最短路博弈群体单调分配方案构造

群体单调分配方案(Population Monotonic Allocation Scheme, 后简称PMAS)是合作博弈的一类分配机制。在合作博弈中, PMAS为每一个子博弈提供一个满足群体单调性的核中的分配方案, 从而保证大联盟的动态稳定性。本文主要贡献为利用线性规划与对偶理论构造与求解一类基于最短路问题的合作博弈(最短路博弈)的PMAS。我们首先借助对偶理论, 利用组合方法为最短路博弈构造了一个基于平均分摊思想的PMAS。然后借鉴计算核仁的Maschler方案, 将PMAS的存在性问题转化为一个指数规模的线性规划的求解问题, 并通过巧妙的求解得到了与之前组合方法相同的最短路博弈的PMAS。     

最短路博弈群体单调分配方案构造

群体单调分配方案(Population Monotonic Allocation Scheme, 后简称PMAS)是合作博弈的一类分配机制。在合作博弈中, PMAS为每一个子博弈提供一个满足群体单调性的核中的分配方案, 从而保证大联盟的动态稳定性。本文主要贡献为利用线性规划与对偶理论构造与求解一类基于最短路问题的合作博弈(最短路博弈)的PMAS。我们首先借助对偶理论, 利用组合方法为最短路博弈构造了一个基于平均分摊思想的PMAS。然后借鉴计算核仁的Maschler方案, 将PMAS的存在性问题转化为一个指数规模的线性规划的求解问题, 并通过巧妙的求解得到了与之前组合方法相同的最短路博弈的PMAS。     

Dynamic demand fulfillment in spare parts networks with multiple customer classes

We study real-time demand fulfillment for networks consisting of multiple local warehouses, where spare parts of expensive technical systems are kept on stock for customers with different service contracts. Each service contract specifies a maximum response time in case of a failure and hourly penalty costs for contract violations. Part requests can be fulfilled from multiple local warehouses via a regular delivery, or from an external source with ample capacity via an expensive emergency delivery. The objective is to minimize delivery cost and penalty cost by smartly allocating items from the available network stock to arriving part requests. We propose a dynamic allocation rule that belongs to the class of one-step lookahead policies. To approximate the optimal relative cost, we develop an iterative calculation scheme that estimates the expected total cost over an infinite time horizon, assuming that future demands are fulfilled according to a simple static allocation rule. In a series of numerical experiments, we compare our dynamic allocation rule with the optimal allocation rule, and a simple but widely used static allocation rule. We show that the dynamic allocation rule has a small optimality gap and that it achieves an average cost reduction of 7.9% compared to the static allocation rule on a large test bed containing problem instances of real-life size.     

Managing capacity flexibility in make-to-order production environments

This paper addresses the problem of managing flexible production capacity in a make-to-order (MTO) manufacturing environment. We present a multi-period capacity management model where we distinguish between process flexibility (the ability to produce multiple products on multiple production lines) and operational flexibility (the ability to dynamically change capacity allocations among different product families over time). For operational flexibility, we consider two polices: a fixed allocation policy where the capacity allocations are fixed throughout the planning horizon and a dynamic allocation policy where the capacity allocations change from period to period. The former approach is modeled as a single-stage stochastic program and solved using a cutting-plane method. The latter approach is modeled as a multi-stage stochastic program and a sampling-based decomposition method is presented to identify a feasible policy and assess the quality of that policy. A computational experiment quantifies the benefits of operational flexibility and demonstrates that it is most beneficial when the demand and capacity are well-balanced and the demand variability is high. Additionally, our results reveal that myopic operating policies may lead a firm to adopt more process flexibility and form denser flexibility configuration chains. That is, process flexibility may be over-valued in the literature since it is assumed that a firm will operate optimally after the process flexibility decision. We also show that the value of process flexibility increases with the number of periods in the planning horizon if an optimal operating policy is employed. This result is reversed if a myopic allocation policy is adopted instead.     

Bounds on stochastic convex allocation problems

We consider a stochastic convex program arising in a certain resource allocation problem. The uncertainty is in the demand for a resource which is to be allocated among several competing activities under convex inventory holding and shortage costs. The problem is cast as a two–period stochastic convex program and we derive tight upper and lower bounds to the problem using marginal distributions of the demands, which may be stochastically dependent. It turns out that these bounds are tighter than the usual bounds in the literature which are based on limited moment information of the underlying random variables. Numerical examples illustrate the bounds.     

Multi-period modeling of two-way price commitment under price-dependent demand

This paper examines the use of price-commitment policies in dynamic contracting in multiple-period, finite-time horizons. Two specific forms of price commitment are considered: one on the part of the retailer through a retail-fixed-markup contract and one on the part of the manufacturer through a price-protection contract. Optimal policies for each form of price commitment are analytically derived, as are optimal policies for the traditional price-only and centralized supply chain scenarios that we use as comparisons. We prove that optimal retail price and order size solutions exist in each period under the assumption of non-increasing price-dependent demand. We show that the existence of retailer inventory between periods causes the optimal policies to differ from a static single-period model. Further, we show that a supplier offers a price-protection policy as a signal to the retailer to resolve the gaming that naturally occurs under price-only; this effectively decouples the multi-period dynamic contracting setting into repeated single-period scenarios. However, the resulting behavior can actually inhibit supply chain performance. On the retail commitment side, we find that retail-fixed-markup policies are quite effective in improving supply chain efficiency. We show that such policies can lead to Pareto-improvement over price-only contracts and can even coordinate the supply chain in some situations.     

Sharing risk through concession contracts

In this paper we model concession contracts between a public and a private party, under dynamic uncertainty arising both from the volatility of the cash flow generated by the project and by the strategic behaviour of the two parties. Under these conditions we derive three notions of equilibrium price and apply the model to a case study for one of the most important concession contracts in Italy.     

Dynamic hybrid products with guarantees—An optimal portfolio framework

Dynamic hybrid products are pension products that consist of a dynamic combination of classical with profits participating life insurance contracts (or a bank account) and fund savings plans. To put such products in an optimal utility framework, we derive an optimal combination of a money market account, a CPPI-style fund and a free fund in continuous trading via transforming the original investment problem into a conventional portfolio problem in the presence of a guarantee condition. By this, we obtain (semi-) explicit forms of the dynamic weights for the different ingredients of a dynamic hybrid product.     

On returns policies with exogenous price

We contribute to current research on single-period returns policies by making a clear distinction between models in which transfer price is exogenous and models in which one dominant party unilaterally declares a price. We compare the equilibrium contracts that result from these two approaches and derive conditions for the equilibrium returns policy to be Pareto-efficient when transfer price is exogenous. Our main result is distribution free, but we make some interesting observations on channel performance when demand is uniformly distributed.     

The infinite horizon non-stationary stochastic inventory problem: Near myopic policies and weak ergodicity

In this paper we consider a periodic review dynamic inventory problem with non-stationary demands. The purpose of this paper is to show that near myopic policies are sufficiently close to optimal decisions for the infinite horizon inventory problem. In order to show this we pay attention to the fact that inventory processes with base-stock policies are weakly ergodic, and we discuss how the weak ergodicity is related to near myopic policies. Then we derive the error bounds of near myopic policies for the optimal decisions and evaluate them with a number of numerical experiments.     

基于收益管理和仿真的第三方仓储资源分配

针对不确定市场需求条件下第三方仓储资源的能力规划与分配问题,构建随机数学规划模型,理论分析证明了最优资源分配量的存在性,并指出最优资源分配量是单位资源成本的递减函数、单位资源收益和单位损失成本的递增函数。鉴于解析求解的复杂性,基于收益管理思想,结合离散事件仿真技术和响应曲面法,提出一种新的分析求解框架:收益管理用于细分顾客、构建资源分配策略,仿真模型刻画系统随机特性并评估系统绩效指标,响应曲面法则优化分配策略并探寻绩效改进方向。案例研究和仿真实验结果显示,根据顾客类别分配仓储能力的策略优于传统的先到先服务策略,收益管理、响应曲面法与仿真的综合集成,能够提高系统收益,从而使本文所提方法体系得到了有效验证。     

Bayesian planning of step‐stress accelerated degradation tests under various optimality criteria

Step‐stress accelerated degradation testing (SSADT) has become a common approach to predicting lifetime for highly reliable products that are unlikely to fail in a reasonable time under use conditions or even elevated stress conditions. In literature, the planning of SSADT has been widely investigated for stochastic degradation processes, such as Wiener processes and gamma processes. In this paper, we model the optimal SSADT planning problem from a Bayesian perspective and optimize test plans by determining both stress levels and the allocation of inspections. Large‐sample approximation is used to derive the asymptotic Bayesian utility functions under 3 planning criteria. A revisited LED lamp example is presented to illustrate our method. The comparison with optimal plans from previous studies demonstrates the necessity of considering the stress levels and inspection allocations simultaneously.     

Scheduling trams in the morning

In this note, we prove —›-completeness of the following problem: Given a set of trams of different types, which are stacked on sidings in their depot and an order in which trams of specified types are supposed to leave. Is there an assignment of trams to departure times without any shunting movements? In the particular case where the number of sidings is fixed, the problem is solvable in polynomial time. We derive a dynamic program and improve its performance by a state elimination scheme. We implemented three variants of the dynamic program and applied them to random data as well as to real-world data.     

Furniture supply chain tactical planning optimization using a time decomposition approach

We study the supply chain tactical planning problem of an integrated furniture company located in the Province of Québec, Canada. The paper presents a mathematical model for tactical planning of a subset of the supply chain. The decisions concern procurement, inventory, outsourcing and demand allocation policies. The goal is to define manufacturing and logistics policies that will allow the furniture company to have a competitive level of service at minimum cost. We consider planning horizon of 1 year and the time periods are based on weeks. We assume that customer’s demand is known and dynamic over the planning horizon. Supply chain planning is formulated as a large mixed integer programming model. We developed a heuristic using a time decomposition approach in order to obtain good solutions within reasonable time limit for large size problems. Computational results of the heuristic are reported. We also present the quantitative and qualitative results of the application of the mathematical model to a real industrial case.     

The uncertain mortality intensity framework: Pricing and hedging unit-linked life insurance contracts

We study the valuation and hedging of unit-linked life insurance contracts in a setting where mortality intensity is governed by a stochastic process. We focus on model risk arising from different specifications for the mortality intensity. To do so we assume that the mortality intensity is almost surely bounded under the statistical measure. Further, we restrict the equivalent martingale measures and apply the same bounds to the mortality intensity under these measures. For this setting we derive upper and lower price bounds for unit-linked life insurance contracts using stochastic control techniques. We also show that the induced hedging strategies indeed produce a dynamic superhedge and subhedge under the statistical measure in the limit when the number of contracts increases. This justifies the bounds for the mortality intensity under the pricing measures. We provide numerical examples investigating fixed-term, endowment insurance contracts and their combinations including various guarantee features. The pricing partial differential equation for the upper and lower price bounds is solved by finite difference methods. For our contracts and choice of parameters the pricing and hedging is fairly robust with respect to misspecification of the mortality intensity. The model risk resulting from the uncertain mortality intensity is of minor importance.     

Optimal Control of a Stochastic Hybrid System with Discounted Cost

We address the optimal control problem of a very general stochastic hybrid system with both autonomous and impulsive jumps. The planning horizon is infinite and we use the discounted-cost criterion for performance evaluation. Under certain assumptions, we show the existence of an optimal control. We then derive the quasivariational inequalities satisfied by the value function and establish well-posedness. Finally, we prove the usual verification theorem of dynamic programming.     

Optimal dispatching in a tandem queue

Motivated by a capacity allocation problem within a finite planning period, we conduct a transient analysis of a single-server queue with Lévy input. From a cost minimization perspective, we investigate the error induced by using stationary congestion measures as opposed to time-dependent measures. Invoking recent results from fluctuation theory of Lévy processes, we derive a refined cost function, that accounts for transient effects. This leads to a corrected capacity allocation rule for the transient single-server queue. Extensive numerical experiments indicate that the cost reductions achieved by this correction can be significant.     

Decomposition results for general polling systems and their applications

In this paper we derive decomposition results for the number of customers in polling systems under arbitrary (dynamic) polling order and service policies. Furthermore, we obtain sharper decomposition results for both the number of customers in the system and the waiting times under static polling policies. Our analysis, which is based on distributional laws, relaxes the Poisson assumption that characterizes the polling systems literature. In particular, we obtain exact decomposition results for systems with either Mixed Generalized Erlang (MGE) arrival processes, or asymptotically exact decomposition results for systems with general renewal arrival processes under heavy traffic conditions. The derived decomposition results can be used to obtain the performance analysis of specific systems. As an example, we evaluate the performance of gated Markovian polling systems operating under heavy traffic conditions. We also provide numerical evidence that our heavy traffic analysis is very accurate even for moderate traffic. This revised version was published online in June 2006 with corrections to the Cover Date.     

Linear programming based decomposition methods for inventory distribution systems

We consider an inventory distribution system consisting of one warehouse and multiple retailers. The retailers face random demand and are supplied by the warehouse. The warehouse replenishes its stock from an external supplier. The objective is to minimize the total expected replenishment, holding and backlogging cost over a finite planning horizon. The problem can be formulated as a dynamic program, but this dynamic program is difficult to solve due to its high dimensional state variable. It has been observed in the earlier literature that if the warehouse is allowed to ship negative quantities to the retailers, then the problem decomposes by the locations. One way to exploit this observation is to relax the constraints that ensure the nonnegativity of the shipments to the retailers by associating Lagrange multipliers with them, which naturally raises the question of how to choose a good set of Lagrange multipliers. In this paper, we propose efficient methods that choose a good set of Lagrange multipliers by solving linear programming approximations to the inventory distribution problem. Computational experiments indicate that the inventory replenishment policies obtained by our approach can outperform several standard benchmarks by significant margins.