TREATMENT VERSUS PREVENTION OF NITROGEN FERTILIZER POLLUTION: AN INTER‐SECTORAL EXTERNALITY POLICY MODEL

Abstract This article presents an economic, hydrological, dynamic optimization model, which describes the negative external effects of nitrogen fertilizers on groundwater quality. The relative merits of treatment versus prevention of nitrogen pollution were analyzed. A dynamical water and nitrogen flow between land surface, the unsaturated zone, and groundwater was employed. A specific treatment technology, which gives rise to a discontinuous cost function, was also used. Applying the model to the coastal aquifer in Israel, our results showed that in a joint (agricultural and domestic) water source area that supplies a relatively small quantity of drinking water, it is more efficient to combine a policy that imposes restrictions on the use of nitrogen with a drinking‐water treatment process. However, when a relatively large quantity of drinking water is involved, imposing restrictions on the use of nitrogen only is more efficient. The paper, thus, is useful to planners of fast growing urban population centers with regard to regulation and can be used to calculate and evaluate specific policies.     

Lease expiration management for a single lease term in the apartment industry

Lease expiration management (LEM) in the apartment industry aims to control the number of lease expirations and thus achieve maximal revenue growth. We examine rental rate strategies in the context of LEM for apartment buildings that offer a single lease term and face demand uncertainty. We show that the building may incur a significant revenue loss if it fails to account for LEM in the determination of the rental rate. We also show that the use of LEM is a compromise approach between a limited optimization, where no future demand information is available, and a global optimization, where complete future demand information is available. We show that the use of LEM can enhance the apartment building’s revenue by as much as 8% when the desired number of expirations and associated costs are appropriately estimated. Numerical examples are included to illustrate the major results derived from our models and the impact on the apartment’s revenue of sensitivity to the desired number of expirations and associated costs.     

Supply chain design considering economies of scale and transport frequencies

In this paper we consider a 3-echelon, multi-product supply chain design model with economies of scale in transport and warehousing that explicitly takes transport frequencies into consideration. Our model simultaneously optimizes locations and sizes of tank farms, material flows, and transport frequencies within the network. We consider all relevant costs: product cost, transport cost, tank rental cost, tank throughput cost, and inventory cost. The problem is based on a real-life example from a chemical company. We show that considering economies of scale and transport frequencies in the design stage is crucial and failing to do so can lead to substantially higher costs than optimal. We solve a wide variety of problems with branch-and-bound and with the efficient solution heuristics based on iterative linearization techniques we develop. We show that the heuristics are superior to the standard branch-and-bound technique for large problems like the one of the chemical company that motivated our research.     

Optimal Tax Enforcement with Imperfect Tax Payers and Inspectors

A mathematical model of tax enforcement is analyzed for the case when the probability of detecting tax evasion depends on the inspector's efforts. Contrary to the case with fixed inspection costs, the optimal tax enforcement strategy does not fully eliminate tax evasion. We examine how tax payers' random mistakes and the inspectors' corruptibility affect the optimal tax enforcement mechanism. We show that, contrary to the model with fixed inspection costs, corruption among inspectors reduces the optimal tax revenue.     

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.     

突发公共卫生事件中地方政府与社会公众间的演化博弈研究

近年来,突发公共卫生事件频发,社会公众与地方政府相互配合是及时、高效解决突发公共卫生事件的必然选择。本文以全球抗击新冠肺炎疫情为背景,讨论在突发公共卫生事件中社会公众与地方政府之间的博弈关系,基于有限理性假设,构建演化博弈模型,分析博弈双方决策行为的动态调整过程,得到在不同条件下社会公众和地方政府的演化稳定策略。同时,利用MATLAB进行仿真实验,分析在博弈过程中政府的奖惩、上级部门的处罚等主要因素对博弈双方策略选择的影响。研究结果表明,完善相关的补贴政策,普及疫情防控的相关法律法规,加大对社会公众随意流动、违反疫情相关规章制度的惩罚力度,提高对地方政府宽松防疫的处罚等措施可以有效促进社会公众和地方政府之间的相互协作,最终实现共同积极防疫。     

The central warehouse location problem revisited

This paper is concerned with the optimal location of a centralwarehouse, given a fixed number and the locations of the localwarehouses. We investigate whether the solution determined bythe traditional model that minimizes total transportation costdiffers from the one determined by a model that also takes intoaccount the inventory and service costs. We build simple modelsto address this question. Numerical results show that ignoringinventory costs in modelling location models may lead to inferiorlocation solutions.     

An equitable method for allocating fixed costs by using data envelopment analysis

This paper concerns the shared cost allocation problem by using Data Envelopment Analysis (DEA), which is observed in practical applications such as public services and production processes. In the management context, the cost allocation problem tries to balance the different desires of two management layers: central manager and each sector manager. The cost can be assigned in an equitable way to the various Decision Making Units (DMUs). To achieve this goal, we present a new DEA-based method for dividing a fixed cost among DMUs. In the proposed method, the fixed cost is assigned to DMUs such that the efficiency measures and the Returns to Scale classifications of all DMUs before and after assigning the fixed cost remain unchanged. Also, the gaps among the costs allocated to DMUs will be minimized. The proposed method has the flexibility to consider the management standpoints. Finally, numerical results of an elucidatory example are furnished to demonstrate the applicability and reliability of our scheme.     

Going beyond the basics: creating and inspiring problem solvers

This paper offers a general discussion of a complex student project used in a first-semester, first-year mathematics course that goes beyond the basics taught in the class and inspires creative problem solving. The project requires the student to model the transition of vehicles among regions of a vehicle rental company. A penalty cost is introduced when the regional inventory drops below an established threshold. The project allows the company to move vehicles by rail among regions to reduce or alleviate the penalty cost. In this phase of the project, student teams attempt to minimize the total cost to the company (penalty cost plus transportation costs), thus searching for an ‘optimal’ solution. The project allows the students to use technology to numerically develop an approximate solution to a problem that is easily understood, but whose analytical solution goes well beyond the scope of the course.     

Cooperation in assembly systems: The role of knowledge sharing networks

Process improvement plays a significant role in reducing production costs over the life cycle of a product. We consider the role of process improvement in a decentralized assembly system in which a buyer purchases components from several first-tier suppliers. These components are assembled into a finished product, which is sold to the downstream market. The assembler faces a deterministic demand/production rate and the suppliers incur variable inventory costs and fixed setup production costs. In the first stage of the game, which is modeled as a non-cooperative game among suppliers, suppliers make investments in process improvement activities to reduce the fixed production costs. Upon establishing a relationship with the suppliers, the assembler establishes a knowledge sharing network – this network is implemented as a series of meetings among suppliers and also mutual visits to their factories. These meetings facilitate the exchange of best practices among suppliers with the expectation that suppliers will achieve reductions in their production costs from the experiences learned through knowledge sharing. We model this knowledge exchange as a cooperative game among suppliers in which, as a result of cooperation, all suppliers achieve reductions in their fixed costs. In the non-cooperative game, the suppliers anticipate the cost allocation that results from the cooperative game in the second stage by incorporating the effect of knowledge sharing in their cost functions. Based on this model, we investigate the benefits and challenges associated with establishing a knowledge sharing network. We identify and compare various cost allocation mechanisms that are feasible in the cooperative game and show that the system optimal investment levels can be achieved only when the most efficient supplier receives the incremental benefits of the cost reduction achieved by other suppliers due to the knowledge transfer.     

Mathematical analysis of a model describing the number of antibiotic resistant bacteria in a polluted river

In France, 90% of surface water suffer from antibiotic pollution that increases the number of antibiotic resistant bacteria. The first indicator of water quality is revealed by the fish quality. According to the Le Conseil Supérieur de la Pêche, only 15% of rivers in France are considered in good condition, whereas 22% are in very bad condition. The bacterial resistance to antibiotics is a public health problem as it affects humans through drinking water; the treatment of water is costly. Mathematical modeling may estimate and predict the quantity of bacteria in rivers. In this paper, we investigate properties of the mathematical model estimating the number of bacteria in a river presented by Lawrence, Mummert and Somerville. Global analysis of equilibria is presented, using a Lyapunov function. Moreover, the existence of positive periodic solutions is proven. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal process control policies under a time-varying cost structure

Quality experts have recognized two types of quality costs resulting from failure of control; namely, internal and external failure costs of control. Explicitly considering the difference between internal and external failure costs in designing statistical process control procedures is especially important in today’s business environment because (1) inventory holding time is strategically kept very short because of the just-in-time philosophy, and (2) product values decrease at a very fast rate over time because of advances in technology and keen competition. In this paper, we develop a process control model under a time-varying cost structure, based on internal and external failure costs. Using the model, we also study the process control policies when the value of the product may decrease over time. We consider two forms of product perishability. The first is an exponential product value drop, and the second is a fixed life product life.     

Introducing competition in healthcare services: The role of private care and increased patient mobility

We study the operational implications from competition in the provision of healthcare services, in the context of national public healthcare systems in Europe. Specifically, we study the potential impact of two alternative ways through which policy makers have introduced such competition: (i) via the introduction of private hospitals to operate alongside public hospitals and (ii) via the introduction of increased patient choice to grant European patients the freedom to choose the country they receive treatment at. We use a game-theoretic framework with a queueing component to capture the interactions among the patients, the hospitals and the healthcare funders. Specifically, we analyze two different sequential games and obtain closed form expressions for the patients’ waiting time and the funders’ reimbursement cost in equilibrium. We show that the presence of a private provider can be beneficial to the public system: the patients’ waiting time will decrease and the funders’ cost can decrease under certain conditions. Also, we show that the cross-border healthcare policy, which increases patient mobility, can also be beneficial to the public systems: when welfare requirements across countries are sufficiently close, all funders can reduce their costs without increasing the patients’ waiting time. Our analysis implies that in border regions, where the cost of crossing the border is low, “outsourcing” the high-cost country’s elective care services to the low-cost country is a viable strategy from which both countries’ systems can benefit.     

Intermodal shipments as recourse in logistics disruptions

This research deals with the flexibility of transportation systems when faced with disruptions. A network optimization model is used to investigate the feasibility of using intermodal shipments as recourse to disruptions in a transportation network. In a study of US interstate highways and intermodal rail networks, performance of over-the-road and intermodal shipments is compared under different disruption scenarios. The results show that the topology of US transportation system and locations of existing intermodal terminals provide required path redundancies and a strategic benefit for intermodal shipments to bypass disrupted regions with lower costs and competitive shipment times compared to rerouted road shipments.     

TOWARD CONTROLLING NONPOINT SOURCE POLLUTION OF GROUNDWATER: A HIERARCHICAL POLICY FORMULATION GAME

An integrative approach to formulating agricultural policy instrument levels is suggested for controlling groundwater quality deterioration from agricultural chemical-use, while reconciling the conflicting goals of primary interest groups in the farm policy process. The paper develops a Stackelberg game-theoretic model of public policy formation that simultaneously determines endogenous price supports and nitrogen-use quota, as well as the optimal permissible water contamination. The analysis distinguishes between the private and social opportunity costs of producing agricultural crops and using groundwater as a repository for nitrate leachate from agricultural sources. It is recognized that the social benefit of using nitrogen in agriculture is less than the private benefit to producers. Private and social benefits, as well as optimal production and pollution solutions, will vary as the relative weights which policymakers attach to different social constituents change. The method developed in this paper may be applicable to any policy process in which policymakers exercise indirect influence over industrial production decisions through economic instruments.     

Multi-location transshipment problem with capacitated transportation

We consider coordination among stocking locations through replenishment strategies that take explicitly into consideration transshipments, transfer of a product among locations at the same echelon level. We incorporate transportation capacity such that transshipment quantities between stocking locations are bounded due to transportation media or the location’s transshipment policy. We model different cases of transshipment capacity as a capacitated network flow problem embedded in a stochastic optimization problem. Under the assumption of instantaneous transshipments, we develop a solution procedure based on infinitesimal perturbation analysis to solve the stochastic optimization problem, where the objective is to find the policy that minimizes the expected total cost of inventory, shortage, and transshipments. Such a numerical approach provides the flexibility to solve complex problems. Investigating two problem settings, we show the impact of transshipment capacity between stocking locations on system behavior. We observe that transportation capacity constraints not only increase total cost, they also modify the inventory distribution throughout the network.     

Allocating fixed costs or resources and setting targets via data envelopment analysis

In many applications of data envelopment analysis (DEA), there is often a fixed cost or input resource which should be imposed on all decision making units (DMUs). Cook and Zhu [W.D. Cook, J. Zhu, Allocation of shared costs among decision making units: A DEA approach, Computers and Operations Research 32 (2005) 2171-2178] propose a practical DEA approach for such allocation problems. In this paper, we prove that when some special constraints are added, Cook and Zhu’s approach probably has no feasible solution. The research of this paper focuses on two main aspects: to obtain a new fixed costs or resources allocation approach by improving Cook and Zhu’s approach, and to set fixed targets according to the amount of fixed resources shared by individual DMUs. When such special constraints are attached, our model is proved to be able to achieve a feasible costs or resources allocation. Numerical results for an example from the literature are presented to illustrate our approach.     

绿色技术创新利益相关者的三群体演化博弈及其仿真

基于利益相关者和演化博弈理论,探讨绿色技术创新活动中相关利益主体的角色和作用,并构建政府、企业和公众间的三群体演化博弈模型,运用MATLAB仿真分析政府、企业及公众在不同稳定性条件下演化决策行为。研究表明:绿色技术创新活动中政府、企业及公众三个参与主体间行为选择策略存在路径依赖;政府的公众环保宣传力度并非越强越好,适度的公众环保宣传有助于推动绿色技术创新发展,过度宣传反而会因高成本而阻碍绿色技术创新;政府征收污染税费并采取技术创新激励会推动企业采纳绿色技术创新,但高额的技术创新激励会抑制政府的环境规制。因此,政府应完善环境规制的政策法规,增强企业绿色技术创新主体地位,激励公众的监督积极性,形成政府-企业-公众合力,共同推动绿色技术创新发展。     

Stochastic impulse control with regime switching for the optimal dividend policy when there are business cycles,taxes and fixed costs

We consider the problem of finding the optimal dividend policy for a company whose cash reserve follows a Brownian motion with drift and volatility modulated by an observable finite-state continuous-time Markov chain. The Markov chain represents the regime of the economy. We allow fixed costs and taxes associated with the dividend payments. This optimization problem generates a stochastic impulse control problem with regime switching. We solve this problem and obtain the first analytical solutions for the optimal dividend policy when there are simultaneously fixed costs, taxes and business cycles. Our results show that the optimal dividend policy depends strongly on the regime of the economy, on fixed costs and on taxes.     

新能源分时租赁汽车监管机制的演化博弈分析

目前我国新能源分时租赁汽车正处于发展初期,其发展过程中存在的问题接踵而至,如运营不力、安全隐患以及骗取补贴金等,对消费者和政府造成了较大的困扰。本文运用演化博弈理论构建了政府部门、企业与消费者之间的三方动态博弈模型,基于复制动态方程和雅可比矩阵对模型进行求解分析,并通过Python软件对模型结果进行数值仿真模拟。研究表明,当关键参数取值位于不同数值区间时,系统分别呈现出四种演化稳定结果。适当加大补贴额度与惩罚力度、增加消费者得到的补偿系数比例、敦促企业降低努力经营成本,有利于新能源分时租赁汽车行业的健康发展。研究结论为政府部门政策制定及决策实施提供理论依据与参考。