A dynamic rationing policy for continuous-review inventory systems

Stock rationing is an inventory policy that allows differential treatment of customer classes without using separate inventories. In this paper, we propose a dynamic rationing policy for continuous-review inventory systems, which utilizes the information on the status of the outstanding replenishment orders. For both backordering and lost sales environments, we conduct simulation studies to compare the performance of the dynamic policy with the static critical level and the common stock policies and quantify the gain obtained. We propose two new bounds on the optimum dynamic rationing policy that enables us to tell how much of the potential gain the proposed dynamic policy realizes. We discuss the conditions under which stock rationing – both dynamic and static – is beneficial and assess the value of the dynamic policy.     

Dynamic inventory rationing strategies for inventory systems with two demand classes,Poisson demand and backordering

We study inventory systems with two demand classes (critical and non-critical), Poisson demand and backordering. We analyze dynamic rationing strategies where the number of items reserved for critical demand depends on the remaining time until the next order arrives. Different from results in the literature, we do not discretize demand but derive a set of formulae that determine the optimal rationing level for any possible value of the remaining time. Moreover, we show that the cost parameters can be captured in a single relevant dimension, which allows us to present the optimal rationing levels in charts and lookup tables that are easy to implement. Numerical examples illustrate that the optimal dynamic rationing strategy outperforms all static strategies with fixed rationing levels.     

Multi-commodity rationing problems with maxmin payoffs

We address a multi-dimensional extension of standard rationing problems in which several commodities have to be shared among a set of agents who exhibit maxmin preferences on the results they obtain. In this context we investigate efficiency and introduce a property of stability which is supported on a transferable utility game. We also propose a procedure to construct rules for obtaining stable allocations for the special case where all commodities have the same weight.     

Rationing with baselines: the composition extension operator

We introduce a new operator for general rationing problems in which, besides conflicting claims, individual baselines play an important role in the rationing process. The operator builds onto ideas of composition, which are not only frequent in rationing, but also in related problems such as bargaining, choice, and queuing. We characterize the operator and show how it preserves some standard axioms in the literature on rationing. We also relate it to recent contributions in such literature.     

双边配给问题的Shapley解及其在博物馆通票问题中的应用

双边配给问题描述了现实生活中一类带有二部图结构的稀缺资源配置问题, 例如, 在自然灾害期间救援物资的配给; 电力和天然气等自然资源按需分配; 高校引进人才调配等。本文通过求解线性规划, 并从联盟边际贡献的角度出发定义了双边配给问题的一个Shapley解。之后, 通过合作对策模型和解的公理化方法说明新解的合理性。首先, 建立双边配给问题的合作对策模型, 论证了新解与双边配给合作对策的Shapley值一致; 其次, 证明了Shapley解是唯一满足优先一致性的有效配给方案。最后, 将Shapley解应用于博物馆通票问题的研究, 探讨了博物馆合作制定通票后所得单票和通票收益的分配方式。     

双边配给问题的Shapley解及其在博物馆通票问题中的应用

双边配给问题描述了现实生活中一类带有二部图结构的稀缺资源配置问题, 例如, 在自然灾害期间救援物资的配给; 电力和天然气等自然资源按需分配; 高校引进人才调配等。本文通过求解线性规划, 并从联盟边际贡献的角度出发定义了双边配给问题的一个Shapley解。之后, 通过合作对策模型和解的公理化方法说明新解的合理性。首先, 建立双边配给问题的合作对策模型, 论证了新解与双边配给合作对策的Shapley值一致; 其次, 证明了Shapley解是唯一满足优先一致性的有效配给方案。最后, 将Shapley解应用于博物馆通票问题的研究, 探讨了博物馆合作制定通票后所得单票和通票收益的分配方式。     

An Investigation into the Decision Rules of Capital Investment Using Simulation

The paper explores the effectiveness of the major decision rules commonly applied to the selection of investment alternatives. The rules are applied to a continual stream of simulated investments, as they arise period by period throughout the planning horizon. Thus the dynamics of investing now rather than later, with capital rationing, are taken into account. The practitioners' preference for the payback period is examined for a typical series of simulated investments, and the returns are compared against the returns of the more academically acceptable discounting decision rules. Particular attention is devoted to the benefits of each of the decision rules with reference to both risk and average returns.     

On robust mean-variance portfolios

We derive closed-form portfolio rules for robust mean–variance portfolio optimization where the return vector is uncertain or the mean return vector is subject to estimation errors, both uncertainties being confined to an ellipsoidal uncertainty set. We consider different mean–variance formulations allowing short sales, and derive closed-form optimal portfolio rules in static and dynamic settings.     

Bi-criteria optimization problems for decision rules

We consider bi-criteria optimization problems for decision rules and rule systems relative to length and coverage. We study decision tables with many-valued decisions in which each row is associated with a set of decisions as well as single-valued decisions where each row has a single decision. Short rules are more understandable; rules covering more rows are more general. Both of these problems—minimization of length and maximization of coverage of rules are NP-hard. We create dynamic programming algorithms which can find the minimum length and the maximum coverage of rules, and can construct the set of Pareto optimal points for the corresponding bi-criteria optimization problem. This approach is applicable for medium-sized decision tables. However, the considered approach allows us to evaluate the quality of various heuristics for decision rule construction which are applicable for relatively big datasets. We can evaluate these heuristics from the point of view of (i) single-criterion—we can compare the length or coverage of rules constructed by heuristics; and (ii) bi-criteria—we can measure the distance of a point (length, coverage) corresponding to a heuristic from the set of Pareto optimal points. The presented results show that the best heuristics from the point of view of bi-criteria optimization are not always the best ones from the point of view of single-criterion optimization.     

Berth allocation with time-dependent physical limitations on vessels

We consider a berth allocation problem in container terminals in which the assignment of vessels to berths is limited by water depth and tidal condition. We model the problem as a parallel-machine scheduling problem with inclusive processing set restrictions, where the time horizon is divided into two periods and the processing sets in these two periods are different. We consider both the static and dynamic cases of the problem. In the static case all of the vessels are ready for service at time zero, while in the dynamic case the vessels may have nonzero arrival times. We analyze the computational complexity and develop efficient heuristics for these two cases. Computational experiments are performed to test the effectiveness of the heuristics and to evaluate the benefits of taking tidal condition into consideration when making berth allocation decisions.     

Discrete and dynamic versus continuous and static loading policy for a multi-compartment vehicle

In this paper, we address the problem of loading non-intermixable products in a vehicle consisting of compartments of different sizes. The demands of the products are different but uniform over time. The objective is to meet product demands and minimize setup rate (that is, the number of deliveries per unit time). Two approaches, namely, dynamic and static, are investigated and their performances are compared with each other. In the dynamic approach, deliveries are made in several discrete periods and, then, repeated in a cyclic fashion. In each of these deliveries, the allocation of products to compartments can be different. The static approach, on the other hand, assumes a continuous time scale and determines a single assignment of products to compartments that maximizes the time in which the product demands are fully satisfied by this single delivery. The comparison between the two approaches shows that the dynamic approach is superior to the static approach when a discrete time scale is considered. However, even when the discrete time scale constraint is relaxed, the dynamic approach still provides better results for relatively long cycle times.     

Dynamic Network-Based Discriminatory Pricing

We study the dynamic pricing decisions for competitive network service providers. We assume that each competing firm follows a three-part pricing scheme, which consists of an ongoing membership fee, a usage fee for communications within the networks, and another usage fee for communications across the networks. The difference between the two usage fees is the network-based price discount that allows price discrimination. We study the firms problems as a differential game and establish the optimal pricing policy as a Nash equilibrium feedback strategy depending on only the network sizes (i.e., the number of subscribers). We compare the dynamic network-based discount with the static discount. In the special case of a uniform calling pattern, we find that the firm network-based dynamic discount is always lower than the static discount; we find also that the firm that has a larger network can offer a bigger discount. These results are useful particularly for managers. To get further insights into the dynamic pricing policies, we explore the case of symmetric competition using numerical simulation.Communicated by G. Leitmann     

Optimal pricing for tandem queues with finite buffers

We consider optimal pricing for a two-station tandem queueing system with finite buffers, communication blocking, and price-sensitive customers whose arrivals form a homogeneous Poisson process. The service provider quotes prices to incoming customers using either a static or dynamic pricing scheme. There may also be a holding cost for each customer in the system. The objective is to maximize either the discounted profit over an infinite planning horizon or the long-run average profit of the provider. We show that there exists an optimal dynamic policy that exhibits a monotone structure, in which the quoted price is non-decreasing in the queue length at either station and is non-increasing if a customer moves from station 1 to 2, for both the discounted and long-run average problems under certain conditions on the holding costs. We then focus on the long-run average problem and show that the optimal static policy performs as well as the optimal dynamic policy when the buffer size at station 1 becomes large, there are no holding costs, and the arrival rate is either small or large. We learn from numerical results that for systems with small arrival rates and no holding cost, the optimal static policy produces a gain quite close to the optimal gain even when the buffer at station 1 is small. On the other hand, for systems with arrival rates that are not small, there are cases where the optimal dynamic policy performs much better than the optimal static policy.

     

Axiomatic characterizations of the CEA solution for rationing problems

Situations abound in the real world, where aggregate demand for a commodity exceeds aggregate supply. When such situations of excess demand occur, what is required is some kind of rationing. The literature on rationing problems has an interesting origin in the Babylonian Talmud. The purpose of this paper is to characterize axiomatically and analyze the constrained equal award solution for rationing problems.     

Tracking error: a multistage portfolio model

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.     

A new dynamic programming algorithm for the single item capacitated dynamic lot size model

We develop a new dynamic programming method for the single item capacitated dynamic lot size model with non-negative demands and no backlogging. This approach builds the Optimal value function in piecewise linear segments. It works very well on the test problems, requiring less than 0.3 seconds to solve problems with 48 periods on a VAX 8600. Problems with the time horizon up to 768 periods are solved. Empirically, the computing effort increases only at a quadratic rate relative to the number of periods in the time horizon.This research was supported in part by NSF grants DDM-8814075 and DMC-8504786.     

Two-level dynamic optimization methods

The search for the optimum control of complex static or dynamic processes according toconventional optimization methods involves many problems due, in particular, to the volume and complexity of calculations. And, as the dimensions of the systems studied increases steadily, even if a theoretical solution is still possible, an acceptable solution from the economic standpoint can no longer be hoped for. To overcome these difficulties, an effective means is certainly the introduction of multilevel optimization methods. The use of such a technique for a static optimization of complex systems has already been discussed, and the problems of dynamic optimization are dealt with here. As for static systems, three decomposition methods can be applied. The different tasks to which they lead are examined for each of the levels, and the stability of coordinators is studied.     

Dynamic priority rule-based forward-backward heuristic algorithm for resource levelling problem in construction project

Resource levelling aims at minimizing the fluctuation of resource usage, which is accomplished by shifting non-critical activities within their float according to some heuristic rules. Most of these rules adopted a unidirectional scheduling based on a static priority rule. In this paper, we propose a dynamic priority rule-based forward-backward heuristic algorithm (FBHA). The FBHA optimizes resource allocation by shifting non-critical activities within their forward free float (FFF), forward total float (FTF) and backward free float (BFF), successively. A project is divided into several phases during each forward/backward scheduling module. In each phase, the shifting sequence and days of non-critical activities depend on a dynamic priority rule set. The FBHA is integrated into the Microsoft Project 2007 commercial software package to improve the performance of the software and facilitate the project planners. One example is analysed to illustrate the iteration process of the proposed FBHA. Another example with multiple precedence constraints is used to demonstrate the effectiveness of the proposed FBHA in complicated construction projects.     

Reduced RLT representations for nonconvex polynomial programming problems

This paper explores equivalent, reduced size Reformulation-Linearization Technique (RLT)-based formulations for polynomial programming problems. Utilizing a basis partitioning scheme for an embedded linear equality subsystem, we show that a strict subset of RLT defining equalities imply the remaining ones. Applying this result, we derive significantly reduced RLT representations and develop certain coherent associated branching rules that assure convergence to a global optimum, along with static as well as dynamic basis selection strategies to implement the proposed procedure. In addition, we enhance the RLT relaxations with v-semidefinite cuts, which are empirically shown to further improve the relative performance of the reduced RLT method over the usual RLT approach. We present computational results for randomly generated instances to test the different proposed reduction strategies and to demonstrate the improvement in overall computational effort when such reduced RLT mechanisms are employed.