Stochastic optimization model for distribution and evacuation planning (A case study of Tehran earthquake)

In this study, a stochastic multi-objective mixed-integer mathematical programming is proposed for logistic distribution and evacuation planning during an earthquake. Decisions about the pre- and post-phases of the disaster are considered seamless. The decisions of the pre-disaster phase relate to the location of permanent relief distribution centers and the number of the commodities to be stored. The decisions of the second phase are to determine the optimal location for the establishment of temporary care centers to increase the speed of treating the injured people and the distribution of the commodities at the affected areas. Humanitarian and cost issues are considered in the proposed models through three objective functions. Several sets of constraints are also considered in the proposed model to make it flexible to handle real issues. Demands for food, blood, water, blanket, and tent are assumed to be probabilistic which are related to several complicated factors and modeled using a complicated network in this study. A simulation is setup to generate the probabilistic distribution of demands through several scenarios. The stochastic demands are assumed as inputs for the proposed stochastic multi-objective mixed integer mathematical programming model.The model is transformed to its deterministic equivalent using chance constraint programming approach. The equivalent deterministic model is solved using an efficient epsilon-constraint approach and an evolutionary algorithm, called non-dominated sorting genetic algorithm (NSGA-II). First several illustrative numerical examples are solved using both solution procedures. The performance of solution procedures is compared and the most efficient solution procedure, i.e., NSGA-II, is used to handle the case study of Tehran earthquake. The results are promising and show that the proposed model and the solution approach can handle the real case study in an efficient way.     

Stochastic error specification in primal and dual production systems

In this paper we derive both primal and dual‐cost systems in which the stochastic specifications arise from the model (random environment or measurement errors and optimization errors)—not tacked on at the end after the deterministic system is worked out. Derivation of the error structures is based on cost‐minimizing behavior on the firms. The primal systems constitute the production function and the first‐order conditions of cost minimization. We consider two dual‐cost systems. The first dual system is based on the cost function and cost share equations. The second dual system is based on a multiplicative general error production model that is an alternative to McElroy's additive general error production model. Our multiplicative general error model gives a clear and intuitive economic meaning to the error components. The resulting cost system is easy to estimate compared to the alternative cost systems. The error components in the multiplicative general error model can capture heterogeneity in the technology parameters even in a cross‐sectional model. Panel data are not necessary to estimate either the primal or dual systems. The models are estimated using data on 72 fossil fuel‐fired steam electric power generation plants (observed for the period 1986–1999) in the USA. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimal policy in Markov-switching rational expectations models

In this paper we consider the optimal quadratic control problem of Markov-switching linear rational expectation models. These models are general and flexible tools for modelling not only regime but also model or parameter uncertainty. We show, first, how to find the solution of a Markov-switching linear rational expectation model. Based on this solution we then show how to apply dynamic programming to find the optimal time-consistent policy and the resulting Nash-Stackelberg equilibrium. Suitable modifications of the algorithm allow to deal with the (non-RE) case in which the policymaker and the private sector hold different beliefs or probabilities over regime change. We also show how the optimisation procedure can be employed to obtain the optimal policy under commitment. As an illustration we compute the optimal policy in a small open economy subject to stochastic structural breaks in some of its key parameters.     

Linear programming-based estimators in simple linear regression

In this paper we introduce a linear programming estimator (LPE) for the slope parameter in a constrained linear regression model with a single regressor. The LPE is interesting because it can be superconsistent in the presence of an endogenous regressor and, hence, preferable to the ordinary least squares estimator (LSE). Two different cases are considered as we investigate the statistical properties of the LPE. In the first case, the regressor is assumed to be fixed in repeated samples. In the second, the regressor is stochastic and potentially endogenous. For both cases the strong consistency and exact finite-sample distribution of the LPE is established. Conditions under which the LPE is consistent in the presence of serially correlated, heteroskedastic errors are also given. Finally, we describe how the LPE can be extended to the case with multiple regressors and conjecture that the extended estimator is consistent under conditions analogous to the ones given herein. Finite-sample properties of the LPE and extended LPE in comparison to the LSE and instrumental variable estimator (IVE) are investigated in a simulation study. One advantage of the LPE is that it does not require an instrument.     

An optimization model for the allocation of resources in family planning programs

In this paper we present a quadratic programming model for the allocation of resources in a family planning program. A quadratic cost function is minimized subject to three sets of linear constraints: one for a diffusion model of the acceptance, switching and dropout behavior of the target population; one for manpower limitations; and one for incorporating government policies on desired levels of birth rate. There are two important features to be noted. First, a recruitment cost parameter is introduced to account for the effects of market saturation on new acceptance. Second, by treating the problem as one of cost minimization rather than one of birth rate minimization, the model can be utilized to evaluate the feasibility and the minimum cost requirement of government policies on desired reductions in the birth rate. Computational considerations are also discussed.     

A stochastic cash model with deterministic elements

In this paper we present a simple model which gives a solution to a (one period) stochastic cash problem with a fixed cash outlay at the end of the period. We focus on the role of options as insurance contracts, as to value a constraint on the minimum cash level. It is argued that a cash level adjustment is optimal where the sum of the marginal cost of liquidity and the marginal insurance premium (options value) is zero.We like to thank Edwin O. Fischer, Jaap Spronk and three anonymous referees for helpfull comments. Excellent computational assistance by Henk Hofmans is hereby acknowledged. Of course, the usual disclaimers apply.     

基于随机需求的物流配送中心选址离散模型研究

针对物流需求不确定情况下的物流配送中心选址问题,对传统模型进行改进,将随机需求变量引入离散型选址模型,利用随机规划理论和遗传算法对实例模型进行求解。结果显示物流需求不确定情况下的随机规划模型的求解结果比假设已知需求情况下的结果真实可信,所需物流费用较少。     

DSGE Models in the Frequency Domains

We use frequency domain techniques to estimate a medium‐scale dynamic stochastic general equilibrium (DSGE) model on different frequency bands. We show that goodness of fit, forecasting performance and parameter estimates vary substantially with the frequency bands over which the model is estimated. Estimates obtained using subsets of frequencies are characterized by significantly different parameters, an indication that the model cannot match all frequencies with one set of parameters. In particular, we find that: (i) the low‐frequency properties of the data strongly affect parameter estimates obtained in the time domain; (ii) the importance of economic frictions in the model changes when different subsets of frequencies are used in estimation. This is particularly true for the investment adjustment cost and habit persistence: when low frequencies are present in the estimation, the investment adjustment cost and habit persistence are estimated to be higher than when low frequencies are absent. Copyright © 2014 John Wiley & Sons, Ltd.     

Likelihood Inference for Gibbs Processes in the Analysis of Spatial Point Patterns*

Several authors have proposed stochastic and non‐stochastic approximations to the maximum likelihood estimate (MLE) for Gibbs point processes in modelling spatial point patterns with pairwise interactions. The approximations are necessary because of the difficulty of evaluating the normalizing constant. In this paper, we first provide a review of methods which yield crude approximations to the MLE. We also review methods based on Markov chain Monte Carlo techniques for which exact MLE has become feasible. We then present a comparative simulation study of the performance of such methods of estimation based on two simulation techniques, the Gibbs sampler and the Metropolis‐Hastings algorithm, carried out for the Strauss model.     

Stochastic programming in production planning: a case with none-simple recourse

Abstract  In modeling real world planning problems as optimization programs the assumption that all parameters are known with certainty is often more seriously violated than the assumption that the objective function and the constraints can be approximated sufficiently accurate by lineair functions. In this paper we discuss the concrete application of stochastic programming to a multiperiod production planning problem in which the demand for the products during the various periods is assumed stochastic with known probability distribution. Since the resulting stochastic program does not possess the property of "simple" recourse no direct use can be made of existing methods that have been proposed in literature for solving problems of this type.     

Specification of Distance Functions Using Semi- and Nonparametric Methods with an Application to the Dynamic Performance of Eastern and Western European Air Carriers

In this paper we examine the productive performance of a group of three East European carriers and compare it to thirteen of their West European competitors during the period 1977–1990. We first model the multiple output/multiple input technology with a stochastic distance frontier using recently developed semiparametric efficient methods. The endogeneity of multiple outputs is addressed in part by introducing multivariate kernel estimators for the joint distribution of the multiple outputs and potentially correlated firm random effects. We augment estimates from our semiparametric stochastic distance function with nonparametric distance function methods, using linear programming techniques, as well as with extended decomposition methods, based on the Malmquist index number. Both semi- and nonparametric methods indicate significant slack in resource utilization in the East European carriers relative to their Western counterparts, and limited convergence in efficiency or technical change between them. The implications are rather stark for the long run viability of the East European carriers in our sample.     

Two-stage stochastic integer programming: a survey

Stochastic integer programming is more complicated than stochastic linear programming, as will be explained for the case of the two-stage stochastic programming model. A survey of the results accomplished in this recent field of research is given.     

Robust and stable flexible blood supply chain network design under motivational initiatives

To improve the coordination of blood supply and demand, the efficient design of the blood supply chain network (BSCN) is a proper strategy. In this regard, this paper is the first-ever study to strive for a simultaneous investigation on three interdependent challenges of the BSCN: (1) donors motivation, (2) optimizing location and capacity decisions, and (3) controlling the reliability and robustness of the network under combinatorial risk. As in reality, blood donors play a critical role in the BSC; this study undertakes motivational initiatives to encourage blood donors for maintaining sufficient blood supply. Advertisement, education and medical credits are the directions incorporated to construct the motivational function. To observe the efficiency as the most critical factor while evaluating the pool of location alternatives for establishing facilities, an augmented version of data envelopment analysis (DEA) is utilized. In addition, a mixed integer programming model is proposed by which the simultaneous location and capacity decisions are supported. The model is also extended to handle the combinatorial risk of uncertainty as well as disruption. Thus, a novel mixed possibilistic-stochastic flexible robust programming (MPSFRP) is developed. Eventually, the proposed model is implemented in a real case study to assess its practicality and then provide applicable insights for administrators.     

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.     

集装箱空箱调运优化问题的研究

在分析集装箱空箱流转过程的基础上,提出建立基于海陆运整体成本最优的集装箱空箱调运随机性优化模型,并将粒子群算法与随机模拟技术相结合用于求解机会约束规划。最后通过对测试算例进行求解,验证了该模型和算法的合理性和有效性。     

A Linear Programming Model of the Consumer Price Index Food Component

A bstract A linear programming model is used to measure the rate of inflation in the food component of the consumer price index A diet model to minimize the cost of a diet subject to constraints on nutritive requirements, variety, pal-atabihty, and menu-function is constructed and the rates of increase in a strict minimum cost model and an expanded constraint model are measured for the period 1980-87 Consistent with the consumer utility literature, it is found that the current Laspeyres index approach to measuring the cost of living in fact provides an upper limit on true cost of living increases Results also show that the cost of maintaining a minimum level of subsistence increases more rapidly than the cost of a more palatable diet Finally, the results show that in fact there is very little room for substitution among food items within a reasonable diet model     

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.     

Robust stochastic frontier analysis: a Student’s t-half normal model with application to highway maintenance costs in England

The presence of outliers in the data has implications for stochastic frontier analysis, and indeed any performance analysis methodology, because they may lead to imprecise parameter estimates and, crucially, lead to an exaggerated spread of efficiency predictions. In this paper we replace the normal distribution for the noise term in the standard stochastic frontier model with a Student’s t distribution, which generalises the normal distribution by adding a shape parameter governing the degree of kurtosis. This has the advantages of introducing flexibility in the heaviness of the tails, which can be determined by the data, as well as containing the normal distribution as a limiting case, and we outline how to test against the standard model. Monte Carlo simulation results for the maximum simulated likelihood estimator confirm that the model recovers appropriate frontier and distributional parameter estimates under various values of the true shape parameter. The simulation results also indicate the influence of a phenomenon we term ‘wrong kurtosis’ in the case of small samples, which is analogous to the issue of ‘wrong skewness’ previously identified in the literature. We apply a Student’s t-half normal cost frontier to data for highways authorities in England, and this formulation is found to be preferred by statistical testing to the comparator normal-half normal cost frontier model. The model yields a significantly narrower range of efficiency predictions, which are non-monotonic at the tails of the residual distribution.

     

Dynamic inventory decisions for humanitarian aid materials considering budget limitations

In case of disaster, providing relief supplies to the affected people has vital importance. Governmental or non-governmental organizations (NGOs) prepare for disasters by purchasing and stockpiling these aid materials in appropriate quantities. They operate under a limited budget and this budget can either be used before the disaster for stocking decisions under uncertainty or it can be used after the disaster to satisfy the required demand at a higher cost when the uncertainty is resolved. If all the budget is used before the disaster, and if there is no disaster in a long term, there will be a high holding cost. On the other hand, if all the budget is reserved for use after the disaster, meeting the demand will be more costly or the demand may not be met within a certain period of time. Thus, NGOs need to decide how to allocate the budget for pre and post-disaster usage. In this system, the budget of NGOs may also change over time through donations or other incomes. In this point of view, NGOs need to make dynamic stock and budget allocation decisions, under the available budget at hand. In our study, we analyze the dynamic stocking decisions of NGOs using stochastic dynamic programming formulations under budget constraints. We develop infinite horizon stochastic dynamic programming models with and without budget considerations, and compare the results of these models via numerical analysis. Detailed numerical studies and results of the sensitivity analysis show the significance of budget considerations in inventory decisions and the effects of different parameters on the system results.     

Optimal technology choice in a dynamic-stochastic environment

The issue of technology management has become particularly relevant to operations planners as a result of the introduction of new, computer-aided process technologies in recent years. At the same time, the fields of economics and management science have developed a number of models and paradigms for technology management and equipment replacement. In this article we present a model structure that builds on this theory and that is directed toward providing insights into the particular issues associated with fixed versus variable cost trade-offs.A fairly general, dynamic, stochastic model is presented. This model links production planning with technology selection in a direct manner. The model computes optimal production plans in the face of uncertain demand in the course of evaluating the costs and benefits of each technology alternative. The key result of the article concerns conditions for the optimality of moves to lower variable cost technologies.