Integration of Fuzzy Lead Time and Network Reliability Evaluation of Stochastic Flow Networks

Network reliability evaluation for flow networks is an important issue in quality management. Many real-life systems can be modeled as stochastic-flow networks, in which each branch is multistate due to complete failure, partial failure, maintenance, etc. That is, each branch has several capacities with a probability distribution, and may fail. Hence, network reliability is the probability that a specified flow can be transmitted through the network successfully. Although there are many researches related to the evaluation of network reliability for a stochastic-flow network, how to assign a set of multistate components to the network so that the network reliability is maximal is never discussed. Therefore, this paper devotes to evaluating the optimal network reliability under components-assignments subject to a transmission budget, in which the transmission cost depends on each component's capacity. The network reliability under a components-assignment can be computed in terms of minimal paths, and state-space decomposition. Subsequently, we propose an optimization method based on a genetic algorithm. The experimental results show that the proposed method can be executed efficiently in a reasonable time.

Network reliability of a stochastic flow network by wrapping linear programming models into a Monte-Carlo simulation

The effect of lead time plays an important role in inventory management. It is also important to study the optimal strategies when the lead time is not precisely known to the decision makers. The aim of this paper is to examine the inventory model for deteriorating items with fuzzy lead time, negative exponential demand, and partially backlogged shortages. This model is unique in its nature due to probabilistic deterioration along with fuzzy lead time. The fuzzy lead time is assumed to be triangular, parabolic, trapezoidal numbers and the graded mean integration representation method is used for the defuzzification purpose. Moreover, three different types of probability distributions, namely uniform, triangular and Beta are used for rate of deterioration to find optimal time and associated total inventory cost. The developed model is validated numerically and values of optimal time and total inventory cost are given in tabular form, corresponding to different probability distribution and fuzzy lead-time. The sensitivity analysis is performed on variation of key parameters to observe its effect on the developed model. Graphical representations are also given in support of derived optimal inventory cost vs. time.

This article presents a mixed integer programming model for the design of global multi-echelon supply chains while considering lead time constraints. Indeed, we impose that the delivery lead time that can be promised by the company must be smaller than the lead time required by the customer. The delivery lead time is calculated based on the lead times of purchasing, manufacturing and transportation that are triggered by the customer order while considering the stock levels of purchased, intermediate and final products that must be kept at the different facilities. Computational studies are conducted in order to analyse the impacts of including lead times on the supply chain design decisions and to prove the solvability of the model.

In this paper, a new defuzzification method is proposed which can provide improved performance in fuzzy control for DC-DC converters. A comparative study of different defuzzification methods adopted in fuzzy logic control (FLC), such as center of area (COA), center of sums (COS), height method (HM), middle of maxims (MOM), center of largest area (COLA), and first of maxims (FM), for application to DC-DC buck-converters is presented. The distinction among the characteristics which lead to varying performance is outlined. A new method called height weighted second maxims (HWSM) is proposed and its performance is assessed. The paper also presents simulation results of the performance of the closed-loop converters from the standpoint of start-up transient, bad regulation and line regulation. The simulations show that COA, COS, and HM defuzzification methods have better dynamic performance and less steady state error. The new HWSM defuzzification method provides further improvement.

For inventory management purposes, lead time refers to the amount of time it takes for a purchase order to be completed. Its effect is an important phenomenon in inventory management system. It also plays a significant role when lead time unknown to the decision makers. This paper deals with an inventory model for deteriorating items under fuzzy lead time. The stock dependent demand with partially backlogged shortages are considered in the proposed model. The total inventory costs for both crisp model and fuzzy model are derived. The fuzzy lead time is assumed to be triangular and trapezoidal numbers. The signed distance methods (SD) is used for defuzzification purpose. The developed model is validated with the help of numerical illustration under both crisp and fuzzy scenario. A pictorial presentation is furnished to explain the behaviour of the total inventory costs towards lead-crisp, lead-triangular and lead-trapezoidal values. Lastly a sensitivity analysis is performed to judge the sensitive behaviour of the total cost towards changes of the cost parameters.

In order to make a better performance analysis and reliability evaluation of communication networks, a new definition of Delay-Reliability in communication networks, an algorithm to calculate approximate solutions of the Delay-Reliability in communication networks and a delay failure model in communication networks are presented in this paper. Inspired by the road resistance function in transportation networks, we analyze the similarities and differences between communication networks and transportation networks, and use OPNET simulation to build a new delay failure model in communication networks. Based on probabilistic user equilibrium model and our delay failure model, in stochastic-flow networks, we use discrete random variables to characterize delay in a single link and the link's degraded conditions to propose a new definition of Delay-Reliability in communication networks and its corresponding approximate algorithm. The approximate algorithm is especially useful and practical in large scale backbone network engineering due to its major computational advantage. For illustration, an example is given to show that our definition, algorithm and delay failure model can make a reasonable performance analysis and reliability evaluation of communication networks.

ABSTRACTThe ability to meet target production lead times is of fundamental importance in modern manufacturing systems producing perishable products, where the product quality or value deteriorates with the time parts spend in the system, and in manufacturing contexts where strict lead time constraints are imposed due to tight shipping schedules. In these settings, traditional manufacturing system engineering methods and token-based production control policies lose effectiveness as they aim at achieving target production rates while minimizing inventory, without directly taking into account the effect on the lead time distribution. In this article, a production control policy for unreliable manufacturing systems that aims at maximizing the throughput of parts that respect a given lead time constraint is proposed for the first time. The proposed policy jointly considers the actual level of the buffer and the state of the second machine in the system and stops the part loading at the first machine if there is unacceptable risk of exceeding the lead time constraint. The effectiveness of this new policy against the traditional kanban policy is quantified by numerical analysis. The results show that this new policy outperforms the kanban policy by providing a tighter control on the production lead time. This approach paves the way to the introduction of new lead time–oriented production control policies to maximize the effective throughput in real manufacturing systems.

Do lead time constraints only lead to re-think and re-optimise the inventory positioning along the supply chain or can they impact on the design of the supply chain itself? To answer such a question, we integrate the lead time constraints in a multi-echelon supply chain design model and challenge the difficulty of combining in the same model the long-term decisions (facility location, supplier selection) with the midterm decisions (inventory placement and replenishment, delivery lead time). The model guarantees the respect of the quoted lead time associated with each customer order and the replenishment of the different stocks (raw materials, intermediate and final products) in the different stages of the supply chain between any pair of consecutive orders. We use the model to investigate the impact of the quoted lead time and customer’s order frequency on supply chain design decisions and costs. Some of our results indicate that the lead time constraints can lead to bringing the sites of manufacturing and distribution close to the demand zone and to select local suppliers in spite of their higher cost.

This paper proposes a fuzzy multi-objective integer linear programming (FMOILP) approach to model a material requirement planning (MRP) problem with fuzzy lead times. The objective functions minimise the total costs, back-order quantities and idle times of productive resources. Capacity constraints are included by considering overtime resources. Into the crisp MRP multi-objective model, we incorporate the possibility of occurrence of each uncertain lead time using fuzzy numbers. Then FMOILP is transformed into an auxiliary crisp mixed-integer linear programming model by a fuzzy goal programming approach for each fuzzy lead time combination. In order to defuzzify the set of solutions associated with each fuzzy lead time combination, a solution method based on the centre of gravity concept is addressed. Model validation with a numerical example is carried out by a novel rolling horizon procedure where uncertain lead times are updated during each planning period according to the centre of gravity obtained. For illustration purposes, the proposed solution approach is satisfactorily compared to a rolling horizon approach in which lead times are allocated when the possibility of occurrence is established at one.

A network with multi-state (stochastic) elements (arcs or nodes) is commonly called a stochastic flow network. It is important to measure the system reliability of a stochastic flow network from the perspective of operations management. In the real world, the system reliability of a stochastic flow network can vary over time. Hence, a critical issue emerges—characterizing the time attribute in a stochastic flow network. To solve this issue, this study bridges (classical) reliability theory and the reliability of a stochastic flow network. This study utilizes Weibull distribution as a possible reliability function to quantify the time attribute in a stochastic flow network. For more general cases, the proposed model and algorithm can apply any reliability function and is not limited to Weibull distribution. First, the reliability of every single component is modeled by Weibull distribution to consider the time attribute, where such components comprise a multi-state element. Once the time constraint is given, the capacity probability distribution of elements can be derived. Second, an algorithm to generate minimal component vectors for given demand is provided. Finally, the system reliability can be calculated in terms of the derived capacity probability distribution and the generated minimal component vectors. In addition, a big data architecture is proposed for the model to collect and estimate the parameters of the reliability function. For future research in which very large volumes of data may be collected, the proposed model and architecture can be applied to time-dependent monitoring.

A stochastic-flow network (SFN) is a network whose flow has stochastic behavior or probabilistic multi-states. A timed stochastic-flow network (TSFN) is a SFN whose flow spends time to go through the network. Traditionally, the evaluation of network reliability does not consider time consumption for the flow to get through the network. However, there are lots of daily-life networks which can be regarded as TSFNs, such as the transportation network, the production network, etc. Their flow spends time to get through the network, and they are not yet explored in the literature. This paper proposes approaches to evaluate the reliability of such networks. Some numerical examples are discussed to illustrate the proposed method.

Evaluation of system reliability in stochastic flow networks under time constraints depends on the transmission time of minimal paths. The lead-time of a minimal path plays an important role in calculating the transmission time. Component assignments not only affect on the lead-time of a path but also the reliability value. Components assignment problem subject to total lead-time is never discussed. Thus, this paper focuses on solving this problem under total-lead time constraint, in which each component has an assignment lead-time. Subsequently an optimization method based on genetic algorithm is proposed to search the optimal components for a minimum total lead-time that maximizes the system reliability. The mathematical programming formulation for the assignment problem with optimal network reliability subject to total lead-time is formulated and solved by the presented genetic algorithm. The presented algorithm is applied on two given examples with different number of available components to assert its efficiency in solving the given assignment problem.

A network with multi-state arcs or nodes is commonly called a multi-state network. In the real world, the system reliability of a multi-state network can vary over time. Hence, a critical issue emerges to characterize the time attribute in a stochastic flow network. To solve this issue, this study bridges conventional reliability theory and the reliability of multi-state network. This study utilizes exponential distribution as a possible reliability function to quantify the time attribute in a multi-state network. First, the reliability of every single component is modeled by exponential distribution, where such components comprise a multi-state element. Once the time constraint is given, the capacity probability distribution of arcs can be derived. Second, an algorithm to generate minimal capacity vectors for given demand is provided. Finally, the system reliability can be calculated in terms of the derived capacity probability distribution and the generated minimal capacity vectors. A maintenance issue is further discussed according to the result of system reliability.

Service-level agreements for data transmission often define criteria such as availability, delay, and loss. Internet service providers and enterprise customers are increasingly focusing on tolerable error rate during transmission. Focusing on a stochastic flow network (SFN), this study extends reliability evaluation to considering tolerable error rate, in which network reliability is the probability that demand can be satisfied. In such an SFN, each component (branch or node) has several capacities and a transmission error rate. Network reliability can be regarded as a performance index for assessing the SFN. We propose an efficient algorithm based on minimal paths to find all minimal capacity vectors that allow the network to transmit d units of data under tolerable error rate E. Network reliability is computed in terms of such vectors by the recursive sum of disjoint products algorithm. The proposed algorithm is tested for a benchmark network and the National Science Foundation Network. The computational complexity of the proposed algorithm is analyzed as well.