A multi-objective healthcare inventory routing problem; a fuzzy possibilistic approach

This paper presents a new multi-objective mathematical model to address a Healthcare Inventory Routing Problem (HIRP) for medicinal drug distribution to healthcare facilities. The first part of objective function minimizes total inventory and transportation costs, while satisfaction is maximized by minimizing forecast error which caused by product shortage and the amount of expired drugs; Greenhouse Gas (GHG) emissions are also minimized. A demand forecast approach has been integrated into the mathematical model to decrease drug shortage risk. A hybridized possibilistic method is applied to cope with uncertainty and an interactive fuzzy approach is considered to solve an auxiliary crisp multi-objective model and find optimized solutions.     

Coordinated inventory replenishment and outsourced transportation operations

We consider a one-warehouse N retailers supply chain with stochastic demand. Inventory is managed in-house whereas transportation is outsourced to a 3PL provider. We develop analytical expressions for the operating characteristics under both periodic and continuous joint replenishment policies. We identify the settings where a periodic review policy is comparable to a continuous review one. In our numerical test-bed, the periodic policy performed best in larger supply chains operating with larger trucks. We also observed that if the excess utilization charge is less than 25%, outsourcing becomes beneficial even if outsourcing cost is 25% more than the in-house fleet costs.     

Hybrid metaheuristic solutions to inventory location routing problem

This paper considers a supply chain network with multiple depots and geographically dispersed customers, each of which faces non-constant demand over a discrete planning horizon. The goal is to determine a set of depots to open, the delivery quantities to customers per period and the sequence in which they are replenished by a vehicle fleet such that the total system-wide cost is minimized. To solve it, first we construct a mixed integer program, and then propose a hybrid metaheuristic consisting of initialization, intensification and post-optimization. Results show that the proposed heuristic is considerably efficient and effective for many classical instances.     

A robust optimization approach for the road network daily maintenance routing problem with uncertain service time

This paper studies the robust optimization approach for the routing problem encountered in daily maintenance operations of a road network. The uncertainty of service time is considered. The robust optimization approach yields routes that minimize total cost while being less sensitive to substantial deviations of service times. A robust optimization model is developed and solved by the branch-and-cut method. In computational experiments, the behavior of the robust solutions and their performance are analyzed using Monte Carlo simulation. The robust optimization model is also compared with a classic chance-constrained programming model. The experimental analysis provides managerial insights for decision makers to determine an appropriate routing strategy.     

Combined fleet deployment and inventory management in roll-on/roll-off shipping

In maritime transportation of automobiles, roll-on/roll-off (ro–ro) shipping companies operate liner shipping services across major trade routes. Large ro–ro shipping companies are well placed to offer end-to-end integrated logistics services to auto manufacturers engaged in international trade of vehicles. Therefore, we present a new mixed integer programming model for fleet deployment including inventory management at the ports along each trade route. Due to the complexity of the problem, a rolling horizon heuristic (RHH) is proposed. The RHH solves the problem by iteratively solving sub-problems with shorter planning horizon. Computational results based on real instances are presented.     

Combining service frequency and vehicle routing for managing supplier shipments

This paper proposes a new approach to designing inbound material collection routes that considers pick-up frequency and spatial design as joint decisions to minimize total logistics (transportation plus inventory) cost. The clustering-based optimization uses an approximation to the actual cost of a routing solution without actual route construction. We show that the problem is analogous to a single-source fixed-charge facility location problem, and near-optimal solutions can be found using an efficient heuristic algorithm. Tests show the effectiveness of how this model is formulated and a case study demonstrates that substantial total cost savings can be achieved in realistic applications.     

A robust mathematical model and heuristic algorithms for integrated aircraft routing and scheduling,with consideration of fleet assignment problem

One of the most important airline's products is to determine the aircraft routing and scheduling and fleet assignment. The key input data of this problem is the traffic forecasting and allocation that forecasts traffic on each flight leg. The complexity of this problem is to define the connecting flights when passengers should change the aircraft to reach the final destination. Moreover, as there exists various types of uncertainties during the flights, finding a solution which is able to absorb these uncertainties is invaluable. In this paper, a new robust mixed integer mathematical model for the integrated aircraft routing and scheduling, with consideration of fleet assignment problem is proposed. Then to find good solutions for large-scale problems in a rational amount of time, a heuristic algorithm based on the Simulated Annealing (SA) is introduced. In addition, some examples are randomly generated and the proposed heuristic algorithm is validated by comparing the results with the optimum solutions. The effects of robust vs non-robust solutions are examined, and finally, a hybrid algorithm is generated which results in more effective solution in comparison with SA, and Particle Swarm Optimization (PSO).     

A metaheuristic approach to the reliable location routing problem under disruptions

This paper examines a reliable capacitated location–routing problem in which depots are randomly disrupted. Customers whose depots fail must be reinserted into the routes of surviving depots. We present a scenario-based mixed-integer programming model to optimize depot location, outbound delivery routing, and backup plans. We design a metaheuristic algorithm that is based on a maximum-likelihood sampling method, route-reallocation improvement, two-stage neighborhood search and simulated annealing. Numerical tests show that the heuristic is able to generate results that would keep operating costs and failure costs well balanced. Managerial insights on scenario identification, facility deployment and model simplification are drawn.     

Efficient aircraft spare parts inventory management under demand uncertainty

In airline industries, the aircraft maintenance cost takes up about 13% of the total operating cost. It can be reduced by a good planning. Spare parts inventories exist to serve the maintenance planning. Compared with commonly used reorder point system (ROP) and forecasting methods which only consider historical data, this paper presents two non-linear programming models which predict impending demands based on installed parts failure distribution. The optimal order time and order quantity can be found by minimizing total cost. The first basic mathematical model assumes shortage period starts from mean time to failure (MTTF). An iteration method and GAMS are used to solve this model. The second improved mathematical model takes into account accurate shortage time. Due to its complexity, only GAMS is applied in solution methodology. Both models can be proved effective in cost reduction through revised numerical examples and their results. Comparisons of the two models are also discussed.     

A Linear Programming approach for robust network revenue management in the airline industry

The classical revenue management problem consists of allocating a fixed network capacity to different customer classes, so as to maximize revenue. This area has been widely applied in service industries that are characterized by a fixed perishable capacity, such as airlines, cruises, hotels, etc.It is traditionally assumed that demand is uncertain, but can be characterized as a stochastic process (See Talluri and van Ryzin (2005) for a review of the revenue management models). In practice, however, airlines have limited demand information and are unable to fully characterize demand stochastic processes. Robust optimization methods have been proposed to overcome this modeling challenge. Under robust optimization framework, demand is only assumed to lie within a polyhedral uncertainty set (Lan et al. (2008); Perakis and Roels (2010)).In this paper, we consider the multi-fare, network revenue management problem for the case demand information is limited (i.e. the only information available is lower/upper bounds on demand). Under this interval uncertainty, we characterize the robust optimal booking limit policy by use of minimax regret criterion. We present an LP (Linear Programming) solvable mathematical program for the maximum regret so our model is able to solve large-scale problems for practical use. A genetic algorithm is proposed to find the booking limit control to minimize the maximum regret. We provide computational experiments and compare our methods to existing ones. The results demonstrate the effectiveness of our robust approach.     

An integer programming approach to the bloodmobile routing problem

Every day, a blood center must determine a set of locations among a group of potential sites to route their vehicles for blood collection so as to avoid shortfalls. In this study, a vehicle routing problem is modeled using an integer programming approach to simultaneously identify number of bloodmobiles to operate and minimize the distance travelled. Additionally, the model is extended to incorporate uncertainty in blood potentials and variable durations in bloodmobile visits. Optimal routings are determined using CPLEX solver and branch-and-price algorithm. Results show that proposed algorithm solve the problem to optimality up to 30 locations within 3600 s.     

Age-based policy for blood transshipment during blood shortage

This paper introduces the properties of inventory structure for both rescue and affected banks during blood shortage. An age-based transshipment model is developed, with two preference selection methods for transshipping blood units being presented. Compared to quantity-based policy, the age-based policy under first-in-first-transship is recommended as it can reduce the expired rate more efficiently. Under simulation operating scenarios with time-varying demand and supply, we analyzed the sensitivity of parameters, which include expected supply period, shelf life and blood shortage period. Additionally, this study reveals that the transshipment decision will increase the expired ratio and the overstock ratio after blood shortage.     

Intermodal routing of Canada–Mexico shipments under NAFTA

This paper obtains the optimal routings for intermodal containerized transport from Canada to Mexico. Such traffic is being stimulated by the North American Free Trade Agreement (NAFTA), but the cost and lead times of feasible routes are not well known. We summarize the links and routes to Mexico on which one or more carriers now operate, and then determine non-dominated tradeoffs between cost and service. Every southbound route from Canada requires a transshipment point in the southern or southwestern U. S. Feasible transshipment points are also candidate locations for a manufacturing ‘twin plant’, a distribution centre, or a transportation hub. Here, as a first step in this bigger problem, a network is constructed between five Canadian origins and three important Mexican destinations. Each link employs available intermodal services whose transit time and transportation cost are obtained through industry sources. A shortest-path algorithm enables calculation of the route requiring least time and the route of minimum cost. Non-dominated time/cost tradeoffs are identified for each origin–destination pair. After including inventory expenses (by parametrizing the unit value of lead time), total-cost curves then eliminate some routing alternatives. Guidelines are provided on the effects of mode, carrier, and O–D locations on selection of intermodal routes to Mexico. Finally, two new intermodal services are proposed and their benefits discussed.     

A novel hybrid-link-based container routing model

Container routing determines how to transport containers from their origins to their destinations in a liner shipping network. Container routing needs to be solved a number of times as a subproblem in tactical-level decision planning of liner shipping operations. Container routing is similar to the multi-commodity flow problem. This research proposes a novel hybrid-link-based model that nests the existing origin-link-based and destination-link-based models as special cases. Moreover, the hybrid-link-based model is at least as compact as the origin-to-destination-link-based, origin-link-based and destination-link-based models in the literature.     

A hybrid population heuristic for the heterogeneous vehicle routing problems

The heterogeneous vehicle routing problem (HVRP) plays an important role in supply chain logistics. Two variants of HVRP are treated in this paper: one with fixed and variable costs (HVRPFD), and the other with only variable cost (HVRPD). A hybrid population heuristic that is able to solve both variants is proposed, in which a population of solutions are progressively evolved by crossovers and local searches. Computational results on a set of eight benchmark test problems from literature show that the proposed heuristic produces excellent solutions in short computing times.     

A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges

This paper presents several heuristics for a variation of the vehicle routing problem in which the transportation fleet is composed of electric vehicles with limited autonomy in need for recharge during their duties. In addition to the routing plan, the amount of energy recharged and the technology used must also be determined. Constructive and local search heuristics are proposed, which are exploited within a non deterministic Simulated Annealing framework. Extensive computational results on varying instances are reported, evaluating the performance of the proposed algorithms and analyzing the distinctive elements of the problem (size, geographical configuration, recharge stations, autonomy, technologies, etc.).     

A hierarchical clustering and routing procedure for large scale disaster relief logistics planning

We describe a hierarchical cluster and route procedure (HOGCR) for coordinating vehicle routing in large-scale post-disaster distribution and evacuation activities. The HOGCR is a multi-level clustering algorithm that groups demand nodes into smaller clusters at each planning level, enabling the optimal solution of cluster routing problems. The routing problems are represented as capacitated network flow models that are solved optimally and independently by CPLEX on a parallel computing platform. The HOGCR preserves the consistency among parent and child cluster solutions obtained at consecutive levels. We assess the performance of the algorithm by using large scale scenarios and find satisfactory results.     

A spatiotemporal partitioning approach for large-scale vehicle routing problems with time windows

For VRP with time windows (VRPTW) solved by conventional cluster-first and route-second approach, temporal information is usually considered with vehicle routing but ignored in the process of clustering. We propose an alternative approach based on spatiotemporal partitioning to solving a large-scale VRPTW, considering jointly the temporal and spatial information for vehicle routing. A spatiotemporal representation for the VRPTW is presented that measures the spatiotemporal distance between two customers. The resulting formulation is then solved by a genetic algorithm developed for k-medoid clustering of large-scale customers based on the spatiotemporal distance. The proposed approach showed promise in handling large scale networks.     

Fulfillment source allocation,inventory transshipment,and customer order transfer in e-tailing

We consider an inventory fulfillment-allocation and transshipment problem in an e-tailing environment. For a typical e-tailer, each customer demand is fulfilled from the closest fulfillment center if there are enough inventories. Otherwise, the e-tailer would transship stock from a nearby facility or transfer the customer order so it is fulfilled from another facility, depending on the economics of transportation. We develop a mixed-integer programming model to help e-tailers optimally fulfill customer orders while minimizing logistics costs. We propose a Benders decomposition-based approach to efficiently find optimal solutions. Our computational results demonstrate the importance of considering inventory transshipments in online deliveries.     

Models for relief routing: Equity, efficiency and efficacy

In humanitarian relief operations, vehicle routing and supply allocation decisions are critically important. Similar routing and allocation decisions are studied for commercial settings where efficiency, in terms of minimizing cost, is the primary objective. Humanitarian relief is complicated by the presence of multiple objectives beyond minimizing cost. Routing and allocation decisions should result in quick and sufficient distribution of relief supplies, with a focus on equitable service to all aid recipients. However, quantifying such goals can be challenging. In this paper, we define and formulate performance metrics in relief distribution. We focus on efficacy (i.e., the extent to which the goals of quick and sufficient distribution are met) and equity (i.e., the extent to which all recipients receive comparable service). We explore how efficiency, efficacy, and equity influence the structure of vehicle routes and the distribution of resources. We identify trends and routing principles for humanitarian relief based on the analytical properties of the resulting problems and a series of computational tests.