Reliability allocation problem is commonly treated using a closed-form expression relating the cost to reliability. A recent approach has introduced the use of discrete integer technique for un-repairable systems. Thi...Reliability allocation problem is commonly treated using a closed-form expression relating the cost to reliability. A recent approach has introduced the use of discrete integer technique for un-repairable systems. This research addresses the allocation problem for repairable systems. It presents an integer formulation for finding the optimum selection of components based on the integer values of their Mean Time to Failure （MTTF） and Mean Time to Repair （MTTR）. The objective is to minimize the total cost under a system reliability constraint, in addition to other physical constraints. Although, a closed-form expression relating the cost to reliability may not be a linear; however, in this research, the objective function will always be linear regardless of the shape of the equivalent continuous closed-form function. An example is solved using the proposed method and compared with the solution of the continuous closed-form version. The formulation for all possible system configurations, components and subsystems are also considered.展开更多
Roadway design usually involves choices regarding grade selection and earthwork (transportation) that can be solved using linear programming. Previous work considered the road profile as series of interconnected linea...Roadway design usually involves choices regarding grade selection and earthwork (transportation) that can be solved using linear programming. Previous work considered the road profile as series of interconnected linear segments. In these models, constraints are included in the linear programming formulation to insure continuity of the road, which cause sharp connectivity points at the intersection of the linear segments. This sharp connectivity needs to be smoothed out after l;he linear programming solution is found and the earth in the smoothed portion of the roadway has to be moved to the landfill. In previous research, the smoothing issue is dealt with after an optimal solution is found. This increases the work required by the design engineer and consequently increases the construction cost; furthermore, the optimal solution is violated by this smoothing operation. In this paper, the issue of sharp connectivity points is resolved by representing the road profile by a quadratic function. The continuity constraints are dropped (unneeded) and global optimality is guaranteed. Moreover, no violation is incurred to implement the optimum results. Although a quadratic function is used to represent the road profile, the mathematical model is purely linear in nature.展开更多
文摘Reliability allocation problem is commonly treated using a closed-form expression relating the cost to reliability. A recent approach has introduced the use of discrete integer technique for un-repairable systems. This research addresses the allocation problem for repairable systems. It presents an integer formulation for finding the optimum selection of components based on the integer values of their Mean Time to Failure （MTTF） and Mean Time to Repair （MTTR）. The objective is to minimize the total cost under a system reliability constraint, in addition to other physical constraints. Although, a closed-form expression relating the cost to reliability may not be a linear; however, in this research, the objective function will always be linear regardless of the shape of the equivalent continuous closed-form function. An example is solved using the proposed method and compared with the solution of the continuous closed-form version. The formulation for all possible system configurations, components and subsystems are also considered.
文摘Roadway design usually involves choices regarding grade selection and earthwork (transportation) that can be solved using linear programming. Previous work considered the road profile as series of interconnected linear segments. In these models, constraints are included in the linear programming formulation to insure continuity of the road, which cause sharp connectivity points at the intersection of the linear segments. This sharp connectivity needs to be smoothed out after l;he linear programming solution is found and the earth in the smoothed portion of the roadway has to be moved to the landfill. In previous research, the smoothing issue is dealt with after an optimal solution is found. This increases the work required by the design engineer and consequently increases the construction cost; furthermore, the optimal solution is violated by this smoothing operation. In this paper, the issue of sharp connectivity points is resolved by representing the road profile by a quadratic function. The continuity constraints are dropped (unneeded) and global optimality is guaranteed. Moreover, no violation is incurred to implement the optimum results. Although a quadratic function is used to represent the road profile, the mathematical model is purely linear in nature.
