Asymptotic analysis for multi-objective sequential stochastic assignment problems

ABSTRACT

We provide an asymptotic analysis of multi-objective sequential stochastic assignment problems (MOSSAP). In MOSSAP, a fixed number of tasks arrive sequentially, with an n-dimensional value vector revealed upon arrival. Each task is assigned to one of a group of known workers immediately upon arrival, with the reward given by an n-dimensional product-form vector. The objective is to maximize each component of the expected reward vector. We provide expressions for the asymptotic expected reward per task for each component of the reward vector and compare the convergence rates for three classes of Pareto optimal policies.     

A stochastic control model of investment,production, and consumption on a finite horizon

In this paper, we consider a stochastic control problem on a finite time horizon. The unit price of capital obeys a logarithmic Brownian motion, and the income from production is also subject to the random Brownian fluctuations. The goal is to choose optimal investment and consumption policies to maximize the finite horizon expected discounted hyperbolic absolute risk aversion utility of consumption. A dynamic programming principle is used to derive a time‐dependent Hamilton–Jacobi–Bellman equation. The Leray–Schauder fixed point theorem is used to obtain existence of solution of the HJB equation. At last, we derive the optimal investment and consumption policies by the verification theorem. The main contribution in this paper is the use of PDE technique to the finite time problem for obtaining optimal polices. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis for some properties of discrete time Markov decision processes

This paper investigates properties of the optimality equation and optimal policies in discrete time Markov decision processes with expected discounted total rewards under weak conditions that the model is well defined and the optimality equation is true. The optimal value function is characterized as a solution of the optimality equation and the structure of optimal policies is also given.     

Coordinating a decentralized supply chain with customer returns and price-dependent stochastic demand using a buyback policy

We investigate a decentralized supply chain that consists of a manufacturer and a retailer where the retailer simultaneously determines the retail price and order quantity while experiencing customer returns and price dependent stochastic demand. We propose an agreement between the manufacturer and the retailer that includes two buyback prices, one for unsold inventory and a second for customer returns, and show that this type of easy-to-implement agreement can achieve perfect supply chain coordination and be a win-win for both manufacturer and retailer when a complementary profit-sharing agreement is included.     

A solution approach for optimizing long- and short-term production scheduling at LKAB’s Kiruna mine

We present a mixed-integer program to schedule long- and short-term production at LKAB’s Kiruna mine, an underground sublevel caving mine located in northern Sweden. The model minimizes deviations from monthly preplanned production quantities while adhering to operational constraints. Because of the mathematical structure of the model and its moderately large size, instances spanning a time horizon of more than a year or two tend to be intractable. We develop an optimization-based decomposition heuristic that, on average, obtains better solutions faster than solving the model directly. We show that for realistic data sets, we can generate solutions with deviations that comprise about 3-6% of total demand in about a third of an hour.     

The impact of sharing customer returns information in a supply chain with and without a buyback policy

In this paper, we examine a single period problem in a supply chain in which a Stackelberg manufacturer supplies a product to a retailer who faces customer returns and demand uncertainty. We show that the manufacturer incurs a significant profit loss with and without a buyback policy if it fails to account for customer returns in the wholesale price decision. Under the assumption that the retailer is better informed than the manufacturer on customer returns information, we show that without a buyback policy, the retailer prefers not to share if the manufacturer overestimates while it prefers to share customer returns information if the manufacturer underestimates this information. If the manufacturer offers a buyback policy, we have the opposite results. We also discuss incentives to share the customer returns information and some of the issues that are raised in sharing this information.     

The impact of dynamic pricing on the economic order decision

This paper analyzes the impact of dynamic pricing on the single product economic order decision of a monopolist retailer. Items are procured from an external supplier according to the economic order quantity (EOQ) model and are sold to customers on a single market without competition following the simple monopolist pricing problem. Coordinated decision making of optimal pricing and ordering is influenced by operating costs – including ordering and inventory holding costs – and the demand rate obtained from a price response function. The retailer is allowed to vary the selling price, either in a fixed number of discrete points in time or continuously. While constant and continuous pricing have received much attention in the literature, problems with a limited number of price changes are rather rare. This paper illustrates the benefit of dynamically changing prices to achieve operational efficiency in the EOQ model, that is to trigger high demand rates when inventories are high. We provide structural properties of the optimal time instants when the price should be changed. Taking into account costs for changes in price, it provides numerical guidance on number, timing, and size of price changes during an order cycle. Numerical examples show that the benefits of dynamic pricing in an EOQ framework can be achieved with only a few price changes and that products being unprofitable under static pricing may become profitable under dynamic pricing.     

Optimal intervention policies for a multidimensional simple epidemic process

We consider a deterministic simple epidemic process in which the susceptibles are exposed to n+1 diseases. It is assumed that one disease is relatively harmless while the others cause serious symptoms. Policies for introducing infection by the harmless disease are considered and, under a suitable cost structure, the optimal policy that minimises the future cost for every initial state is found. For the corresponding stochastic model, the optimal policy is found by implementing a suitable dynamic programming algorithm, and is compared numerically with the optimal policy for the deterministic model.     

再制造中零件供应系统整合优化研究

再制造企业里,在决策购买新零件或修复旧零件时,经常面对有限的拆卸修复信息和不确定的订货提前期.为了得到科学的决策,人们试图尽早地掌握拆卸修复零件的确切信息,与有能力的供应商建立良好的关系,或在企业建立管理信息系统来统计分析废旧品的状态和数量等.根据市场需求和产品批发价,以满足市场需求所要购买新零件数和拆卸修复机器数为决策变量,并考虑拆卸修复成功的概率,建立企业期望利润的数学模型,求得可能情况下的最优解或现实满意解.洞察再制造企业取得最大利润的主要影响因数及这些因数间的关系,为制作生产计划提供理论依据.最后指出进一步的研究问题.     

Influence of Grafted Chain Length of a Phenolic Copolymer on Its Complex Formation with Poly(vinyl Pyrrolidone) and Poly(ethylene Oxide)

A phenolic copolymer has been grafted with oligomers of different chain lengths. Polymer-polymer complexation has been studied between graft copolymers and nonionic polymers, such as polyvinyl pyrrolidone) and poly(ethylene oxide), in an acetone-methanol mixture by several methods, e.g., viscosity, conductance, and apparent pH measurements. A distinct stepwise complexation between PVP and graft copolymers has been observed. The length of the side chain also seemed to influence interpolymer complex formation. Some of these observations have been interpreted with reference to the actual structure of the graft copolymers.