Number Of Capacity Constraints Research Articles

Hybrid capacity modeling for alternative machine types in linear programming production planning

Processing by alternative machines is very common in today's manufacturing environment, especially in the semiconductor industry. Leachman and Carmon (1992) have presented a novel approach to model alternative machine capacitated problems for Linear Programming (LP) production planning. Their approach makes possible the modeling of complex processes with re-entry into alternative machines in large scale LP production planning. However, there are difficulties in using their approach in industrial applications. In order to use their approach, a uniform assumption must be satisfied. But in many industrial applications, this assumption cannot be satisfied. In addition, their approach creates new alternative machine sets by performing union operations on existing alternative machine sets with common machine types. This will increase the number of capacity constraints, which may increase the solution time of the LP formulation. This study compares their approach and the partition approach outlined herein in terms of CPU times used. Finally, this study proposes a hybrid capacity modeling approach that is more suitable for industrial applications.

Hybrid capacity modeling for alternative machine types in linear programming production planning

Processing by alternative machines is very common in today's manufacturing environment, especially in the semiconductor industry. Leachman and Carmon (1992) have presented a novel approach to model alternative machine capacitated problems for Linear Programming (LP) production planning. Their approach makes possible the modeling of complex processes with re-entry into alternative machines in large scale LP production planning. However, there are difficulties in using their approach in industrial applications. In order to use their approach, a uniform assumption must be satisfied. But in many industrial applications, this assumption cannot be satisfied. In addition, their approach creates new alternative machine sets by performing union operations on existing alternative machine sets with common machine types. This will increase the number of capacity constraints, which may increase the solution time of the LP formulation. This study compares their approach and the partition approach outlined herein in terms of CPU times used. Finally, this study proposes a hybrid capacity modeling approach that is more suitable for industrial applications.

A statistical analysis of the knapsack problem

We investigate the dependence of the multi-knapsack objective function on the knapsack capacities and on the number of capacity constraints P, in the case when all N objects are assigned the same profit value and the weights are uniformly distributed over the unit interval. A rigorous upper bound to the optimal profit is obtained employing the annealed approximation and then compared with the exact value obtained through the Lagrangian relaxation method. The analysis is restricted to the regime where N goes to infinity and P remains finite.