Second best temporally repeated flows

FORD and FULKERSON have shown that a stationary maximal dynamic flow can be obtained by solving a transhipment problem associated with the static network and thereby finding the maximal temporally repeated dynamic flow. This flow is known to be an optimal dynamic flow. This paper presents an algorithm for second best temporally repeated flows. A numerical example is presented.     

Solution procedures for sizing of warehouses

In the past, researchers presented a linear programming formulation for the economic sizing of warehouses when demand is highly seasonal and public warehouse space is available on a monthly basis. The static model was extended for the dynamic sizing problem in which the warehouse size is allowed to change over time. By applying simplex routine, the optimal size of the warehouse to be constructed could be determined. In this paper, an alternative and simple method of arriving at an optimal solution for the static problem is given. Three extensions of the static model are given. These extensions involve costs varying over time, economies of scale in capital expenditure and/or operating cost and stochastic version. The dynamic warehouse sizing problem is shown to be a network flow problem which could be solved by using network flow algorithms. The structure of an optimal solution is also given. The concave cost version of the dynamic warehouse sizing problem is also discussed and it is shown that this problem can be solved efficiently using dynamic programming.     

Optimal Control of a Parabolic Equation with Dynamic Boundary Condition

We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L ^p function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.     

Optimal switching for alternating processes

This paper is concerned with the problems of optimal switching for general stochastic processes. We show the existence of the maximal element of a class of dynamic programming inequalities by the method of impulsive control. We obtain results on the existence of optimal control for general and cyclic switching problems.     

Dynamics of an Infinite Beam under Stochastic Moving Forces

The problem regarding the dynamic response of an infinite beam resting on two-parametric foundation to the passage of a train of random forces is studied. This train of forces idealizes the flow of vehicles having random weights and travelling at the same speed. It is assumed that the occurrence process is either a Poisson or a renewal (Erlang) process. Two different situations and solutions are presented: one for the arbitrary locations of the forces and another when one of the forces is located in such a way that the response of the beam has the maximal value. The first model can be used to estimate the reliability of the beam with respect to fatigue, the second model can be useful in the reliability with respect to the maximal response. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal flows in networks with multiple sources and sinks

The concept of an optimal flow in a multiple source, multiple sink network is defined. It generalizes maximal flow in a single source, single sink network. An existence proof and an algorithm are given.     

The circumpolygon with maximal area

The convex circumpolygon with maximal area to a given convex polygon can be determined by means of dynamic programming. The effort of this method increases cubically with respect to the number of sides. It is further shown that the optimal circum-polygon can be constructed with ruler and circle. The applied version of dynamic programming can be also used for solving Steiner's problem of the inpoiygon with minimal circumference but it demands a higher effort than Phú's method.     

Investigating the underlying Markovian dynamics of ECG rhythms by information flow

Several approaches have been recently introduced to characterize and classify signals based on the underlying hidden dynamic. Markov models represent a natural choice for describing the dynamic evolution of a signal. However, the right selection of the memory of the process is essential for the correctness of the Markov model and a mathematically well-founded criterion is necessary to establish when the Markov model is a good approximation of the process. We review an information-theoretic based method that introduces the concept of information flow as such a criterion. The information flow describes the progressive loss of statistical dependence between the entire past and a point ahead in the future, which is indirectly related with the hidden dynamic of the signal. An approximated measure of information flow can be used as the discriminating statistic for selecting the optimal Markov model in terms of the shortest memory required. This technique is applied to investigate the underlying Markovian dynamics of the heart rate variability (HRV) for subjects in different patho-physiological conditions. Markov models with different memories seem to be associated with the circadian cycle and with different pathologies. Furthermore, the precursor character of the information flow for predicting ventricular tachycardia (VT) is discussed.     

An approach for optimization of loading cycles of hydraulic mining excavators

The present paper describes an optimization multi-stage approach for computing the optimal loading cycle of a heavy weight excavator along a predefined trajectory under dynamic constraints such as maximal ensuing forces, accelerations, and maximal allowed hydraulic power. The approach involves the use of splines of 3rd and 5th order for smooth interpolation of the spatial trajectory up to the level of linear and angular accelerations, as well as an SQP optimization routine to find the optimal end-effector motion law along the trajectory, which finally leads to strokes and pressures at the hydraulic actuators as a function of time. The approach can also be extended to other multi-body systems following a predetermined trajectory. The solution scheme can be included in a more general optimization routine aiming to optimize the trajectory itself. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluid approximation of a controlled multiclass tandem network

A two-station, four-class queueing network with dynamic scheduling of servers is analyzed. It is shown that the corresponding Markov decision problem converges under fluid scaling to a fluid optimal control model. The structure of the optimal policy for the fluid network, and of an asymptotically optimal policy for the queueing network are derived in an explicit form. They concur with the tandem μ-rule, if this policy gives priority to the same flow of customers in both stations. In general, they are monotone with a linear switching surface. This revised version was published online in June 2006 with corrections to the Cover Date.     

DYNAMIC CORRECTIVE TAXES WITH FLOW AND STOCK EXTERNALITIES: A FEEDBACK APPROACH

In confronting a consumer good whose production process is associated with both flow and stock externalities, a corrective tax is introduced to restore efficiency. The objective is to maximize social welfare over time when the stock pollutant obeys an arbitrary dynamic process. The model makes it possible to derive the optimal corrective tax as a closed form feedback control law. This feedback rule can be applied for qualitative purposes such as parameter analysis or studying the time path of the corrective tax. It can also be used for quantitative purposes, for example, evaluating an actual policy or assessment of the optimal tax for a certain case. It is here used to study how the optimal corrective tax, both as a function of time and as a function of the pollution level, depends upon the decay function. It is shown that, depending upon the initial conditions and the structure of the economy and the decay function, most outcomes are possible.     

On Solving Quickest Time Problems in Time-Dependent, Dynamic Networks

In this paper, a pseudopolynomial time algorithm is presented for solving the integral time-dependent quickest flow problem (TDQFP) and its multiple source and sink counterparts: the time-dependent evacuation and quickest transshipment problems. A more widely known, though less general version, is the quickest flow problem (QFP). The QFP has historically been defined on a dynamic network, where time is divided into discrete units, flow moves through the network over time, travel times determine how long each unit of flow spends traversing an arc, and capacities restrict the rate of flow on an arc. The goal of the QFP is to determine the paths along which to send a given supply from a single source to a single sink such that the last unit of flow arrives at the sink in the minimum time. The main contribution of this paper is the time-dependent quickest flow (TDQFP) algorithm which solves the TDQFP, i.e. it solves the integral QFP, as defined above, on a time-dependent dynamic network, where the arc travel times, arc and node capacities, and supply at the source vary with time. Furthermore, this algorithm solves the time-dependent minimum time dynamic flow problem, whose objective is to determine the paths that lead to the minimum total time spent completing all shipments from source to sink. An optimal solution to the latter problem is guaranteed to be optimal for the TDQFP. By adding a small number of nodes and arcs to the existing network, we show how the algorithm can be used to solve both the time-dependent evacuation and the time-dependent quickest transshipment problems. This revised version was published online in August 2006 with corrections to the Cover Date.     

Optimal Planning of a Multi-Station System with Sojourn Time Constraints

This paper studies a dynamic production system where multiple products must visit stations where inventories are constrained by maximum and minimum sojourn times with neither negative flow nor backlog being allowed. A resource availability constraint limits the aggregate throughput of the stations. The objective is to minimize the sum of flow and inventory cost. The problem is broken down into several single-product serial systems that serve as subroutines of a Lagrangian relaxation routine. This model is implemented in a spreadsheet so that it can be used by the officials of a Chilean institution for planning the operations and defining the optimal allocation of resources.     

基于Leslie-Gower捕食-被食模型的渔业收获问题

考虑了基于Leslie-Gower模型的生物经济学捕获问题,通过对税收政策的控制影响渔业生态系统,研究了系统的动力学行为,并通过Pontryagins最大值原理考虑了最优的税收政策,最后给出了系统仿真.     

Multitime Dynamic Programming for Curvilinear Integral Actions

This paper justifies dynamic programming PDEs for optimal control problems with performance criteria involving curvilinear integrals. The main novel feature, relative to the known theory, is that the multitime dynamic programming PDEs are now connected to the multitime maximum principle. For the first time, an interesting and useful connection between the multitime maximum principle and the multitime dynamic programming is given, characterizing the optimal control by means of a PDE system that may be viewed as a multitime feedback law.     

Transient and steady-state analysis of a manufacturing system with setup changes

This paper deals with the optimal scheduling of a one-machine two-product manufacturing system with setup, operating in a continuous time dynamic environment. The machine is reliable. A known constant setup time is incurred when switching over from a part to the other. Each part has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a production flow control problem. The objective is to minimize the sum of the backlog and inventory costs incurred over a finite planning horizon. The global optimal solution, expressed as an optimal feedback control law, provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady-state, the optimal cyclic schedule (Limit Cycle) is determined. This is equivalent to solving a one-machine two-product Lot Scheduling Problem. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region is associated an optimal control policy. A novel algorithm (Direction Sweeping Algorithm) is developed to obtain the optimal state trajectory (optimal policy that minimizes the sum of inventory and backlog costs) for this last case.     

基于营运资金信息匹配平台的供应链金融动态折扣决策研究

当前逐渐受到实业界关注的一种新型供应链金融模式是基于营运资金信息匹配平台的动态折扣。本文针对两级供应链的动态折扣决策问题进行建模,揭示了动态折扣的应用对于改善供应链参与方现金流的影响机理。首先通过考虑供需双方动态折扣的独立决策,得出日折扣率的边界条件、双方效用最大时的日折扣率、买方混合还款方式下营运资金的最优准备方案和最低边界值;其次考虑供需双方动态折扣的最优决策,推导出在不同折扣率和利率关系下的最优还款策略,研究表明动态折扣可以明显提升供需双方的利润情况。     

A Note on Feasible Flows in Lower-Bounded Multicommodity Networks

This note considers the feasibility for two types of multicommodity flow problems: maximal flow problems with both upper and lower arc capacities, and capacitated minimal cost trans-shipment problems. Although closed form conditions analogous to those known for single commodity problems cannot be derived, it is shown that feasibility is equivalent to finding a maximal multicommodity flow of a specified value on a related network with zero lower bounds, a direct extension of well-known results for single commodity networks.