Optimal placement of add /drop multiplexers static and dynamic models

We study further a problem that has arisen recently in the design of telecommunications transmission networks at France Telecom. Given a set of centers in a city or conglomeration linked together on a ring architecture, given the expected demands between the centers and an essentially unlimited availability of rings of fixed capacity on the network, assign demand pairs and corresponding add/drop multiplexers to the rings so as to satisfy the demands and minimize the number of ‘costly’ multiplexers installed.     

A bi-level stochastic optimization model for reliable supply chain in competitive environments: Hybridizing exact method and genetic algorithm

Managing supply chain operations in a reliable manner is a significant concern for decision-makers in competitive industries. In this article, two mathematical models considering competition and integrity in a three-echelon supply chain under uncertainty are proposed. The competition is formulated as a Stackelberg game such that the distribution centers have more power than the retailers. In the first model, decisions are made about the location and number of distribution centers (DCs), allocation of retailers, and the selling price of products. In the second model, based on the real world, the probability of risk and failure for the distribution centers are considered. Backup facilities should be established for unreliable facilities to meet the demands of retailers during disruption. To capture uncertainty, a two-stage stochastic approach is applied to model the problems. The first stage of the model belongs to the strategic planning and is not affected by randomness, while the second stage deals with tactical decisions depending on the realization of the first stage's random vector. In order to solve the problem, a hybrid genetic algorithm has been applied to large-scale problems. Numerical experiments have been conducted to assess the effectiveness of the proposed algorithm. Next, a sensitivity analysis is performed to recognize the most important parameters and evaluate the accuracy of our approach. Finally, to demonstrate the applicability of the model, the proposed model was implemented on the data of Alborz Pharmaceutical Company.     

Capacitated location model with online demand pooling in a multi-channel supply chain

This paper presents a location model that assigns online demands to the capacitated regional warehouses currently serving in-store demands in a multi-channel supply chain. The model explicitly considers the trade-off between the risk pooling effect and the transportation cost in a two-echelon inventory/logistics system. Keeping the delivery network of the in-store demands unchanged, the model aims to minimize the transportation cost, inventory cost, and fixed handling cost in the system when assigning the online demands. We formulate the assignment problem as a non-linear integer programming model. Lagrangian relaxation based procedures are proposed to solve the model, both the general case and an important special case. Numerical experiments show the efficiency of our algorithms. Furthermore, we find that because of the pooling effect the variance of in-store demands currently served by a warehouse is an important parameter of the warehouse when it is considered as a candidate for supplying online demands. Highly uncertain in-store demands, as well as low transportation cost per unit, can make a warehouse appealing. We illustrate with numerical examples the trade-off between the pooling effect and the transportation cost in the assignment problem. We also evaluate the cost savings between the policy derived from the model, which integrates the transportation cost with the pooling effect, and the commonly used policy, which is based only on the transportation cost. Results show that the derived policy can reduce 1.5–7.5% cost in average and in many instances the percentage of cost savings is more than 10%.     

考虑老年人感知满意度的社区居家养老护理人员调度策略研究

近年来,随着人口老龄化进程不断加快,社区居家养老模式越来越受到社会各界的高度关注。为了向社区居家养老服务中心护理人员调度提供决策支持,研究考虑老年人感知满意度的护理人员调度问题。以社区居家养老预约服务为背景,首先融合前景理论和模糊理论分别从老年人等待时间、老年人对护理人员偏好和老年人对服务价格偏好三个方面建立老年人感知满意度函数;其次确定主要目标为最大化老年人综合感知满意度,次要目标为最小化社区居家养老服务中心运营成本的优化调度问题,并且构建了相应的混合整数非线性规划数学模型;最后综合应用遗传算法和模拟植物生长算法(PGSA)对该模型进行求解,其中遗传算法用于求解护理人员的服务顺序,PGSA用于求解护理人员调度方案,并且利用MATLAB软件进行仿真,同时引入粒子群算法与PGSA进行计算对比,发现PGSA在性能参数和计算时间方面都有明显的优势。通过算例验证分析,结果表明该模型在考虑老年人感知满意度的基础上,能够获得最优的护理人员调度方案,证明了上述优化模型和算法的可行性和有效性。     

Supply chain network competition among blood service organizations: a Generalized Nash Equilibrium framework

In this paper we present a Generalized Nash Equilibrium model of supply chain network competition among blood service organizations which compete not only for blood donors but also for business from hospitals and medical centers. The model incorporates not only link capacities and associated arc multipliers to capture perishability, but also bounds on the number of donors in regions as well as lower and upper bounds on the demands at the demand points in order to ensure needed amounts for surgeries, treatments, etc., while reducing wastage. The concept of a variational equilibrium is utilized to transform the problem into a variational inequality problem, and alternative formulations are given. A Lagrange analysis yields economic insights. The proposed algorithmic procedure is then applied to a series of numerical examples in order to illustrate the impacts of disruptions in the form of a reduction on the number of donors as well as that of decreases in capacities of critical links such as testing and processing on RBC prices, demands, net revenues of the blood service organizations, and their overall utilities.

     

Robust weighted vertex p-center model considering uncertain data: An application to emergency management

This paper presents a generalized weighted vertex p-center (WVPC) model that represents uncertain nodal weights and edge lengths using prescribed intervals or ranges. The objective of the robust WVPC (RWVPC) model is to locate p facilities on a given set of candidate sites so as to minimize worst-case deviation in maximum weighted distance from the optimal solution. The RWVPC model is well-suited for locating urgent relief distribution centers (URDCs) in an emergency logistics system responding to quick-onset natural disasters in which precise estimates of relief demands from affected areas and travel times between URDCs and affected areas are not available. To reduce the computational complexity of solving the model, this work proposes a theorem that facilitates identification of the worst-case scenario for a given set of facility locations. Since the problem is NP-hard, a heuristic framework is developed to efficiently obtain robust solutions. Then, a specific implementation of the framework, based on simulated annealing, is developed to conduct numerical experiments. Experimental results show that the proposed heuristic is effective and efficient in obtaining robust solutions. We also examine the impact of the degree of data uncertainty on the selected performance measures and the tradeoff between solution quality and robustness. Additionally, this work applies the proposed RWVPC model to a real-world instance based on a massive earthquake that hit central Taiwan on September 21, 1999.     

Robust and data-driven approaches to call centers

We propose both robust and data-driven approaches to a fluid model of call centers that incorporates random arrival rates with abandonment to determine staff levels and dynamic routing policies. We test the resulting models with real data obtained from the call center of a US bank. Computational results show that the robust fluid model is significantly more tractable as compared to the data-driven one and produces overall better solutions to call centers in most experiments.     

Solving a multi periodic stochastic model of the rail–car fleet sizing by two-stage optimization formulation

We propose a formulation and solution procedure for optimizing the fleet size and freight car allocation under uncertainty demands. There are important interactions between decisions on sizing a rail–car fleet and utilizing that fleet. Consequently, the optimum use of empty rail–cars for demands response in the length of the time periods one of advantages the proposed model. The model also provides rail network information such as yard capacity, unmet demands, and number of loaded and empty rail–car at any given time and location. Consequently, the model helping managers or decision makers of any train company for planning and decision making. We propose two-stage solution procedure for solve rail–car fleet sizing problem. Numerical examples are given to illustrate the model and solution methodology.     

Research on the vehicle routing problem with interval demands

In this paper, a vehicle routing problem with interval demands is investigated based on the motivation of dispatching vehicles to deliver perishable products in practice. A nonlinear interval-based programming method is used to build a model for the vehicle routing problem with interval demands, which assumes that demands of customers are uncertain but fall in given intervals and actual demand of a customer becomes known only when the vehicle visited the customer. A vehicle-coordinated strategy was designed to solve the service failure problem. A hybrid algorithm based on the artificial immune system is also proposed to solve the model for vehicle routing problem with interval demands. The validity of methods and sensitivity analysis are illustrated by conducting some numerical examples. We find that the tolerant possibility degree of interval number has significant impacts on the distances. The planned distance strictly increased, while the additional distance strictly decreased and the total distance after coordinated transport has a U-typed relationship with the tolerant possibility degree of interval number.     

A two-echelon stochastic facility location model for humanitarian relief logistics

We develop a two-stage stochastic programming model for a humanitarian relief logistics problem where decisions are made for pre- and post-disaster rescue centers, the amount of relief items to be stocked at the pre-disaster rescue centers, the amount of relief item flows at each echelon, and the amount of relief item shortage. The objective is to minimize the total cost of facility location, inventory holding, transportation and shortage. The deterministic equivalent of the model is formulated as a mixed-integer linear programming model and solved by a heuristic method based on Lagrangean relaxation. Results on randomly generated test instances show that the proposed solution method exhibits good performance up to 25 scenarios. We also validate our model by calculating the value of the stochastic solution and the expected value of perfect information.     

Supporting strategic conversations: the significance of a quantitative model building process

This paper reports on the use of a quantitative system dynamics simulation model building process that followed on from a ‘soft OR’ strategy making intervention with a top management team. The work was carried out for the Chief Constable and top team of a UK police force. The output of the ‘soft OR’ strategy making process provided the reason for, and so focus of, the simulation model. The focus of the strategic conversation was on exploring the tension between the supply of resources (in this case police officers) and the demands placed on those officers. The project involved a series of strategic conversations with members of the top team that were stimulated through the process of building a system dynamics model. The process was facilitated by two modellers—one focussing on managing the strategic enquiry, while the other considered the implications of the conversation for the construction of the system dynamics model. Through the process of gradually building the system dynamics model, a number of issues and lessons were raised for the development and delivery of effective strategy making and the strategic management of public organisations. In addition there were implications for operational research model building processes, especially when operating at senior levels and within a strategic context.     

A Benders decomposition approach for a distribution network design problem with consolidation and capacity considerations

We develop a model for a strategic freight-forwarding network design problem in which the design decisions involve the locations and capacities of consolidation and deconsolidation centers, and capacities on linehaul linkages as well as the shipment routes from origins to destinations through centers. We devise a solution approach based on Benders decomposition and conduct a computational study that illustrates the efficiency and the effectiveness of the approach.     

多年时滞教育经济投入占用产出模型与教育结构研究

提出一个新的考虑多年时滞的动态投入占用产出模型研究教育结构,采用阶变法处理投入产出模型的非线性系数,编制2000年教育经济投入占用产出表,计算教育规模和人力资本需求和教育经费投入,发现高级人力资本在总量上,特别是结构上的短缺是中国经济发展的一个严重问题.     

Inventory management with partially observed nonstationary demand

We consider a continuous-time model for inventory management with Markov modulated non-stationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also assume that demands are observed only when they are completely met. We first derive the explicit filtering equations and pass to an equivalent fully observed impulse control problem in terms of the sufficient statistics, the a posteriori probability process and the current inventory level. We then solve this equivalent formulation and directly characterize an optimal inventory policy. We also describe a computational procedure to calculate the value function and the optimal policy and present two numerical illustrations.     

带覆盖需求约束的设施选址问题

带覆盖需求约束的设施选址问题(FLPWCDL)研究:客户必须在规定的响应半径内被服务,并要求服务站能够覆盖规定的需求数量,如何选择合适的服务站,使总成本(建站成本+路线成本)最小.FLPWCDL广泛应用于应急服务、物流、便利店等服务站的选址.建立了问题的混合整数规划模型,并构造了求解FLPWCDL的Benders分解算法,计算实验显示Benders分解算法具有非常高的求解效率与求解质量.     

Telecommunication Network Capacity Design for Uncertain Demand

The expansion of telecommunication services has increased the number of users sharing network resources. When a given service is highly demanded, some demands may be unmet due to the limited capacity of the network links. Moreover, for such demands, telecommunication operators should pay penalty costs. To avoid rejecting demands, we can install more capacities in the existing network. In this paper we report experiments on the network capacity design for uncertain demand in telecommunication networks with integer link capacities. We use Poisson demands with bandwidths given by normal or log-normal distribution functions. The expectation function is evaluated using a predetermined set of realizations of the random parameter. We model this problem as a two-stage mixed integer program, which is solved using a stochastic subgradient procedure, the Barahona's volume approach and the Benders decomposition.     

Indifference prices of structured catastrophe (CAT) bonds

We present a method for pricing structured CAT bonds based on utility indifference pricing. The CAT bond considered here is issued in two distinct notes called tranches, specifically senior and junior tranches each with its own payment schedule. Our contributions to the literature of CAT bond pricing are two-fold. First, we apply indifference pricing to structured CAT bonds. We find a price for the senior tranche as a relative indifference price, that is, relative to the price of the junior tranche. Alternatively, one could take the approach that the senior tranche is priced first and the price of the junior tranche is relative to that. Second, instead of simply supposing that the “not-issue-a-CAT-bond” strategy of the reinsurer is to do nothing, we suppose that the reinsurer reduces its risk by reinsuring proportionally less claims. We assume that the reinsurance claims follow a (Poisson) jump-diffusion process.     

A supply chain network equilibrium model with random demands

In this paper, we develop a supply chain network model consisting of manufacturers and retailers in which the demands associated with the retail outlets are random. We model the optimizing behavior of the various decision-makers, derive the equilibrium conditions, and establish the finite-dimensional variational inequality formulation. We provide qualitative properties of the equilibrium pattern in terms of existence and uniqueness results and also establish conditions under which the proposed computational procedure is guaranteed to converge. Finally, we illustrate the model through several numerical examples for which the equilibrium prices and product shipments are computed. This is the first supply chain network equilibrium model with random demands for which modeling, qualitative analysis, and computational results have been obtained.     

A multi-product risk-averse newsvendor with exponential utility function

We consider a multi-product newsvendor using an exponential utility function. We first establish a few basic properties for the newsvendor regarding the convexity of the model and monotonicity of the impact of risk aversion on the solution.When the product demands are independent and the ratio of the degree of risk aversion to the number of products is sufficiently small, we obtain closed-form approximations of the optimal order quantities. The approximations are as easy to compute as the risk-neutral solution. We prove that when this ratio approaches zero, the risk-averse solution converges to the corresponding risk-neutral solution. When the product demands are positively (negatively) correlated, we show that risk aversion leads to lower (higher) optimal order quantities than the solution with independent demands.Using a numerical study, we examine convergence rates of the approximations and thoroughly study the interplay of demand correlation and risk aversion. The numerical study confirms our analytical results and further shows that an increased risk aversion does not always lead to lower order quantities, when demands are strongly negatively correlated.