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We consider stochastic flow lines with limited buffer sizes and limited material supply. In these systems, the configuration of the flow line parameters and the configuration of the material supply...

The goal of this paper is to establish the Lipschitz and W2,∞ estimates for a second-order parabolic PDE ∂tu(t,x)=12Δu(t,x)+f(t,x) on Rd with zero initial data and f satisfying a Ladyzhenskaya–Prod...

In a stochastic-flow network with budget constraint, the network reliability for level (d, b), i.e., R(d,b), where d is a given demand value and b is a budget limit, is the probability of transmitt...

We prove the existence of a stochastic flow of Hölder homeomorphisms for solutions of SDEs with singular time dependent drift having only certain integrability properties. We also show that the solution map x → X x is differentiable in a weak sense.

This article proposes an approximate algorithm to solve the robust design problem in a stochastic-flow network. Conventionally, the robust design is an issue in quality engineering where the designed product functions well even in a versatile environment. However, in the context of a stochastic-flow network, it means the network functions well even in a node's failure situation. This can be solved by properly assigning capacity. Because the problem is known to be NP-hard, a relatively fast approximation algorithm would be beneficial. Some numerical examples are presented to illustrate the usefulness of the proposed approach.

System reliability evaluation for flow networks is an important issue for quality performance. This paper studies the system reliability that a given amount of multicommodity can be transmitted through a stochastic-flow network under the budget constraint, where each node and each arc has several possible capacities. Such reliability is named multicommodity reliability throughout this paper. A simple algorithm is proposed to generate all lower boundary points for (d^1, d^2,…,d(superscript p);C) where d(superscript i) is the demand of commodity i and C is the budget. The multicommodity reliability can then be calculated in terms of such points.

This paper is mainly to extend the multi‐commodity minimum cost flow problem from deterministic cases to stochastic cases. Under budget constraint, we propose an approach to calculate the probability that the required amount of multiple commodities can be transported simultaneously through a stochastic flow network. Such a probability is called system reliability. An algorithm is proposed first to find out all lower boundary points for the requirement in terms of minimal paths. The system reliability can then be calculated in terms of such lower boundary points.

From the point of view of quality management, it is an important issue to develop some performance indexes for a flow network. This paper studies the performance indexes for a stochastic-flow network in which each arc has several possible capacities. For the case that multiple types of commodity are transmitted through the same stochastic-flow network, this paper defines the system capacity as a vector and then proposes a new performance index. An algorithm in terms of minimal cuts is proposed to evaluate such a performance index.

This paper defines the problem of buffer space allocation in flow lines as an investment problem. A model is developed and solution techniques are described that can be used to determine buffer allocations that maximize the expected net present value of the investment, including machines, buffers and inventory. Production rates and inventory levels are explicitly linked to projected cash flow to assess the economic consequences of the buffer allocation. Several examples of linear flow lines as well as assembly/disassembly systems and flow lines with rework loops are analysed numerically. These examples demonstrate the importance of the buffer allocation problem and provide intuition with respect to the structure of optimized solutions. A result is that as product quality in a system with a rework loop improves, an optimally designed system can receive more buffer spaces and may use more inventory. This possibly counterintuitive result is due to the economic perspective on the buffer allocation problem.

In a stochastic-flow network, each arc has several capacity levels. Given the system demand d, the reliability of such a network for demand d (i.e., the probability that the maximum flow is not less than d) can be computed in terms of d-MCs. Jane, Lin and Yuan have presented an algorithm to generate all d-MCs in terms of minimal cuts. This article proposes another algorithm, which is based on the more publicly accepted “comparison” method, to evaluate the reliability. To compare such two algorithms, one example is illustrated to show how d-MCs are generated differently. Also, the computational complexity is analyzed.

This study evaluates how the procedures followed in splitting job lots on the shop floor influence both material handling and lot integrity in stochastic flow shop environments. Former work has shown that lot splitting improves flow time and customer service performance, but with an increased number of transfers along with a corresponding increase in material handling costs. Physical lot integrity, which is important to lot tracing, has not been considered in prior literature. In order to overcome these limitations and address material handling concerns better, we define a new measure of performance called the lot integrity loss exposure (LILE). We use this and other measures to show that the traditional 'push' approach that has been followed in modelling lot splitting complicates lot traceability in the shop and leads to an excessive number of transfers. As an alternative, we propose a 'pull' approach in which an order is split between any successive pair of machines only on an as-needed basis. The push ...

We prove that the solutions of SDE with smooth coefficients have ¥ ‐modifications and constitute quasi‐sure stochastic flows of C¥ ‐diffeomorphisms.

Consider an isotropic stochastic flow in Rd (i.e. a simultaneous random, correlated motion of all points in space), where d=l,2 or 3, such that the joint law of the motion of two particles allows the particles to meet and coalesce in finite time. The coalescent set J t is a random subset of Rd consisting of the initial positions of particles which have coalesced by time t with the particle which started at 0. We show that the expected volume of J t grows at a rate proportional to when d=1, and at rates close to proportional to t/log t (resp. t) when d = 2 (resp. d=3). We give an example of a coalescing stochastic flow when d = 3. These results are analogous to growth rates of expected population size of a surviving type in the "invasion process" described by Clifford and Sudbury

In this paper we consider a flow shop with blocking, n jobs, m machines, and stochastic processing times. We show that if the jobs can be stochastically ordered, then a SEPT sequence minimizes the expected flowtime on two machines.

This paper examines the foundation for economic analysis in unreliable metal cutting processes. Using queueing models, we present some observations on the effect of cutting speed upon tool life, rate of acceptance of work, and mean flow time in machining parameter optimization. Handled by the Manufacturing Engineering Department.