Application of average dynamic programming to inventory systems

We show the existence ofaverage cost (AC-) optimal policy for an inventory system withuncountable state space; in fact, the AC-optimal cost and an AC-optimal stationary policy areexplicitly computed. In order to do this, we use a variant of thevanishing discount factor approach, which have been intensively studied in recent years but the available results not cover the inventory problem we are interested in.The work of the first author (OVA) was partially supported by Fondo del Sistema de Investigación del Mar de Cortéz under grant SIMAC/94/CT-005. The work of the second author (RMdO) was partially supported by Consejo Nacional de Ciencia y Tecnologia (CONACyT) under grant 0635P-E9506.     

On the evaluation of fixed permutations as strategies in stochastic scheduling

A general model is proposed for the stochastic version of the single-machine allocation problem. Sufficient conditions are given to ensure that there is an optimal strategy given by a fixed permutation of the job set. Additional results are given for an important special case of the general model involving simple jobs. The paper concludes with material concerning the evaluation of fixed permutations as strategies under conditions more general than the sufficient conditions mentioned above.     

考虑最佳入口温度的多股流换热器网络循环优化

针对于多股流换热器网络的应用优势,本文在衍生网络优化方法基础上,提出了考虑最佳入口温度的多股流换热器循环优化方法,即利用多股流换热器网络小面积换热器合并而不产生固定投资费用这一特点,将优化结果中存在公用工程的流体返回到另一种流体的入口并与其入口流体进行循环优化。结果表明,这种优化方法能够进一步发挥多股流换热器网络的优点,得到年综合费用更小、运行费用更低的网络结构。     

Scaling and long-range dependence in option pricing III: A fractional version of the Merton model with transaction costs

A model for option pricing of fractional version of the Merton model with ‘Hurst exponent’ H being in [1/2,1) is established with transaction costs. In particular, for H(1/2,1) the minimal price C_min(t,S_t) of an option under transaction costs is obtained, which displays that the timestep δt and the ‘Hurst exponent’ H play an important role in option pricing with transaction costs.     

Dynamic repositioning for vehicle sharing with setup costs

This study considers a multi-period two-region repositioning problem with setup repositioning costs involved for vehicle sharing systems. We find that incorporating such costs can influence the total cost significantly and complicate the structure of the optimal policy. Moreover, we manage to partially characterize the optimal policy, and then develop an easy-to-implement heuristic policy. The performance of the heuristic policy and the influence of setup repositioning costs on policies are assessed numerically.     

Expected gain–loss pricing and hedging of contingent claims in incomplete markets by linear programming

We analyze the problem of pricing and hedging contingent claims in the multi-period, discrete time, discrete state case using the concept of a “λ gain–loss ratio opportunity”. Pricing results somewhat different from, but reminiscent of, the arbitrage pricing theorems of mathematical finance are obtained. Our analysis provides tighter price bounds on the contingent claim in an incomplete market, which may converge to a unique price for a specific value of a gain–loss preference parameter imposed by the market while the hedging policies may be different for different sides of the same trade. The results are obtained in the simpler framework of stochastic linear programming in a multi-period setting, and have the appealing feature of being very simple to derive and to articulate even for the non-specialist. They also extend to markets with transaction costs.     

A multi-level search strategy for the 0-1 Multidimensional Knapsack Problem

We propose an exact method based on a multi-level search strategy for solving the 0-1 Multidimensional Knapsack Problem. Our search strategy is primarily based on the reduced costs of the non-basic variables of the LP-relaxation solution. Considering that the variables are sorted in decreasing order of their absolute reduced cost value, the top level branches of the search tree are enumerated following Resolution Search strategy, the middle level branches are enumerated following Branch & Bound strategy and the lower level branches are enumerated according to a simple Depth First Search enumeration strategy. Experimentally, this cooperative scheme is able to solve optimally large-scale strongly correlated 0-1 Multidimensional Knapsack Problem instances. The optimal values of all the 10 constraint, 500 variable instances and some of the 30 constraint, 250 variable instances of the OR-Library were found. These values were previously unknown.     

Asymptotic analysis for Merton's problem with transaction costs in power utility case

We revisit the optimal investment and consumption problem with proportional transaction costs. We prove that both the value function and the slopes of the lines demarcating the no-trading region are analytic functions of cube root of the transaction cost parameter. Also, we can explicitly calculate the coefficients of the fractional power series expansions of the value function and the no-trading region.     

On an investment-consumption model with transaction costs: an asymptotic analysis

In this paper we examine the Akian, Menaldi and Sulem (1996) model for the optimal management of a portfolio, when there are transaction costs which are equal to a fixed percentage of the amount transacted. We analyse this model in the realistic limit of small transaction costs. Although the full problem is a free boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility.