Toward a coordination of inventory and distribution schedules for blood in disasters

The need for efficient blood supply is of more significance in the event of disasters, when there is a lack of coordination between distribution and inventory management. The recent earthquake in Kermanshah province in Iran is among such cases that confirmed the need for coordinating such schedules. In this respect, a two-stage stochastic programming (SP) approach is presented for planning supply of blood after disasters that can assist in inventory decisions under hybrid uncertainty, minimizing the shortage and wastages. The uncertainty stems from imprecise parameters and scenario variability, and a robust-fuzzy-stochastic programming (RFSP) approach is devised to hedge against the uncertainty. The perishability of blood, the substitutability of blood groups, and the age-based characteristic of blood are taken into account to make the model more reliable. The compromise programming is applied to solve the multi-objective model. The results illustrate that the RFSP model can make a reasonable trade-off between mean value, feasibility robustness, and optimality robustness, which results in a robust and reliable solution under disastrous conditions.     

Itemized platelet supply chain with lateral transshipment under uncertainty evaluating inappropriate output in laboratories

Demand uncertainty coupled with the short lifespan of itemized platelets has caused a significant shortage at public therapeutic centers. In this regard, this paper presents a multi-objective robust stochastic mixed integer linear programming model for an integrated platelet supply chain considering unidirectional lateral transshipment between hospitals and clinics. In the proposed model, platelets are divided into typical, irradiated and washed platelets with lifespan differentiated for various types of patients. This model evaluates the risk of inappropriate production by concentrating on three different procedures for extracting platelet, including apheresis, platelet rich plasma and buffy coat methods. In this investigation, staff errors, laboratory hygiene and device failure, as well as donors' blood contamination, are considered for obtaining the function of inappropriate production rate. In our model, the logistics costs are considered as the first objective and the maximum unsatisfied demand as the second objective, both also to be minimized. To tackle demand uncertainty, a robust stochastic approach is then developed. Afterwards, to create a more realistic model, the Monte Carlo sampling approach is used for generating required scenarios. Finally, some managerial insights are provided through a real case study to evaluate the applicability of the presented model. The results indicate that the proposed model not only improves the demand satisfaction but also reduces the risk of itemized platelets wastage.     

Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA

Pareto-Koopmans efficiency in Data Envelopment Analysis (DEA) is extended to stochastic inputs and outputs via probabilistic input-output vector comparisons in a given empirical production (possibility) set. In contrast to other approaches which have used Chance Constrained Programming formulations in DEA, the emphasis here is on joint chance constraints. An assumption of arbitrary but known probability distributions leads to the P-Model of chance constrained programming. A necessary condition for a DMU to be stochastically efficient and a sufficient condition for a DMU to be non-stochastically efficient are provided. Deterministic equivalents using the zero order decision rules of chance constrained programming and multivariate normal distributions take the form of an extended version of the additive model of DEA. Contacts are also maintained with all of the other presently available deterministic DEA models in the form of easily identified extensions which can be used to formalize the treatment of efficiency when stochastic elements are present.     

A multimodal,multicommodity, and multiperiod planning problem for coal distribution to poor families

Tackling poverty has been one of the greatest global challenges and a prerequisite to sustainable development of countries. Countries implement nationally appropriate social protection systems and measures to address poverty. This paper addresses an aid system adopted by the government in Turkey where significant amounts of coal is distributed to poor families each year. The objective of the coal aid system is to complete the delivery of coal to poor families by the start of winter. However, an analysis of the data from previous years indicates that the distribution to many families cannot be completed on time. This results from the fact that planning is done manually and by trial-and-error as there is no system that can be used for distribution planning. This paper describes the planning problem encountered and develops a mathematical model to solve it. The proposed model is a multimodal, multicommodity, and multiperiod linear programming (LP) model. The model can be used to develop and update a distribution plan as well as to answer several what-if questions with regard to capacities, time constraints, and so forth. The model is solved using CPLEX for several problem instances obtained under different scenarios using data for the year 2012. The results show that at least 9% cost savings and about 40% decrease in distribution completion time can be achieved when the model is used. We analyze scenario results qualitatively and quantitatively and provide several insights to the decision makers. As a part of quantitative analysis, we develop regression models to predict optimal costs based on several factors. Our main contribution is to provide an efficient and effective tool to handle a large-scale real-world problem. The model has also helped to prove that the organization responsible for distribution planning may move from the current planning practice to an all-encompassing top-down approach.     

Multi-objective linear programming with partial ranking of objectives

This paper is concerned with multi-objective linear programming problems in which the objective functions can be partially ranked. We represent the set of admissible weight vectors by a system of linear constraints and solve for the policy most likely to be optimum. If each admissible weight vector has the same probability of being correct, the optimum policy maximizes the hypervolume of the polytope of weight vectors having this policy as a solution. The proposed algorithm requires the enumeration of the subset of admissible efficient solutions of a multi-objective linear program. For each admissible solution, we estimate the ratio of the volumes of the corresponding polytope of weight vectors and the polytope of all admissible weight vectors. An algorithm is outlined for numerical integration using the Monte Carlo method. The model is extended to the case where several objectives are expressed as linear constraints with multiple parameter vectors and there is uncertainty about the weighting of these parameters. A numerical example is provided.     

Modeling integrated supply chain logistics in real-time large-scale disaster relief operations

The goal of this research is to develop a comprehensive model that describes the integrated logistics operations in response to natural disasters. We propose a mathematical model that controls the flow of several relief commodities from the sources through the supply chain and until they are delivered to the hands of recipients. The structure of the network is in compliance with FEMA's complex logistics structure. The proposed model not only considers details such as vehicle routing and pick up or delivery schedules; but also considers finding the optimal locations for several layers of temporary facilities as well as considering several capacity constraints for each facility and the transportation system. Such an integrated model provides the opportunity for a centralized operation plan that can eliminate delays and assign the limited resources to the best possible use.A set of numerical experiments is designed to test the proposed formulation and evaluate the properties of the optimization problem. The numerical analysis shows the capabilities of the model to handle the large-scale relief operations with adequate details. However, the problem size and difficulty grows rapidly by extending the length of the operations or when the equity among recipients is considered. In these cases, it is suggested to find fast solution algorithms and heuristic methods in future research.     

A logistics model for emergency supply of critical items in the aftermath of a disaster

This paper proposes a logistics model for delivery of prioritized items in disaster relief operations. It considers multi-items, multi-vehicles, multi-periods, soft time windows, and a split delivery strategy scenario, and is formulated as a multi-objective integer programming model. To effectively solve this model we limit the number of available tours. Two heuristic approaches are introduced for this purpose. The first approach is based on a genetic algorithm, while the second approach is developed by decomposing the original problem. We compare these two approaches via a computational study. The multi-objective problem is converted to a single-objective problem by the weighted sum method. A case study is presented to illustrate the potential applicability of our model. Also, presented is a comparison of our model with that proposed in a recent paper by Balcik et al. [6]. The results show that our proposed model outperforms theirs in terms of delivering prioritized items over several time periods.     

Stochastic Programming

This report presents an approach to stochastic programming. It treats mainly the difficulties arising in formulating the problem and the possibilities to derive a deterministic problem by which it can be replaced. In a sense the approach of this report unifies different viewpoints on stochastic programming problems as they have been published in the literature.     

震后模糊道路破损率条件下应急物资调配研究

应急物资调配是应急物流系统重要研究问题之一,直接关系到应急物流活动的成败。考虑到灾后运输道路破损率不能立即确定,构建了道路破损率与物资需求量为梯形模糊数的多目标应急物资调配模型。通过将其转化为具有确定系数的多目标规划模型来进行求解,并提出了求得该模型满意解的算法。最后通过算例分析说明该方法的有效性。     

Stochastic population forecasts and their uses

"The properties and uses of stochastic forecasts are discussed here. For linear stochastic projections, we show how the computation of forecast moments and the statistical distribution of forecasts depend on the multiplicative and autoregressive structure of the dynamics. Both scalar and vector projection methods are discussed, and their similarities are explored. Next we discuss the uses of stochastic forecasts, arguing that it is important to relate forecasts to the specific decision-making criteria of particular forecast users. The example of [the U.S. system of] Social Security is used to show how a dynamic programming approach may be used to explore alternative decisions in a probabilistic context."     

Mathematical methods of optimization for multi-objective transportation systems

Transportation systems have multi-objective functions and there are multi-factor decision situations. A general mathematical optimization model for such systems is developed which has broad applications for the planning, system design and evaluation of many transportation systems. Three types of solution techniques are discussed. For multi-objective linear programs, a solution is obtained which satisfies the decision maker's preferences and optimization from the decision maker's point of view is considered. A goal programming solution technique is given when goals for the system can be defined. If this is not possible, an overall utility function is defined on the various objective functions and a concept of additive utilities is explored and a parametric programming solution is given.     

Regression Revisited

Sir Francis Galton introduced median regression and the use of the quantile function to describe distributions. Very early on the tradition moved to mean regression and the universal use of the Normal distribution, either as the natural ‘error’ distribution or as one forced by transformation. Though the introduction of ‘quantile regression’ refocused attention on the shape of the variability about the line, it uses nonparametric approaches and so ignores the actual distribution of the ‘error’ term. This paper seeks to show how Galton's approach enables the complete regression model, deterministic and stochastic elements, to be modelled, fitted and investigated. The emphasis is on the range of models that can be used for the stochastic element. It is noted that as the deterministic terms can be built up from components, so to, using quantile functions, can the stochastic element. The model may thus be treated in both modelling and fitting as a unity. Some evidence is presented to justify the use of a much wider range of distributional models than is usually considered and to emphasize their flexibility in extending regression models.     

Discussion of dynamic programming and linear programming approaches to stochastic control and optimal stopping in continuous time

This paper seeks to highlight two approaches to the solution of stochastic control and optimal stopping problems in continuous time. Each approach transforms the stochastic problem into a deterministic problem. Dynamic programming is a well-established technique that obtains a partial/ordinary differential equation, variational or quasi-variational inequality depending on the type of problem; the solution provides the value of the problem as a function of the initial position (the value function). The other method recasts the problems as linear programs over a space of feasible measures. Both approaches use Dynkin’s formula in essential but different ways. The aim of this paper is to present the main ideas underlying these approaches with only passing attention paid to the important and necessary technical details.     

Sustainable inventory management in blood banks considering health equity using a combined metaheuristic-based robust fuzzy stochastic programming

This study examines the challenges of healthcare systems toward sustainable inventory management of blood products. In this regard, three main goals are pursued; First, promoting social equity in providing medical services to various patients and reducing the risk to lives. Second, the optimal management of medical products in a way that minimizes economic costs. Third, optimal management of biological waste due to inventory corruption and reduction of greenhouse gas emissions caused by transportation, to the least environmental pollution. To achieve these purposes, a practical demand-driven multi-objective inventory model is presented by utilizing hybrid policies in an uncertain environment. In the proposed model, the demands are in two types, including elective and non-elective. These demands are classified according to their medical urgency, substitution allowance, and product freshness. A hybrid robust fuzzy stochastic programming approach is applied to capture real-world uncertainties. The proposed model is implemented for blood platelet. The solution is obtained using a combined metaheuristic technique established on genetic algorithms and simulated annealing according to global and local search paradigms. To create a proper perspective for decision-makers, sensitivity analysis is performed. Besides, the performance of the model is proved by the realization. The results show that the performance of the proposed RFSP model is better than the Nominal model. Also, it performs well in minimizing the overall system costs and environmental degradation, besides reducing shortage and wastage. It is also effective for taking steps toward equity in health and suggests a proper strategy for dealing with emergencies.     

Designing an integrated humanitarian logistics network for the preparedness and response phases under uncertainty

In the current paper, a model of possibilistic location-allocation is proposed for designing a multi-period bi-objective humanitarian logistics network that pursues a reduction in the total cost and maximizes the total network coverage. The model considers the inventory management of perishable relief items and the flow of affected and wounded people in pre-disaster and post-disaster phases, simultaneously. Moreover, wounded people are categorized according to the injury severity. The uncertainty associated with key parameters is also addressed. To handle the uncertainty, a fuzzy chance-constrained programming method originated in the Me measure is used. The purpose of this measure is to prevent the extreme attitudes of the decision maker by considering the combination of possibility and necessity measures and using the optimistic-pessimistic parameter. This paper presents a solution procedure derived from a fuzzy interactive programming approach and two meta-heuristic algorithms, imperialist competitive algorithm and invasive weed optimization, so as to solve the study model. As for the validation of the proposed model and solution procedures, a number of test problems have been generated. A real-life case study is also implemented to instantiate whether the proposed model is applicable or not.     

A unified approach to Bermudan and barrier options under stochastic volatility models with jumps

Many financial assets, such as currencies, commodities, and equity stocks, exhibit both jumps and stochastic volatility, which are especially prominent in the market after the financial crisis. Some strategic decision making problems also involve American-style options. In this paper, we develop a novel, fast and accurate method for pricing American and barrier options in regime switching jump diffusion models. By blending regime switching models and Markov chain approximation techniques in the Fourier domain, we provide a unified approach to price Bermudan, American options and barrier options under general stochastic volatility models with jumps. The models considered include Heston, Hull–White, Stein–Stein, Scott, the 3/2 model, and the recently proposed 4/2 model and the α-Hypergeometric model with general jump amplitude distributions in the return process. Applications include the valuation of discretely monitored contracts as well as continuously monitored contracts common in the foreign exchange markets. Numerical results are provided to demonstrate the accuracy and efficiency of the proposed method.     

A mixed PDE-Monte Carlo approach for pricing credit default index swaptions

Abstract The problem of numerically pricing credit default index swaptions on a large number of names is considered. We place ourselves in a stochastic intensity framework, where Ornstein-Uhlenbeck-type correlated processes are used to model both firms’ distance to default and a macroeconomic state variable. Here the default of the firms’ follows the reduced-form approach and the (random) intensity of the default depends on the behavior of the diffusion processes. We propose here a numerical method based on both a Monte Carlo and a deterministic approach for solving PDEs by finite differences. Numerical tests demonstrate the efficiency and the robustness of the proposed procedure.     

Convergence problems in stochastic programming models with probabilistic constraints

We consider a stochastic programming model with probabilistic constraints and assume to have only empirical estimates of the true probability distribution of the random variables involved in the model. By using properties of semicontinuous and quasi-convex/quasi-concave limetions, we can weaken the traditional assumptions on the functions involved. We generalize both the functional form and the mathematical properties of the functions and then prove the almost sure uniform convergence of the sequence of approximate problems to the true one.     

有竞争的物流配送中心选址模型研究

文章结合迭代算法、AHP和目标规划方法,在已有的关于有竞争的物流配送中心选址问题的研究成果上进行改进,进行了简单的研究。首先根据配送中心与顾客距离计算新配送中心的最大市场占有率,通过迭代算法获得一些相对较优备选地址,然后通过调查得出候选地址的相关信息,通过层次分析法评估各个备选地址的综合水平,最后通过多目标规划来寻找最好的位置建立物流配送中心,文章主要运用MATLAB,yaahp进行求解。     

An analysis of the effect of noise in a heterogeneous agent financial market model

Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the study of HAMs combines theoretical analysis of the underlying deterministic skeleton with numerical analysis of the stochastic model. However, it is well known that this indirect approach may not properly characterise the nature of the stochastic model. This paper aims to tackle this issue by developing a direct and analytical approach to the analysis of a stochastic model of speculative price dynamics involving two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the stationary measures of a stochastic dynamical system. Using the stochastic method of averaging and stochastic bifurcation theory, we show that the stochastic model displays behaviour consistent with that of the underlying deterministic model when the time lag in the formation of price trends used by the chartists is far away from zero. However, when this lag approaches zero, such consistency breaks down.