Multi-criteria logistics modeling for military humanitarian assistance and disaster relief aerial delivery operations

Given that it is not always feasible to reach an affected area via land or sea within the first week following a natural disaster, aerial delivery provides the primary means to rapidly supply the affected population. Further, it is often the case that high density delivery of humanitarian aid supplies are taken over by non-friendly groups within the affected population. By using direct airdrop systems to deliver large quantities of individually wrapped food and water items, dispersion among the affected disaster relief population will occur more quickly. In this paper, we proffer a multiple criteria decision analysis (MCDA) framework to optimize the military humanitarian assistance/disaster relief (HA/DR) aerial delivery supply chain network. The model uses stochastic, mixed-integer, weighted goal programming to optimize network design, logistics costs, staging locations, procurement amounts, and inventory levels. The MCDA framework enables decision-makers to explore the trade-offs between military HA/DR aerial delivery supply chain efficiency and responsiveness, while optimizing across a wide range of real-world, probabilistic scenarios to account for the inherent uncertainty in the location of global humanitarian disasters as well as the amount of demand to be met.     

Fuzzy periodic review system with fuzzy random variable demand

In this paper, a periodic review inventory system has been analyzed in a mixed imprecise and uncertain environment where fuzziness and randomness appear simultaneously. A model has been developed with customer demand assumed to be a fuzzy random variable. The lead-time has been assumed to be a constant. The lead-time demand and the lead-time plus one period’s demand have also been assumed to be fuzzy random variables. A methodology has been developed to determine the optimal inventory level and the optimal period of review such that the total expected annual cost in the fuzzy sense is minimized. A numerical example has been presented to illustrate the model.     

An interactive method for inventory control with fuzzy lead-time and dynamic demand

Normally, the real-world inventory control problems are imprecisely defined and human interventions are often required to solve these decision-making problems. In this paper, a realistic inventory model with imprecise demand, lead-time and inventory costs have been formulated and an inventory policy is proposed to minimize the cost using man–machine interaction. Here, demand increases with time at a decreasing rate. The imprecise parameters of lead-time, inventory costs and demand are expressed through linear/non-linear membership functions. These are represented by different types of membership functions, linear or quadratic, depending upon the prevailing supply condition and marketing environment. The imprecise parameters are first transformed into corresponding interval numbers and then following the interval mathematics, the objective function for average cost is changed into respective multi-objective functions. These functions are minimized and solved for a Pareto-optimum solution by interactive fuzzy decision-making procedure. This process leads to man–machine interaction for optimum and appropriate decision acceptable to the decision maker’s firm. The model is illustrated numerically and the results are presented in tabular forms.     

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.     

A combined forecast—inventory control procedure for spare parts

This paper examines the performance of two different (s, Q) inventory models, namely a simple and an advanced model, for spare parts in a production plant of a confectionery producer in the Netherlands. The simple approach is more or less standard: the undershoot of the reorder level is not taken into account and the normal distribution is used as the distribution of demand during lead-time. The advanced model takes undershoots into account, differentiates between zero and nonzero demands during lead-time, and utilises the gamma distribution for the demand distribution. Both models are fed with parameters estimated by a procedure that forecasts demand sizes and time between demand occurrences separately (intermittent demand). The results show that the advanced approach yields a service level close to the desired one under many circumstances, while the simple approach is not consistent, in that it leads to much larger inventories in meeting the desired service level for all spare parts.     

基于应急救援物资单向转运的受灾点库存策略研究

了研究应急救援物流中存在物资单向转运条件下的受灾点库存策略,考虑由多个受灾点组成的单阶段系统,
各个受灾点之间存在单向转运.首先在各个受灾点物资进货点一定条件下,建立模型确定各个受灾点救援物资
需求依靠从其它受灾点转运得到满足的比例和直接从本身库存中得到满足的比例;其次,建立各个受灾点
救援物资进货水平优化的整数非线性规划模型,并考虑基于时间窗的救援效率水平约束,设计基于隐含
枚举法的模型求解算法;最后,运用算例对模型及其求解算法进行了模拟运算,从而验证了模型的有效性和实用性.     

A multi-criteria optimization model for humanitarian aid distribution

Natural disasters are phenomenons which strike countries all around the world. Sometimes, either by the intensity of the phenomenon or the vulnerability of the country, help is requested from the rest of the world and relief organizations respond by delivering basic aid to those in need. Humanitarian logistics is a critical factor in managing relief operations and, in general, there is a lack of attention on the development of mathematical models and solution algorithms for strategic and tactical decisions in this area. We acknowledge that in humanitarian logistics traditional cost minimizing measures are not central, and postulate that other performance measures such as time of response, equity of the distribution or reliability and security of the operation routes become more relevant. In this paper several criteria for an aid distribution problem are proposed and a multi-criteria optimization model dealing with all these aspects is developed. This model is the core of a decision support system under development to assist organizations in charge of the distribution of humanitarian aid. Once the proposed criteria and the model are described, an illustrative case study based on the 2010 Haiti catastrophic earthquake is presented, showing the usefulness of the proposal.     

Inventory rationing via drop-shipping in Internet retailing: A sensitivity analysis

In this paper, we study a threshold level inventory rationing policy that is of interest to e-tailers, operating in a business to consumer (B2C) environment and selling non-perishable, made-to-stock items such as books, CDs, consumer electronics, and body and bath products. A Monte Carlo simulation model is developed to examine this policy when the demand process is stochastic, lead-time is stochastic, and the e-tailer uses ‘drop-shipping’ as an order fulfillment option. The methodology presented, which includes computer simulation and a full factorial experimental design, permits understanding of the complexity of the decision-making environment and implications of different sources of uncertainty (e.g. demand variability and lead-time variability) on a profit-maximizing threshold level of inventory, a stock level below which low margin orders are drop-shipped directly from the e-tailer’s supplier rather than fulfilled from internal stock.     

A fuzzy random periodic review system with variable lead-time and negative exponential crashing cost

In the present model a fuzzy random periodic review system has been investigated with the annual demand assumed to be a discrete fuzzy random variable with associated imprecise probabilities. Keeping in mind the widespread application of the Just-In-Time manufacturing philosophy and lead-time management being one of its most effective methods of implementation, the lead-time has been assumed to be an added control parameter. Also as it may not be always possible to resolve the lead-time into all its components and estimate their individual crashing costs, the crashing cost has been introduced as a negative exponential function of the lead-time. A methodology has been developed in this regard such that the total inventory cost is minimized and the optimal period of review, the optimal target inventory level and the optimal lead-time are determined in the process. An algorithm has been provided to encapsulate the methodology and it has been illustrated by way of a numerical example.     

An aggregate–disaggregate intermittent demand approach (ADIDA) to forecasting: an empirical proposition and analysis

Intermittent demand patterns are characterised by infrequent demand arrivals coupled with variable demand sizes. Such patterns prevail in many industrial applications, including IT, automotive, aerospace and military. An intuitively appealing strategy to deal with such patterns from a forecasting perspective is to aggregate demand in lower-frequency ‘time buckets’ thereby reducing the presence of zero observations. However, such aggregation may result in losing useful information, as the frequency of observations is reduced. In this paper, we explore the effects of aggregation by investigating 5000 stock keeping units from the Royal Air Force (UK). We are also concerned with the empirical determination of an optimum aggregation level as well as the effects of aggregating demand in time buckets that equal the lead-time length (plus review period). This part of the analysis is of direct relevance to a (periodic) inventory management setting where such cumulative lead-time demand estimates are required. Our study allows insights to be gained into the value of aggregation in an intermittent demand context. The paper concludes with an agenda for further research.     

A robust disaster preparedness model for effective and fair disaster response

Humanitarian network design decisions belonging to the preparedness stage of disaster management life-cycle are of critical importance since they set the frame for all further post-disaster operations. Having an adequate number of strategically located storage and distribution centers for critical supplies is the key that enables effectiveness, efficiency and fairness when responding to a disaster situation. The preparedness model proposed in this study selects locations and inventory levels of these facilities such that the right mix of relief items can be supplied at the right time. Our mixed integer linear model aims to find a robust relief network design that satisfies the demand for all given disaster scenarios, and to help achieve a better response during the response stage when the relief items are distributed. The assumptions and the parameters used in the model are justified by authorities of humanitarian organizations. We propose a logic-based Benders decomposition approach to solve this problem to optimality. Although the problem is NP-hard, our numerical studies demonstrate that it is possible to obtain optimal or very good solutions to problem instances with realistic sizes.     

Humanitarian aid logistics: supply chain management in high gear

This paper builds on the idea that private sector logistics can and should be applied to improve the performance of disaster logistics but that before embarking on this the private sector needs to understand the core capabilities of humanitarian logistics. With this in mind, the paper walks us through the complexities of managing supply chains in humanitarian settings. It pinpoints the cross learning potential for both the humanitarian and private sectors in emergency relief operations as well as possibilities of getting involved through corporate social responsibility. It also outlines strategies for better preparedness and the need for supply chains to be agile, adaptable and aligned—a core competency of many humanitarian organizations involved in disaster relief and an area which the private sector could draw on to improve their own competitive edge. Finally, the article states the case for closer collaboration between humanitarians, businesses and academics to achieve better and more effective supply chains to respond to the complexities of today's logistics be it the private sector or relieving the lives of those blighted by disaster.     

On the tradeoff between optimal order-base-stock levels and demand lead-times

We investigate the tradeoff between finished-goods inventory and advance demand information for a model of a single-stage make-to-stock supplier who uses an order-base-stock replenishment policy to meet customer orders that arrive a fixed demand lead-time in advance of their due-dates. We show that if the replenishment orders arrive in the order that they are placed, then the tradeoff between the optimal order-base-stock level and the demand lead-time is “exhaustive”, in the sense that the optimal order-base-stock level drops all the way to zero if the demand lead-time is sufficiently long. We then provide a sufficient condition under which this tradeoff is linear. We verify that this condition is satisfied for the case where the supply process is modeled as an M/M/1 queue. We also show that the tradeoff between the optimal order-base-stock level and the demand lead-time is linear for the case where the supply process is modeled as an M/D/1 queue. More specifically, for this case, we show that the optimal order-base-stock level decreases by one unit if the demand lead-time increases by an amount equal to the supplier’s constant processing time. Finally, we show that the tradeoff between the optimal order-base-stock level and the demand lead-time is exhaustive but not linear in the case where the supply process is modeled as an M/D/∞ queue. We illustrate these results with a numerical example.     

A multi-objective wholesaler–retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number

This paper develops a single wholesaler and multi retailers mixture inventory distribution model for a single item involving controllable lead-time with backorder and lost sales. The retailers purchase their items from the wholesaler in lots at some intervals throughout the year to meet the customers’ demand. Not to loose the demands, the retailers offer a price discount to the customers on the stock-out items. Here, it is assumed that the lead-time demands of retailers are uncertain in both stochastic and fuzzy sense, i.e., these are simultaneously random and imprecise. To implement this behavior of the lead-time demands, at first, these demands are assumed to be random, say following a normal distribution. With these random demands, the expected total cost for each retailer is obtained. Now, the mean lead-time demands (which are crisp ones) of the retailers are fuzzified. This fuzzy nature of the lead-time demands implies that the annual average demands of the retailers must be fuzzy numbers, suppose these are triangular fuzzy numbers. Using signed distance technique for defuzzification, the estimate of total costs for each retailer is derived. Therefore, the problem is reduced to optimize the crisp annual costs of wholesaler and retailers separately. The multi-objective model is solved using Global Criteria method. Numerical illustrations have been made with the help of an example taking two retailers into consideration. Mathematical analyses have been made for global pareto-optimal solutions of the multi-objective optimization problem. Sensitivity analyses have been made on backorder ratio and pareto-optimal solutions for wholesaler and different retailers are compared graphically.     

An application of Genetic Algorithm in solving an inventory model with advance payment and interval valued inventory costs

The purpose of this research is to solve the mixed integer constrained optimization problem with interval coefficient by a real-coded genetic algorithm (RCGA) with ranking selection, whole arithmetical crossover and non-uniform mutation for non-integer decision variables. In the ranking selection, as well as in finding the best solution in each generation of RCGA, recently developed modified definitions of order relations between interval numbers with respect to decision-making are used. Also, for integer decision variables, new types of crossover and mutation are introduced. This methodology is applied to solve a finite time horizon inventory model with constant lead-time, uniform demand rate and a discount by paying an amount of money in advance. Moreover, different inventory costs are considered to be interval valued. According to the consumption of items during lead-time and reorder level, two cases may arise. For each case, the mathematical model becomes a constrained nonlinear mixed integer problem with interval objective. Our objective is to determine the optimal number of cycles in the finite time horizon, lot-size in each cycle and optimal profit. The model is illustrated with some numerical examples and sensitivity analysis has been done graphically with the variation of different inventory parameters.     

Robust optimization for relief logistics planning under uncertainties in demand and transportation time

Emergency logistics is an essential component of post-disaster relief campaigns. However, there are always various uncertainties when making decisions related to planning and implementing post-disaster relief logistics. Considering the particular environmental conditions during post-disaster relief after a catastrophic earthquake in a mountainous area, this paper proposes a stochastic model for post-disaster relief logistics to guide the tactical design for mobilizing relief supply levels, planning initial helicopter deployments, and creating transportation plans within the disaster region, given the uncertainties in demand and transportation time. We then introduce a robust optimization approach to cope with these uncertainties and deduce the robust counterpart of the proposed stochastic model. A numerical example based on disaster logistics during the Great Sichuan Earthquake demonstrates that the model can help post-disaster managers to determine the initial deployments of emergency resources. Sensitivity analyses explore the trade-off between optimization and robustness by varying the robust optimization parameter values.     

An insurance risk management framework for disaster relief and supply chain disruption inventory planning

Government agencies, not-for-profit organizations, and private corporations often assume leading roles in the delivery of supplies, equipment, and manpower to support initial response operations after a disaster strikes. These organizations are faced with challenging logistics decisions to ensure that the right supplies (including equipment and personnel) are in the right places, at the right times, and in the right quantities. Such logistics planning decisions are further complicated by the uncertainties associated with predicting whether or not a potential threat will materialize into an emergency situation. This paper introduces newsvendor variants that account for demand uncertainty as well as the uncertainty surrounding the occurrence of an extreme event. The optimal inventory level is determined and compared to the classic newsvendor solution and the difference is interpreted as the insurance premium associated with proactive disaster-relief planning. The insurance policy framework represents a practical approach for decision makers to quantify the risks and benefits associated with stocking decisions related to preparing for disaster relief efforts or supply chain disruptions.     

Distress among disaster-affected populations: delay in relief provision

Central to humanitarian logistics is the minimization of distress among impacted populations in the aftermath of a disaster. In this paper, we characterize two levels of distress, termed criticality and destitution, with respect to the delay provision of relief items. Delay in provision of a relief item will lead to destitution for a tolerable number of days, beyond which it will lead to criticality. We develop a mixed-integer goal program that quantifies these two metrics with respect to the number of days without provision of each of a set of relief items. The model determines the allocation of resources and the distribution of available relief items in a manner that minimizes criticality and destitution in affected population segments. The use of the model is demonstrated for the aftermath of a catastrophic earthquake in Istanbul, expected to occur by 2030.     

电子商务环境下考虑退货的选址库存问题模型与算法

选址库存问题(location inventory problem, LIP)是物流系统集成的经典问题之一,也是企业需要面对的管理决策难题。本文考虑在电子商务环境下无质量缺陷的退货商品可简单再包装后重新进入销售市场这一现实情况,对设施选址和库存控制进行集成优化,构建随机需求下有退货的LIP模型。针对此问题求解的复杂性,设计了改进的自适应混合差分进化算法对模型进行整体求解。最后,通过多组算例验证了模型和算法的实用性和优越性,可为设施选址、库存控制和商品配送回收决策提供重要参考依据。     

Fuzzy mixture two warehouse inventory model involving fuzzy random variable lead time demand and fuzzy total demand

This paper considers a two-warehouse fuzzy-stochastic mixture inventory model involving variable lead time with backorders fully backlogged. The model is considered for two cases—without and with budget constraint. Here, lead-time demand is considered as a fuzzy random variable and the total cost is obtained in the fuzzy sense. The total demand is again represented by a triangular fuzzy number and the fuzzy total cost is derived. By using the centroid method of defuzzification, the total cost is estimated. For the case with fuzzy-stochastic budget constraint, surprise function is used to convert the constrained problem to a corresponding unconstrained problem in pessimistic sense. The crisp optimization problem is solved using Generalized Reduced Gradient method. The optimal solutions for order quantity and lead time are found in both cases for the models with fuzzy-stochastic/stochastic lead time and the corresponding minimum value of the total cost in all cases are obtained. Numerical examples are provided to illustrate the models and results in both cases are compared.