Optimal multi-period service capacity allocation and pricing allowing for uncertain competitive entry

A nonlinear programming model is formulated in this paper to determine the optimal scheme of capacity allocation and prices over a multi-period planning horizon for a service provider in the absence and presence of uncertain competitive entry. The model is solved for constant, decreasing, and increasing price sensitivities employing a combination of analytical and numerical methods. The study highlights the importance of advance selling of service prior to its eventual consumption in the spot period and investigates the impact of uncertain competitive entry on the optimal capacity allocation policy and its related profit if the entry is more or less likely or if the rival is more or less influential. The findings of the study reveal that the conclusions drawn from a two-period model are not necessarily generalizable to a model of a multi-period planning horizon.     

E-retailing of restaurant services: pricing strategies in a competing online environment

Establishing online channels and providing online discounts by building business partner relationships with third-party websites have emerged as important and effective marketing strategies in the restaurant industry. This study examines the optimal pricing strategy of restaurants in a competing environment when they participate in this relationship with a third-party website. Results suggest that neither participation nor online price discount should be encouraged for all restaurants. In particular, for a restaurant with a fixed service capacity, participation and online price discount are recommended when the number of offline loyal customers is relatively small. With the increase in the number of loyal offline customers, the optimal online discount rate decreases, whereas the unit commission fee for the third-party website remains constant. When the optimal discount rate reaches zero, the optimal decision for the restaurant is to decrease the unit commission fee. Based on these findings, this study analytically provides the optimal pricing strategies for restaurants and the corresponding boundaries for the strategy set.     

Optimal EOQ Models for Deteriorating Items with Time-Varying Demand

In this paper, optimal inventory lot-sizing models are developed for deteriorating items with general continuous time-varying demand over a finite planning horizon and under three replenishment policies. The deterioration rate is assumed to be a constant fraction of the on-hand inventory. Shortages are permitted and are completely backordered. The proposed solution procedures are shown to generate global minimum replenishment schedules for both general increasing and decreasing demand patterns. An extensive empirical comparison using randomly generated linear and exponential demands revealed that the replenishment policy which starts with shortages in every cycle is the least cost policy and the replenishment policy which prohibits shortages in the last cycle exhibited the best service level effectiveness. An optimal procedure for the same problem with trended inventory subject to a single constraint on the minimum service level (maximum fraction of time the inventory system is out of stock during the planning horizon) is also proposed in this paper.     

Service outsourcing under co-opetition and information asymmetry

Co-opetition refers to the phenomenon that firms simultaneously cooperate and compete in order to maximize their profits. This paper studies the contracting for an outsourcing supply chain (a user company vs. a service provider) in the presence of co-opetition and information asymmetry. The user company outsources part of his service capacity at a discount price to the service provider for sale. The service provider charges a commission for doing outsourcing work and competes with the user company for the service capacity to satisfy their respective demands. We solve for the service provider’s optimal commission decision and the user company’s optimal outsourcing decisions (outsourcing volume and price discount) when the user company has private information about his service capacity. Specifically, we highlight the following observations. For the service provider, a menu of two-part tariffs that consist of a fixed commission and a per-volume commission can reveal the true type of the user company’s capacity; the user company’s optimal outsourcing proportion is quasi-convex and the optimal price discount is non-decreasing in his capacity volume, which is counterintuitive.     

Supply chain analysis under a price-discount incentive scheme for electric vehicles

We investigate an automobile supply chain where a manufacturer and a retailer serve heterogeneous consumers with electric vehicles (EVs) under a government’s price-discount incentive scheme that involves a price discount rate and a subsidy ceiling. We show that the subsidy ceiling is more effective in influencing the optimal wholesale pricing decision of the manufacturer with a higher unit production cost. However, the discount rate is more effective for the manufacturer with a lower unit production cost. Moreover, the expected sales are increasing in the discount rate but may be decreasing in the subsidy ceiling. Analytic results indicate that an effective incentive scheme should include both a discount rate and a subsidy ceiling. We also derive the necessary condition for the most effective discount rate and subsidy ceiling that maximize the expected sales of EVs, and obtain a unique discount rate and subsidy ceiling that most effectively improve the manufacturer’s incentive for EV production.     

Optimal dynamic pricing of inventories with stochastic demand and discounted criterion

We consider a continuous time dynamic pricing problem for selling a given number of items over a finite or infinite time horizon. The demand is price sensitive and follows a non-homogeneous Poisson process. We formulate this problem as to maximize the expected discounted revenue and obtain the structural properties of the optimal revenue function and optimal price policy by the Hamilton-Jacobi-Bellman (HJB) equation. Moreover, we study the impact of the discount rate on the optimal revenue function and the optimal price. Further, we extend the problem to the case with discounting and time-varying demand, the infinite time horizon problem. Numerical examples are used to illustrate our analytical results.     

电子市场与期权合约市场并存下的供应链优化

在电子市场与期权合约市场并存条件下,构建供应商的生产成本函数模型,找出供应商的最优产能决策,分销商的最优期权订货量决策,集成化供应链的最优产能决策等.然后借助数值分析,找出供应商的最优期权合约参数,及各最优解的变化规律.分析得到,电子市场准入程度的增大、电子市场价格的增大都会促使供应商提高产能;电子市场价格的增大、供应商期权预订价格的降低、期权执行价格的降低、终端市场需求的增大都会促使分销商增大期权订货量和期权执行量,供应商应选择(期权预定价格较小,期权执行价格较大)的优化决策,并针对不同的市场风险选择不同的期权合约参数组合.     

Multiple-Project Scheduling with Controllable Project Duration and Hard Resource Constraint: Some Solvable Cases

In many large-scale project scheduling problems, multiple projects are either taking place at the same time or scheduled into a tight sequence in order to efficiently share a common resource. One example of this is the computing resource allocation at an Application Service Provider (ASP) which provides data processing services for multiple paying customers. Typical services provided by ASPs are data mining, payroll processing, internet-based storage backup services and Customer Relation Management (CRM) services. The processing mode of an ASP can be either batch or concurrent, depending on the type service rendered. For example, for CPU intensive or long processing time required services, it would be more economical to processes one customer request at a time in order to minimize the context switching overhead. While the data transaction processes within a service request are subject to certain precedence relationships, the requests from different customers to an ASP are independent of each other, and the total time required to process a service request depends on the computing resource allocated to that request. The related issue of achieving an optimal use of resources at ASPs leads to problem of project scheduling with controllable project duration.In this paper, we present efficient algorithms for solving several special cases of such multi-project scheduling problems with controllable project duration and hard resource constraints. Two types of problems are considered. In type I, the duration of each project includes a constant and a term that is inversely proportional to the amount of resource allocated. In type II, the duration of each individual project is a continuous decreasing function of the amount of resource allocated.     

An inventory model for slow moving items subject to obsolescence

In this paper, we consider a continuous review inventory system of a slow moving item for which the demand rate drops to a lower level at a known future time instance. The inventory system is controlled according to a one-for-one replenishment policy with a fixed lead time. Adapting to lower demand is achieved by changing the control policy in advance and letting the demand take away the excess stocks. We show that the timing of the control policy change primarily determines the tradeoff between backordering penalties and obsolescence costs. We propose an approximate solution for the optimal time to shift to the new control policy minimizing the expected total cost during the transient period. We find that the advance policy change results in significant cost savings and the approximation yields near optimal expected total costs.     

OPTIMAL DISCOUNTING OF BENEFITS FROM CLEANUP AT WASTE SITES

Abstract This paper uses a general equilibrium optimal growth model to discuss the role of optimal discounting of future benefits from cleanup at high‐level toxic waste sites. Cleanup simultaneously generates two streams of benefits. One of these is directly from utility and the other is indirectly from the added productivity of workers. We note that the optimal discount rate is different for these two types of benefits. Along the optimal path, the former are discounted at the rate of time preference and the latter at the market rate of interest. We achieve this by identifying four components of the shadow value of the stock of toxic waste. These are the utility, productivity, cost, and abundance effects. The distinction between discount rates appears to have been overlooked in the literature but has significant implications for environmental cost‐benefit analysis due to the growing interest in applying zero time preference to environmental problems, (like waste cleanup) whose consequences extend many generations into the future. A numerical example is included to illustrate these concepts.     

基于优惠合同的在线租赁策略设计

近年来租赁行业竞争日益激烈,租赁企业为了吸引客户有时会开展一些优惠活动。针对这一现状,本文讨论了存在优惠合同时承租方的在线租赁决策问题,其中假设该优惠合同 给予承租方一次以比较优惠的价格连续租赁设备多期的机会。首先,分析了存在优惠合同时的最优离线策略。其次,利用在线算法和竞争比理论分别设计了承租方放弃优惠合同和签订优惠 合同两种情形下的最优在线策略及最优竞争比。最后,通过汽车租赁优惠的数值算例说明选择签订优惠合同是更好的策略,进一步给出了签订优惠合同和购买设备的最佳时间。     

Harvesting of a phytoplankton–zooplankton model

Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results.     

A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment

For the capacity of any warehouse is limited, it has to rent warehouse (RW) for storing the excess units over the fixed capacity W of the own warehouse (OW) in practice. The RW is assumed to offer better preserving facilities than the OW resulting in a lower rate of deterioration and is assumed to charge higher holding cost than the OW. In this paper, a two-warehouse inventory model for deteriorating items is considered with constant demand under conditionally permissible delay in payment. The purpose of this study is to find the optimal replenishment policies for minimizing the total relevant inventory costs. Useful theorems to characterize the optimal solutions have been derived. Furthermore, numerical examples are provided to illustrate the proposed model, sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.     

Location and allocation for distribution systems with transshipments and transportion economies of scale

Locating transshipment facilities and allocating origins and destinations to transshipment facilities are important decisions for many distribution and logistic systems. Models that treat demand as a continuous density over the service region often assume certain facility locations or a certain allocation of demand. It may be assumed that facility locations lie on a rectangular grid or that demand is allocated to the nearest facility or allocated such that each facility serves an equal amount of demand. These assumptions result in suboptimal distribution systems. This paper compares the transportation cost for suboptimal location and allocation schemes to the optimal cost to determine if suboptimal location and allocation schemes can produce nearly optimal transportation costs. Analytical results for distribution to a continuous demand show that nearly optimal costs can be achieved with suboptimal locations. An example of distribution to discrete demand points indicates the difficulties in applying these results to discrete demand problems.     

Optimizing contracted resource capacity with two advance cancelation modes

Critical resources are often shared among different classes of customers. Capacity reservation allows each class of customers to better manage priorities of its customers but might lead to unused capacity. Unused capacity can be avoided or reduced by advance cancelation. This paper addresses the service capacity reservation for a given class of customers. The reservation process is characterized by: contracted time slots (CTS) reserved for the class of customers, requests for lengthy regular time slots (RTS) and two advance cancelation modes to cancel CTS one-period or two-period before. The optimal control under a given contract is formulated as an average cost Markov Decision Process (MDP) in order to minimize customer waiting times, unused CTS and CTS cancelation. Structural properties of optimal control policies are established via the corresponding discounted cost MDP problem. Numerical results show that two-period advance CTS cancelation can significantly improve the contract-based solution.     

收入管理的MMV动态拍卖机制研究

随着互联网上交易的增多,多单位同质产品销售的拍卖机制成为了一个新的研究方向.针对易逝性服务产品的收入管理问题,提出将产品销售分为多个拍卖期的MMV(Multi-period and Multi-unit Vickrey(Auction with Reserve Pricing)动态拍卖机制,给出每期最优拍卖单位数和保留价格的确定方法,证明了最优拍卖单位数分别关于剩余存量和销售时间单增的性质,以及保留价格关于剩余存量的单降性.最后证明MMV机制的每期实际成交价格将高于Vulcano(2002)提出的MSP(Modified Second-Price)机制,根据易逝性服务产品的需求特点得到MMV机制优于MSP机制的结论.     

Analysis of supply contracts with quantity flexibility

This paper explores a class of supply contracts under which a buyer receives discounts for committing to purchases in advance. The further in advance the commitment is made, the larger the discount. As time rolls forward, the buyer can increase the order quantities for future periods of the rolling horizon based on updated demand forecast information and inventory status. However, the buyer pays a higher per-unit cost for the incremental units. Such contracts are used by automobile and contract manufacturers, and are quite common in fuel oil and natural gas delivery markets. We develop a finite-horizon dynamic programming model to characterize the structure of the optimal replenishment strategy for the buyer. We present heuristic approaches to calculate the order volume in each period of the rolling horizon. Finally, we numerically evaluate the heuristic approaches and draw some managerial insights based on the findings.     

确定性需求下的最优保理融资与生产策略

企业为下游买方提供赊销,由于大量的资金被应收账款占用,企业可能因资金不足而无法生产足够的产品。企业可以通过保理(出售应收账款)进行融资,减小需求损失。在离散时间多周期的确定需求下,使用决策变量描述各周期的系统状态及其状态转移方程,将此问题建模为线性规划。通过分析此问题的结构特点,再提出了一种新颖且等价的建模方法,可以有效减少决策变量和约束条件的数量。在连续时间模型和混合模型中,这种建模方法同样适用,将优化问题写为连续线性规划,极大地降低了优化问题的复杂度。此连续线性规划问题可通过适当的区间划分进行离散化,用分片常量函数代替优化模型中的一般函数(无限维)决策变量,通过求解有限维线性规划得到原问题的可行近似解。最后,通过数值例子分析了贴现率对企业利润的影响。     

A Differential Games Solution to a Logarithmic Advertising Model

A logarithmic excess-advertising model of a duopoly is presented, and Nash optimal open-loop advertising strategies are determined. It turns out that if the two firms use different discount rates, then the optimal strategies will be exponentially decreasing. However, in this case the state equation has no nice solution and must be solved by numerical methods. When both firms use the same discount rate, then the state equation has a simple solution. This solution is also valid for the case where no discounting is performed. Furthermore, when no discounting is performed, the optimal strategies will be simple time-linear decreasing strategies. Finally, it is studied how the optimal strategies and trajectories depend on the parameters of the model.     

Dynamic repositioning strategy in a bike-sharing system; how to prioritize and how to rebalance a bike station

Bike-sharing systems are becoming increasingly popular in large cities. The natural imbalance and the stochasticity of bike’s arrivals and departures lead operators to develop redistribution strategies in order to ensure a sufficiently high quality of service for users. Using a Markov decision process approach, we develop an implementable decision-support tool which may help the operator to decide at any point of time (i) which station should be prioritized, and (ii) which number of bikes should be added or removed at each station. Our objective is to minimize the rate of arrival of unsatisfied users who find their station empty or full. The existence of an optimal inventory level at each station is proven. It may vary over time but does not depend on the capacity of the truck which operates the repositioning. Next, we compute the relative value function of the system, together with the average cost and the optimal state. These results are used to derive a policy for station’s prioritization using a one-step policy improvement method. We evaluate our policy in comparison with the optimal one and with other intuitive ones in an extended version of our model. From our numerical experiments, we show that only a little intervention of the operator can significantly enhance the quality of service, and that the rule of thumb for bike repositioning is to prioritize the closer, the more active, the closer to be full or empty, and the more imbalanced stations if no reversing in the imbalance is anticipated.