. 

The model for the second illustrative example was formulated in GAMS 22.0 and solved using the DICOPT2 solution algorithm. The MIP solver used was CPLEX... 

A number of improvements that can be made to the branching rules will accelerate the convergence of this method. A comprehensive discussion of all these options can be found in Nemhauser and Wolsey (1988). Also, a number of efficient MILP codes have recently been developed, including CPLEX, OSL, XPRESS, and ZOOM. All these serve as excellent large-scale optimization codes as well. A detailed description and availability of these and other MILP solvere... 

The MINLP-model instances comprised 200 binary variables, 588 continuous variables and 1038 constraints. The linearization not only eliminates the nonlinearity but also leads to a reduced number of398 continuous variables and 830 constraints (the number of 200 binary variables is unchanged). The MINLP-problems were solved by the solver architecture DICOPT/CONOPT/CPLEX, and the MILP problems were solved by CP LEX, both on a Windows machine with an Intel Xeon 3 GHz CPU and 4 GB RAM. 

Since the program (DEP) represents a mixed-integer linear program (MILP), it can be solved by commercially available state-of-the-art MILP solvers like CPLEX [3] or XPRESS-MP [4], These solvers are based on implementations of modem branch-and-bound search algorithms with cuts and heuristics. 

In this section, the hybrid evolutionary algorithm described above is applied to a real-world scheduling problem under uncertainty. The performance of this algorithm is compared to that of the state-of-the-art MILP solver CPLEX and to that of... 

CPLEX, a highly advanced commercial MILP solver based on branch-and-bound with cuts and heuristics, and with automatic parameter adaptation is used to address the problem in the form of the large-scale deterministic equivalent program (DEP). After two minutes, the first feasible solution x = 0 with an objective of +29.7 was found. The next feasible solution was found after approximately 90 minutes. The best solution found after eight hours was -17.74. 

Two numerical examples adapted from [4,10] are supplied to demonstrate the efficacy of proposed HEN synthesis strategy. To solve this MO-MILP for the HEN model, GAMS [16] and CPLEX are used as the modeling environment and the MIP solver, respectively. The computing machine is a personal computer with an Intel Pentium IV 2.26 GHz CPU. 

ILOG CPLEX 8.100 IBM Provides flexible, high-performance mathematical programming solvers for linear programming (http //www-Ol.ibm.com/software/integration/ optimization/ cplex-optimizer/)... 

Software for MILP solver includes OSL, CPLEX, and XPRESS which use the LP-based BB algorithm combined with cutting plane techniques. MILP models and solution algorithms have been developed and applied successfully to many industrial problems (e.g. KaUrath, 2000). 

Solution method refers to the method applied to solve the proposed model e.g. (commercial) standard solvers [standard] (such as CPLEX or CONOPT), a specific optimization method [specific], a hierarchical decomposition approach [decomp.j, or a heuristioal procedure [heur.]. For simulation models, often a finite set of scenarios is evaluated and compared [seen.]. But also genetic algorithms are sometimes used for simulation optimzation [GA]. ... 

---