Planning the delivery of relief supplies upon the occurrence of a natural disaster while considering the assembly process of the relief kits

Models for the distribution of relief supplies often assume immediate availability of relief items upon the occurrence of a natural disaster. However, such an assumption does not always apply in realistic settings. In some cases, at least it is necessary to assemble relief items into kits before distributing them among the affected population. This paper presents a rolling horizon methodology that considers dynamic parameters such as demand, capacities and demand priorities for the problem of distributing relief supplies after the occurrence of a natural disaster by including such assembling activities before the delivery.     

A novel option contract integrated with supplier selection and inventory prepositioning for humanitarian relief supply chains

This paper proposes a novel two-period option contract integrated with supplier selection and inventory prepositioning. A two-stage scenario-based mixed possibilistic-stochastic programming model is developed to cope with various uncertainties. The first stage's decisions include supplier selection and capacity reservation level at each supplier/period and the level of inventory prepositioning. Furthermore, decisions regarding the time and exercised amount are made in the second stage. Applicability of the model is validated through a real case study. Finally, several sensitivity analyses are conducted to examine the effect of important parameters on the solutions to gain useful managerial insights.     

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.     

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.     

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.     

A dynamic model for disaster response considering prioritized demand points

This paper addresses the problem of distributing relief supplies after the occurrence of a disaster. We develop a dynamic model to serve demand, while prioritizing the response, according to the level of urgency of demand points. Our model is thought to be applied during a planning horizon and it considers dynamic demand, capacity constraints and priorities. To evaluate the applicability of our model, we use a real case study of a flood occurred in Colombia. We also test the computational solvability of our model and we propose and test different solution methodologies for solving larger instances of our problem.     

考虑需求与价格--质量相关的补货与定价联合决策广义模型

文中基于顾客的购买行为,构建质量-价格敏感的时变需求函数;以利润最大化为目标建立了补货与定价联合决策广义模型,同步确定市场价格、订货批量和时间间隔;证明了模型存在唯一最优解的条件,并给出求解方法;讨论了研究问题的特例形式,表明模型具有广泛适用性。数值算例进一步分析了质量水平影响因子、产品变质率的变化速率对销售利润和决策变量的影响关系。     

时变拖后供给的易变质品生产库存模型

蔬菜、水果和生鲜食品等物品在存储的过程中,随时间的推移会发生大量的损耗,损耗成本不容忽视。文章建立以需求率、生产率和产品损耗率为常数,允许缺货但缺货部分时变拖后供给的生产库存模型,给出了寻求最优解的方法和解的唯一性的证明,并分析了主要参数变化对平均利润和服务率的影响。     

Pre-positioning of relief items in humanitarian logistics considering lateral transhipment opportunities

The main objective of this study is to investigate the inclusion of lateral transhipment opportunities into the humanitarian relief chain and to examine the effect of different parameters on minimizing the average distance travelled per item while serving the beneficiaries. Direct shipment model (DT), lateral transhipment model (LTSP) and maritime lateral transhipment model (MLTSP) are developed and compared between each other by using a real life earthquake scenario prepared for the city of Istanbul by JICA (Japanese International Cooperation Agency). Developed mathematical models decide on the locations and number of disaster relief facilities, quantity of relief items to hold at those facilities, and quantity of lateral transhipment between the facilities. Vulnerability of the roads and heterogeneous capacitated facilities are also considered. It can be concluded that both LTSP and MLTSP models gave better results than DT model and lateral transhipment option helps beneficiaries to obtain relief items faster and with higher service level.     

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.     

A transshipment model for distribution and inventory relocation under uncertainty in humanitarian operations

The number of disasters and humanitarian crises which trigger humanitarian operations is ever-expanding. Unforeseen incidents frequently occur in the aftermath of a disaster, when humanitarian organizations are already in action. These incidents can lead to sudden changes in demand. As fast delivery of relief items to the affected regions is crucial, the obvious reaction would be to deliver them from neighbouring regions. Yet, this may incur future shortages in those regions as well. Hence, an integrated relocation and distribution planning approach is required, considering current demand and possible future developments.For this situation, a mixed-integer programming model is developed containing two objectives: minimization of unsatisfied demand and minimization of operational costs. The model is solved by a rolling horizon solution method. To model uncertainty, demand is split into certain demand which is known, and uncertain demand which occurs with a specific probability. Periodically increasing penalty costs are introduced for the unsatisfied certain and uncertain demand. A sensitivity analysis of the penalty costs for unsatisfied uncertain demand is accomplished to study the trade-off between demand satisfaction and logistical costs. The results for an example case show that unsatisfied demand can be significantly reduced, while operational costs increase only slightly.     

A credibility-based multi-objective temporary logistics hub location-allocation model for relief supply and distribution under uncertainty

Disaster response operations revolve around uncertainties. While uncertainties arising due to randomness can be avoided for post-disaster location problem, those arising because of impreciseness may persist long after the disaster's occurrence. Despite the uncertainties and lack of sufficient information about the extent of the damage, disaster response facilities must be established quickly after the occurrence of the disaster. Moreover, the decisions of whether to open, where to locate, and when to open disaster response facilities are based on the amount and quality of information available during the decision-making period. To address these issues, we develop a multi-objective location-allocation model for relief supply and distribution that accounts for the imprecise and time-varying nature of different parameters and time-varying coverage, while also accommodating the subjective attributes necessary to enable establishment and operation of the temporary logistics hubs (TLHs). A credibility-based fuzzy chance-constrained programming model is employed to account for the impreciseness inherent in predicting parameter values during disaster response. The results show where, when, and how many TLHs to open and how to allocate relief supplies. Meanwhile, the sensitivity analysis provides a broader understanding of the impact of limiting the number of TLHs as well as the confidence level and the spread of the symmetric triangular fuzzy numbers on the attainment of the model objectives.     

Time-dependent demand in requirements planning: An exploratory assessment of the effects of serially correlated demand sequences on lot-sizing performa

The problem of determining the appropriate stock replenishment quantity within a time-phased requirements planning environment has received considerable research attention in recent years. Relative performance characteristics of lot-sizing policies have been assessed as a function of the cost structure, the demand pattern, the product structure, forecast error, the length of the planning horizon, and the interaction between replenishment quantities and sequencing decisions. In particular, the relationship between lot sizing behavior and variability in the requirements profile has been intensely investigated. However, despite these efforts, the empirical evidence linking lotsizing performance with demand variability remains inconclusive. This article suggests that, in part, some of the ambiguity in the literature may be an artifact of a failure to adequately control for other important dimensions of simulated demand sequences. The features that have been thought to describe “lumpy” requirements profiles are discussed and the characteristic of periodicity or time-dependency in the demand entries is identified as a variable that has been insufficiently controlled in prior work. A reanalysis of the demand sequences originally published by Kaimann, and subsequently used in a number of comparative lot-sizing studies, reveals that the patterns differ not only in variability as measured by the coefficient of variation, but also in terms of correlation structure as described by the autocorrelation function. Alternative methods for simulating demand sequences are reviewed and a correlation transfer technique, which has the capability to simultaneously control both the degree of variability and correlation, is suggested as an improved method for the generation of synthetic sequences of “lumpy” demand. Using this technique, five of Kaimann's original sequences are rearranged, resulting in three sets of sequences differing only in the strength of serial correlation. Four lot-sizing procedures are applied to each of these sets to discern if the correlation structure has any appreciable effect on lot-sizing performance. Results indicate that, on average, higher total inventory costs are experienced when the demand environment is characterized by randomness. Economic order quantity and part-period balancing achieve lowest average costs when confronted with highly autocorrelated demand or patterns of few runs; conversely, minimum cost per period and Wagner-Whitin perform best under conditions of many runs. Both economic order quantity and part-period balancing perform most favorably in comparison to Wagner-Whitin when runs are few. In addition, there appears to be a potential interaction between the level of demand variability and the degree of serial correlation. This finding is somewhat disconcerting since high variability demand sequences used in some prior research were also characterized by relatively high levels of autocorrelation; hence it becomes most difficult to identify and decompose the unique influences of each demand pattern dimension on lot-sizing behavior. Because of this phenomenon, it is suggested that future studies direct greater attention to the demand simulating methodology than has heretofore been accorded.     

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.     

带有两仓库需求时变的变质性物品的补货策略

在两仓库的情况下,讨论了需求率时变、变质率为常数的单一变质性物品在允许延期付款但不允许缺货且给予顾客一个信用期情况下的库存策略,证明了最优补货周期的存在性,并给出了求最优补货周期的算例。     

Debris removal during disaster response: A case for Turkey

Debris occurs from the ruin and wreckage of structures during a disaster. Proper removal of debris is of great importance because it blocks roads and prohibits emergency aid teams from accessing disaster-affected regions. Poor disaster management, lack of efficiency and delays in debris removal cause disruptions in providing shelter, nutrition, healthcare and communication services to disaster victims, and more importantly, result in loss of lives. Due to the importance of systematic and efficient debris removal from the perspectives of improving disaster victims quality of life and allowing the transportation of emergency relief materials, the focus of this study is on providing emergency relief supplies to disaster-affected regions as soon as possible by unblocking roads through removing the accumulated debris. We develop a mathematical model for the problem that requires long CPU times for large instances. Since it is crucial to act quickly in an emergency case, we also propose a heuristic methodology that solves instances with an average gap of 1% and optimum ratio of 80.83%.     

基于遗传算法的多周期确定性IRP问题研究

本文主要通过在分析多周期确定性条件的基础上建立的数学模型,研究多周期确定性客户需求下的IRP问题,并利用遗传算法对模型进行求解.同时以小群体规模、指定交叉率和变异率为实例,进行数值模拟实例分析.与利用经济批量采购公式求解的客户补货量进行了对比分析,遗传算法可以有效地解决了IRP中最优补货量的问题.     

Pre-positioning hurricane supplies in a commercial supply chain

Inventory control for retailers situated in the projected path of an observed hurricane or tropical storm can be challenging due to the inherent uncertainties associated with storm forecasts and demand requirements. In many cases, retailers react to pre- and post-storm demand surge by ordering emergency supplies from manufacturers posthumously. This wait-and-see approach often leads to stockout of the critical supplies and equipment used to support post-storm disaster relief operations, which compromises the performance of emergency response efforts and proliferates lost sales in the commercial supply chain. This paper proposes a proactive approach to managing disaster relief inventories from the perspective of a single manufacturing facility, where emergency supplies are pre-positioned throughout a network of geographically dispersed retailers in anticipation of an observed storm's landfall. Once the requirements of a specific disaster scenario are observed, supplies are then transshipped among retailers, with possible direct shipments from the manufacturer, to satisfy any unfulfilled demands. The manufacturer's pre-positioning problem is formulated as a two-stage stochastic programming model which is illustrated via a case study comprised of real-world hurricane scenarios. Our findings indicate that the expected performance of the proposed pre-positioning strategy over a variety of hurricane scenarios is more effective than the wait-and-see approach; currently used in practice.     

A model for planning locations of temporary distribution facilities for emergency response

We propose a network flow model for dynamic selection of temporary distribution facilities and allocation of resources for emergency response planning. The model analyzes the transfer of excess resources between temporary facilities operating in different time periods in order to reduce deprivation. Numerical analysis shows that the location of temporary facilities is determined by the demand and supply points. This work contributes to the emergency response planning that requires a quick response for the supply of relief materials immediately after a disaster hits a particular area.     

Including deprivation costs in facility location models for humanitarian relief logistics

Humanitarian assistance is meant to save lives and alleviate human suffering during and in the aftermath of man-made and natural disasters. To prevent and strengthen preparedness for the occurrence of such situations, having available relief supplies in the short-term becomes crucial. The lack of access to life-sustaining items implies a loss in people's welfare, treated as an externality called deprivation costs which must be incorporated into decision-making processes. Since typical humanitarian applications are extensions of commercial logistic models, they usually do not account for externalities, leading to high social costs and likely to unfeasible or suboptimal solutions.This paper develops a facility location model for prepositioning supplies in preparation for disasters; the key feature of this formulation being the fact that it explicitly considers deprivation costs in the objective function. The model attempts to minimize the global social costs, as the sum of both private costs (i.e. costs of transportation, inventory costs and fixed costs of facilities) and deprivation costs, determining the amount per type of product to be prepositioned for serving the areas affected by a disaster during the initial response. The model focuses on those assistance interventions that should be carried out immediately, i.e. within the first 24 h of a humanitarian crisis. We applied the model, using real information, to the Colombian Caribbean region, which was affected by floods in 2010 and 2011. Results demonstrate that deprivation costs represent more than 50% of the total social cost.