Linear programming problems with alternate solutions are challenging due to the choice of multiple stRategies resulting in the same Optimal value of the objective function. However, searching for these solutions is a tedious task, especially when using mixed integer linear programming (MILP), as previously applied to metabolic models. Therefore, judgment on plurality of Optimal metabolic flux distributions (solutions) a priori to applying MILP approach could prevent unnecessary computations. In this work for the first time, the reduced cost coefficients for the non-basic variables in a current solution of a metabolic model were utilized to inspect the possibility of multiple Optimal flux distributions.If there exists at least one non-basic variable with zero reduced cost coefficient, multiplicity of Optimal solution may occur where MILP can be used to find these solutions. This approach was implemented on a metabolic network of Bacillus subtilis aiming to reduce the cell energy requirement. Solving the model at fixed specific growth Rate of 0.4 1/h resulted in minimum energy requirement of 12.67 mmol/g-h.Inspection of reduced cost coefficients showed that six non-basic variables had zero reduced cost coefficients at current solution, which shows that there can exist multiple Optimal solutions. Subsequently, by applying MILP, five Optimal flux distributions at minimized energy requirement were identified, among which one showing no acid production and minimum glucose consumption Rate was selected as the superior solution.

In this paper, optimization of periodic Inspection interval for a two-component system with failure dependency is presented. Failure of the first component is soft, namely, it does not cause the system stop, but it increases the system operating costs. The second component’s failure is hard, i.e. as soon as it occurs, the system stops operating. Any failure of the second component increases the first component’s failure Rate. Failure of the first component is only detected if Inspection is performed. Thus, the first component is periodically inspected and if found failed, it is perfectly repaired and it is restored to as good as new. Failure of the second component is detected as soon as it occurs. Since this failure causes the system stop, it is immediately replaced. It is assumed that the time for replacement or repaired is negligible. We model the first component’s failure as a non-homogeneous Poisson process (NHPP) with increasing failure Rate and the second component’s failure as a homogeneous Poisson process (HPP) with constant failure Rate. The objective is to find the Optimal Inspection interval for the first component such that the expected total cost per unit time is minimized. A simplified numerical example along with sensitivity analysis on cost parameters is given.

Reliability centered maintenance is a tool for managing the maintenance of deteriorating assets. The basis of this method is the identification of failure mode of equipment, deterioration process, and maintenance scheduling to reduce the risk of failure and maintenance costs. One of the maintenance methods used in reliability-based maintenance is Inspection-based maintenance. In Inspection-based maintenance, a decision about the type of maintenance is made after an Inspection and determination of the deterioration status of equipment. In this paper, a model for annual maintenance scheduling of network equipment is provided. The scheduling problem is formulated as a probabilistic model with binary variables as Inspection times and the Optimal maintenance stRategy is determined. This model is implemented on a transformer and sensitivity analysis is performed to analyze the effect of Inspection and outage cost.

Process adjustment, also known as process targeting, is one of the classical problems in the field of quality control and production economics. In the process adjustment problem, it is assumed that process parameters are variables and the aim is to determine these parameters such that certain economic criteria are Optimally satisfied. The aim of this paper is to determine the Optimal process adjustment in a two-stage production system with rework loops. An absorbing Markov chain model is developed in which all items are inspected for conformance with their specification limits. The cycle time of production process is included in the model for optimizing total profit of the system. Also, effects of Inspection errors are investigated.

Optimal time interval between Inspections of the redundant systems is raised as a substantial issue to plan a preventive maintenance model for maintenance planners. To have an Optimal time period for preventive maintenance of systems, especially complex systems such as redundant systems, two variables of maintenance are mostly connived. Against other studies in the literature of preventive maintenance in which repair time is a negligible factor as an assumption, repair time is considered as a noticeable variable incorpoRated into the model developed in this paper. Another contribution, the number of facilities, is focused as a significant variable used in real applications. Particularly, systems with complex performance needing technical repair facilities (i.e., technical repairmen, tools, materials, outsourced repair, etc.). In this regard, parallel systems have been analyzed stochastically using the way of preventive maintenance in which repair time would be contemplated as an essential factor in maintenance planning. Using Markov chain, a model based on expected total cost per time is made to demonstRate that a proper time interval achieving lowest possible cost is obtained by taking into account repair time and the number of repair facility. Three models are studied as instances of redundant systems to find the Optimal time interval between Inspections. These models differ in the number of repair facilities (i.e., one, two and three repair facilities). A sensitivity analysis is done to depict the variability of input variables over Optimal the expected total cost per time and time interval between Inspections. As a main contribution, the repair time could be an essential factor in maintenance planning, this study contemplates this factor in redundant systems.

Introduction: X-ray is a high energy electromagnetic wave that can pass through many materials including human tissues. X-ray is one of the ionizing electromagnetic waves which have wide spectrums. The waves are used for different purposes including medicine, industrial applications, and research projects. One of the applications of Xray is using it in security screening system at airports. In these places, a lot of operator are exposed to Ionization radiations. In order to prevent the risk of exposure, It is necessary to control the X-ray radiation and also the operator must know the X-ray and its side effects on their body. Airport is on of the workplaces in which x-ray instruments are being used widely. The aim of this study was to measure the x-ray exposure among personnel of Inspection gate units.Methods and Materials: The x-ray machines which are available in Inspection gates at mehrabad airport are RAPISCAN and HEIMANN. In order to measure the Rate of x-ray level in different Inspection gates, the measurement of x-ray Rate was performed in men and women gats and in different conditions.Results: The total mean of measured x-ray was 2.68±0.73.At the exit of luggage (open situation), the mean of x-ray was 4.25±1.75 and close situation it was 2.5±1.2 At the beside of the machine, x-ray Rate was 1.3±0.07 The Rate of x-ray which was measured in men section and in women were 4.07±1.24 and 1.3±0.13, respectively. It must be added that total Rate of x-ray in RAPISCAN and HEIMANN machines were investigated 2.07±0.61 and 3.3±1.34, respectively.Discussion: The Rate of x-ray exposure in different positions was less than occupational standard level. Never the less, these limit, of x-ray would be harmful for health situation, it should be useful for personnel to be informed about safe working with x-ray machine that can reduce the risk of exposure.

Increase in government spending can lead to increase in production, supply of public goods and services as well as utility. However, it should be noted that increasing the role of government in the economy will cause crowding out of the private sector and this will reduce the utility.The present study is looking for Iran's Optimal growth Rate of government's spending using time series data in the years 1978-2014. via a dynamic Optimal control theory approach and the maximum principle.The results show that, the Optimal growth Rate of government’s expenditure is 7% and the main factors affecting this Rate is the ratio of private and public sector investment. Therefore, the current growth Rate of government’s spending is not Optimal and the government needs to control the growth Rate of spending especially current expenditure.

The Circuit Breaker (CB) is one of the most important equipment in power systems. CB must opeRate reliably to protect power systems as well as to perform tasks such as load disconnection, normal interruption, and fault current interruption. Therefore, the reliable operation of CB can affect the security and stability of power network. In this paper, effects of Condition Monitoring (CM) of CB on the maintenance process and related costs are analyzed. For this, A mathematical formulation to categorize and model equipment failures based on their severity is developed. By CM, some of the high severity failures, named major failures, can be early detected and be corrected as a minor failure. This formulation quantifies the effect of CM on the outage Rate and Predictive Maintenance (PDM) Rate of equipment. Also, by combining the predictive maintenance to preventive maintenance, the IntegRated Preventive and Predictive Maintenance Markov model is presented to analyze the effect of CM on the maintenance process. Finally, the Optimal Inspection Rates of CBs based on the minimum maintenance cost in the traditional and the proposed Markov model are determined. To verify the effectiveness and applicability of the method, the proposed approach is applied to the CBs of KREC in Iran.