A multi-stage stochastic programming approach for pre-positioning of relief supplies considering returns

A dynamic pre-positioning problem is proposed to efficiently respond to victims’ need for relief supplies under uncertain and dynamic demand in humanitarian relief. The problem is formulated as a multi-stage stochastic programming model that considers pre-positioning with the dynamic procurement and return decisions about relief supplies over a time horizon. To validate the advantages of dynamic pre-positioning, three additional pre-positioning strategies are presented: pre-positioning with one-time procurement and without returns, pre-positioning with one-time procurement and returns, and pre-positioning with dynamic procurement and without returns. Using data from real-world disasters in the United States in the Emergency Events Database, we present a numerical analysis to study the applicability of the proposed models. We develop a sample average approximation approach to solving the proposed model in large-scale cases. Our main contribution is that we integrate dynamic procurement and return strategies into pre-positioning to decrease both costs and shortage risks in uncertain and dynamic contexts. The results illustrate that dynamic pre-positioning outperforms the other three strategies in cost savings. It also indicates that a higher return price is particularly helpful for decreasing unmet demand. The proposed models can help relief agencies evaluate and choose the solutions that will have the greatest overall effectiveness in the context of different relief practices.     

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。     

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.     

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.     

Planning in an uncertain environment: Stochastic goal programming using the versatility criterion

This article presents a planning model that applies the versatility criterion to goal programming problems with uncertainty about the constraints which define the set of feasible decisions. Some of the constraint parameters are assumed to be stochastic variables with a joint normal distribution. The solution sought maximizes the probability of satisfying all the constraints. A nonlinear programming model is set out which can be solved by using numerical integration at every step. An illustrative example is provided which shows the possible application of the versatility model to land-use planning.     

Numerical solution of dynamic equilibrium models under Poisson uncertainty

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.     

Relief aid stocking decisions under bilateral agency cooperation

We aim to quantify the benefits of cooperation between humanitarian relief agencies in terms of stocking decisions. We consider two agencies that stock the same type of relief item at different locations prone to individual disaster risks and agree to transship the shortage amount from available stocks in case of a disaster. We incorporate the disaster risk to the Newsvendor model by conditioning the stock quantity decisions on the event that a major disaster occurs within the lifetime of the stocked relief item. We optimize the stock quantity for each agency in response to the other's quantity and compute a Nash Equilibrium solution numerically. We apply this game theoretic approach to the case of earthquake preparedness in Istanbul to optimize the stocking decisions of an agency for shelter units in cooperation with another agency. We investigate the characteristics of the solutions under various parameter settings and identify cases in which cooperation may be beneficial to one or both of the agencies.     

Redesign strategies of a comprehensive robust relief network for disaster management

We address the problem of designing as well as redesigning a relief network over multiple periods as a strategic decision which plays a critical role in the post-disaster management. Design of the relief network has a significant impact on the effective performance of disaster response operations. For considering both the uncertainty and dynamism of the decision-making environment, a comprehensive scenario-based robust approach embedded in the rolling horizon framework is proposed. The proposed mixed-integer linear programming model is inspired by a real case study of a disaster management in Iran, which aims to minimize the total cost of network management. Furthermore, restorative strategies are considered to increase the efficiency and robustness of the proposed relief network under disaster. To tackle the proposed optimization model, a heuristic solution algorithm is adopted. The results indicate that the proposed robust relief network provides an affordable access to its demand points in a sustainable manner under disaster. In addition, extensive computational results illustrate the efficiency of the proposed model in dealing with the considered disaster management issues.     

Evolutionary dynamics of supervision-compliance game on optimal pre-positioning strategies in relief supply chain management

Emergency supply reserves are indispensable material bases in relief supply chain management. However, limited in-kind relief resources stockpiled in government-managed depositories may fail to meet the surging demand following the disaster. This paper develops an optimal pre-positioning strategy for emergency supplies with pre-purchasing contracts between local governments (LGs) and emergency supply manufacturers (ESMs) to properly address demand uncertainty in different disaster scenarios. Physical materials and production capacity are integrated into a holistic and hybrid reserve model to mitigate overstock or stock-out risks. Applying an evolutionary game-theoretic framework, contract enforcement has been extensively analyzed to avoid LGs dereliction of duty and ESMs’ breach of contract. A novel dynamic penalty mechanism is proposed to control the fluctuations in strategy choices and effectively improve ESMs’ compliance without LGs’ excessive inputs on supervision. The numerical simulation results, along with sensitivity analyses on major cost-accounting, demand characteristics, and environmental parameters, show that safety stock is the primary guarantee in most cases, while reactive stock acts as an important supplement for disasters with long-term consequences. The joint reserve policy (except for no action strategy) outperforms the price-only contract on the total reserved quantity of emergency supplies at a lower long-term average cost. The initial state and cost-benefit structures dominate the complex interplay and periodical fluctuations in the supervision-compliance game. The doomed cycle of order, disorder, and reorder in contract performance management can be well managed under the proposed dynamic penalty mechanism, which appears much more efficient and incentive-compatible in promoting both parties to fulfill their obligations.     

Government intervention on cooperation,competition, and coopetition of humanitarian supply chains

We considered a humanitarian environment composed of donors and non-governmental organizations (NGOs) that the non-profits may adopt competitive or coopetitive inter-organizational interaction for managing the disasters. We also assumed that the government intervenes in the relief operations by applying one of its two policies; social welfare maximization (SWM) or budget consumption minimization (BCM). Using game theory (GT) approach, we develop 4 scenarios and, as a result, 4 mathematical programming models for examining the effect of the NGOs interactions and the government policies on the performance of donors, NGOs and government. We find that coopetition of NGOs facilitates the achievement of the government's objectives, and it also helps the non-profits to become more successful in providing relief. The government prefers to provide the indirect relief to the nonprofits to manage emergency operations successfully, and the financial aids are given only in the condition of reducing the level of NGOs cooperation. We also conclude that the cooperation of NGOs increases the donors' utility. A numerical example is conducted to test the findings of the models.     

供应链——营销一体化随机模型研究

供应链活动的一体化已成为大多数行业的必需的竞争力。文章研究单工厂、多产品、多周期、多分销中心供应链网络的供应链—营销一体化问题。提出了利用随机混合整数规划方法,建立了一体化模型。随机模型解决了需求的不确定性问题。同时,模型优化了系统的生产批量、车辆调度和库存。数值实例展示了模型的应用,并用优化软件“What’sBest!”求出了结果。最后指出模型还可以在很多方面进行扩展。     

林业投资估价

分析了确定性条件下的林地估价的传统的Faustmann模型。用随机动态规划方法,建立了不确定性条件下林地估价模型,探讨了用LCP方法求解的问题,并得出有关结论。     

一类供应链分销网络的双层多目标规划模型

以多生产商、多分销中心的供应链分销网络为基础,建立了多目标双层机会约束规划模型。基于协同供应链管理思想,充分考虑了多生产厂商相互制约以及决策信息的不完整性、市场需求不确定性,探讨如何实现整体成本的最小化。最后,结合一种算法给出了该模型的求解方法,并结合一个实例证明算法的有效性。     

Asymmetric outcome in a symmetric dynamic duopoly

In a dynamic duopoly, will an initial asymmetry between firms increase or decrease over time? We examine this issue within a stochastic dynamic alternate-move duopoly model that explicitly accounts for action and reaction between firms. We consider two firms that are symmetric with regard to all primitives such as demand, cost and production functions, and which are subject to the same stochastic environment. The only asymmetry is with regard to their initial capital stocks which in turn asymmetrically influences their current and future profit and investment possibilities. We offer a characterization of the stochastic steady state and its supporting ergodic set for each firm. We are then able to identify the precise restrictions on the initial conditions under which the two firms either converge or diverge in the long run.     

Disclosure Policy in a Mixed Market

This paper investigates the optimal disclosure strategy for private information in a mixed duopoly market, where a state-owned enterprise (SOE) and a joint-stock company compete to supply products. I construct a model where the two firms compete in either quantity or price, and uncertainty is associated with either marginal cost or market demand. The model identifies the optimal disclosure strategies that constitute a perfect Bayesian equilibrium by type of competition and uncertainty. In Cournot competition, both firms disclose information under cost uncertainty, while only the SOE or neither firm discloses information under demand uncertainty. Alternatively, in Bertrand competition, only the joint-stock company discloses information under cost uncertainty or demand uncertainty. Recently, developed countries have required the same level of disclosure standards for SOEs as for ordinary joint-stock companies. The findings described in this paper warn that such mandatory disclosure by SOEs can trigger a reaction by joint-stock companies, putting the economy at risk of a reduction in welfare.     

Analysis and forecast of donations at domestic hunger relief organizations impacted by natural disasters

Food banks are non-profit, charitable organizations that distribute food and products to people in need. Food bank facilities become disaster relief centers after natural disasters. The uncertainty associated with the arrival of donations and demand make the planning and operations of food banks challenging during the disaster relief period. The goal of this research is to analyse and forecast the amount of donations received by food bank facilities in the U.S. when operating as disaster relief centers. This paper analyses the donations received by two food bank facilities affected by Hurricane Harvey in 2017. An extensive numerical study is performed that compares the donation behavior at each facility before and after the hurricane event. Multiple forecasting models are evaluated to determine their accuracy in predicting the observed behavior. The results show that under disaster operations, the best performing techniques for both food banks were smoothing techniques (i.e., CMA and Holt) and econometric models.     

供应同一产品的两个销售商的库存决策研究

模型假设两个销售商销售同一产品，因此当一个销售商缺货时，它的客户可能转向另一个销售商购买同样的产品，即他们之间存在替代性。针对两个销售商的这种关系，给出了三种不同的库存决策。并对模型进行了实际算例分析，比较了两个决策者不同合作模式下的订货策略，为决策者制定有效的订货策略提供了依据。     

Inventory policies for humanitarian aid during hurricanes

In this work we present a stochastic programming model minimizing costs, to support the decision process of inventory policy which best satisfies the demand for food in shelters when hurricane winds are about to impact a town. In this model we consider perishable products as well as the first in first out (FIFO) system for their consumption. In order to make the model closer to reality ordering cost is time-varying and we add a penalty cost in case the shortage exceeds a known limit for two days in a row. Finally the cost to dispose of expired food is greater than the purchase cost of the product since throwing away food has ethical implications. Starting from a stochastic programming model, we present a procedure to transform it to a deterministic mixed integer programming model (MIP) with non-convex objective function over its entire domain, which closely states the situation in reality. Preliminary computational results and discussion are presented.     

Managing returnable transport items in a vendor managed inventory system

This paper addresses a closed-loop inventory routing problem with demand uncertainty, which manages the delivery operations to customers and pick-up operations of empty returnable transport items (RTIs) from customers. The problem involves decisions regarding forward and backward vehicle routes, the delivery and collection quantities, the amount of production in terms of the number of filled RTIs, and the number of RTIs produced/ bought by the vendor during the defined planning horizon. The problem considers the holding costs, fixed cost of operating vehicles, fuel consumption cost, producing/buying costs, cleaning costs of RTIs, and loading and unloading costs. We formulate the problem as a mixed integer linear programming model and propose a Relax and Fix based solution approach to solve large instances. We conduct extensive analyses on a case study derived from a fruit and vegetable distribution network and several hypothetical instances. Our analyses investigate the effects of several problem parameter changes (i.e., average collection rate, customer service level, cost of buying crate and handling cost) on the total logistics cost. Additional numerical analyses are performed to demonstrate the usage of the model for evaluating the cost of being more green and environmental-friendly. Moreover, experiments on relatively large-scaled problems allow us to demonstrate the potential benefits of the proposed heuristic     

供应商选择问题中单产品采购量分配模型

研究了在随机需求和增量价格折扣条件下的单产品采购量分配模型。针对供应商选择问题中广泛存在的多目标性以及目标的模糊性,提出了一种用于解决该类问题的模糊多目标规划模型。结合一个算例找到了给定条件下各供应商的采购量分配的最优方案,归纳出了求解该问题的过程与步骤,验证了模型的有效性与可行性。