36,319 research outputs found
Numerical schemes for the optimal input flow of a supply-chain
An innovative numerical technique is presented to adjust the inflow to a
supply chain in order to achieve a desired outflow, reducing the costs of
inventory, or the goods timing in warehouses. The supply chain is modelled by a
conservation law for the density of processed parts coupled to an ODE for the
queue buffer occupancy. The control problem is stated as the minimization of a
cost functional J measuring the queue size and the quadratic difference between
the outflow and the expected one. The main novelty is the extensive use of
generalized tangent vectors to a piecewise constant control, which represent
time shifts of discontinuity points. Such method allows convergence results and
error estimates for an Upwind- Euler steepest descent algorithm, which is also
tested by numerical simulations
A variational approach for continuous supply chain networks
We consider a continuous supply chain network consisting of buffering queues and processors first proposed by [D. Armbruster, P. Degond, and C. Ringhofer, SIAM J. Appl. Math., 66 (2006), pp. 896–920] and subsequently analyzed by [D. Armbruster, P. Degond, and C. Ringhofer, Bull. Inst. Math. Acad. Sin. (N.S.), 2 (2007), pp. 433–460] and [D. Armbruster, C. De Beer, M. Fre- itag, T. Jagalski, and C. Ringhofer, Phys. A, 363 (2006), pp. 104–114]. A model was proposed for such a network by [S. G ̈ottlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559] using a system of coupling ordinary differential equations and partial differential equations. In this article, we propose an alternative approach based on a variational method to formulate the network dynamics. We also derive, based on the variational method, a computational algorithm that guarantees numerical stability, allows for rigorous error estimates, and facilitates efficient computations. A class of network flow optimization problems are formulated as mixed integer programs (MIPs). The proposed numerical algorithm and the corresponding MIP are compared theoretically and numerically with existing ones [A. Fu ̈genschuh, S. Go ̈ttlich, M. Herty, A. Klar, and A. Martin, SIAM J. Sci. Comput., 30 (2008), pp. 1490–1507; S. Go ̈ttlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559], which demonstrates the modeling and computational advantages of the variational approach
Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply
We consider unsteady heat transfer in a one-dimensional harmonic crystal
surrounded by a viscous environment and subjected to an external heat supply.
The basic equations for the crystal particles are stated in the form of a
system of stochastic differential equations. We perform a continualization
procedure and derive an infinite set of linear partial differential equations
for covariance variables. An exact analytic solution describing unsteady
ballistic heat transfer in the crystal is obtained. It is shown that the
stationary spatial profile of the kinetic temperature caused by a point source
of heat supply of constant intensity is described by the Macdonald function of
zero order. A comparison with the results obtained in the framework of the
classical heat equation is presented. We expect that the results obtained in
the paper can be verified by experiments with laser excitation of
low-dimensional nanostructures.Comment: 12 pages, 5 figure
An optimal-control based integrated model of supply chain
Problems of supply chain scheduling are challenged by high complexity, combination of continuous and discrete processes, integrated production and transportation operations as well as dynamics and resulting requirements for adaptability and stability analysis. A possibility to address the above-named issues opens modern control theory and optimal program control in particular. Based on a combination of fundamental results of modern optimal program control theory and operations research, an original approach to supply chain scheduling is developed in order to answer the challenges of complexity, dynamics, uncertainty, and adaptivity. Supply chain schedule generation is represented as an optimal program control problem in combination with mathematical programming and interpreted as a dynamic process of operations control within an adaptive framework. The calculation procedure is based on applying Pontryagin’s maximum principle and the resulting essential reduction of problem dimensionality that is under solution at each instant of time. With the developed model, important categories of supply chain analysis such as stability and adaptability can be taken into consideration. Besides, the dimensionality of operations research-based problems can be relieved with the help of distributing model elements between an operations research (static aspects) and a control (dynamic aspects) model. In addition, operations control and flow control models are integrated and applicable for both discrete and continuous processes.supply chain, model of supply chain scheduling, optimal program control theory, Pontryagin’s maximum principle, operations research model,
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