Savings Algorithm Research Articles

Vehicle flow formulation for two-echelon time-constrained vehicle routing problem

Two-echelon routing problems, including variants such as the two-echelon vehicle routing problem (2E-VRP) and the two-echelon location routing problem (2E-LRP), involve assignment and location decisions. However, the two-echelon time-constrained vehicle routing problem (2E-TVRP) that caters to from-linehaul-to-delivery practices does not involve assignment decisions. This routing problem variant for networks with two echelons has not yet attracted enough research interest. Localized or long-distance services suffer from the lack of the assignment decisions between satellites and customers. Therefore, the 2E-TVRP, rather than using assignment decisions, adopts time constraints to decide the routes on each of the two interacting echelons: large-capacity vehicles transport cargoes among satellites on the first echelon, and small-capacity vehicles deliver cargoes from satellites to customers on the second echelon. This study introduces a mixed integer linear programming model for the 2E-TVRP and proposes a heuristic algorithm that incorporates the savings algorithm followed by a variable neighborhood search phase. Illustrative examples are used to test the mathematical formulation and the heuristic and a case study is used to demonstrate that the heuristic can effectively solve realistic-size instances of the 2E-TVRP.

Reoptimization Heuristic for the Capacitated Vehicle Routing Problem

The solution to a dynamic context of the Capacitated Vehicle Routing Problem (CVRP) is challenging. Routing and replenishment decisions are necessary by considering the assignment of customers to vehicles when the information is gradually revealed over horizon time. The procedure to solve this type of problems is referred to as route reoptimization, which is the best option for minimizing expected transportation cost without incurring failures of unsatisfied demand on a route. This paper proposes a heuristic algorithm for the reoptimization of CVRP in which the number of customers increases. The algorithm uses proposed performance metrics to reduce route dispersion and minimize length. The initial solution is generated using the savings algorithm and then enhanced using the Record-to-Record travel metaheuristic. By including or reducing new customers in the system, a reoptimization is performed which considers the visited nodes and edges as fixed. The optimization of the algorithm is implemented hierarchically by first minimizing dispersion and then minimizing distance. Next, the local search procedure is executed to improve the solution. A classic optimization is performed on all instances using the original and new customers’ information for later comparison to minimize distance. The efficiency of the proposed algorithm was validated using real-world cases from the literature. The results are promising and show the effectiveness of the proposed method for solving the considered problem by using reoptimization procedures in order to achieve good approximation ratios within short computing times.

A two-phase method for multi-echelon location-routing problems in supply chains

The multi-echelon location-routing problems (LRPs) arise from transportation applications such as distribution systems of supply chains in city logistics. The literature review shows that most of the previous studies on location-routing in supply chains involve two-echelon LRPs. The main objective of this study is to develop a two-phase method based on improved Clarke and Wright savings algorithm for three-echelon and four-echelon LRPs. Computational experiments show that compared with other methods, the proposed method can obtain the solution for two LRPs in a shorter time. Moreover, computational experiments show this method can solve three and four location-routing problems in reasonable time. The study also provides managerial insights on the proposed models and method. Finally, the limitations on models and method as well as future research directions are given.

The generalized rollon-rolloff vehicle routing problem and savings-based algorithm

Taking the waste collection management as the practical background, the rollon-rolloff vehicle routing problem (RRVRP) involves tractors pulling large containers between customer locations and the disposal facility. Each used-tractor begins and ends its route at the depot. Customer demand includes emptying a full container, ordering an empty container or changing a container. The objective is to find tractor routes that feature the minimum amount of total nonproductive time. In the literature the RRVRP is formulated as the node routing problem, and the “trip” definition that is the complete transport service of a container is used. To relax some assumptions of the RRVRP to cater to practical desires, we present a variant called the generalized RRVRP (G-RRVRP). The G-RRVRP generalizes the practical background, the objective function and the demand flow, and considers specially container loading and unloading time constraints. The G-RRVRP classifies demand into loaded-container demand and cargo demand with time windows. On condition of respecting container loading/unloading time and customer time windows, the G-RRVRP can design tractor routes for the synchronous scheduling of loaded and empty containers so as to ensure the timeliness of transport service. The G-RRVRP aims to minimize the total running cost of used tractors, instead of the total nonproductive time of tractors adopted by the RRVRP. A mixed integer linear programming model for the G-RRVRP is proposed. The Benders decomposition algorithm involving Pareto-optimal cuts and Benders decomposition-callback implementation, and a two-stage heuristic involving the savings algorithm followed by a local search phase are provided. The mathematical formulation and the two-stage heuristic are tested by solving 40 small-scale instances and 20 benchmark instances. Small-scale instances can be solved directly by CPLEX through the Benders decomposition strategies to find exact solutions. The case study indicates the applicability of the G-RRVRP model and the two-stage heuristic to realistic-size problems abstracted from intercity linehaul systems. The computational experiments and case study indicate that the heuristic can solve various instances of the G-RRVRP such that the solution quality and the computation time are acceptable.

An Application of Analytic Hierarchy Process in Vehicle Routing Problem

Vehicle Routing Problem (VRP) facilitates on finding a set of trips, one for each vehicle and to deliver known quantities of goods from a single depot to a set of geographically dispersed customers. This paper proposes an effective hybrid approach that combines customer prioritization with the Clarke and Wright's savings algorithm to solve the capacitated vehicle routing problem. In this model, in addition to traditional objective of resolving vehicle routing problem, the customer satisfaction have been taken into account. Initially, all the customers have been clustered with the help of Clarke and Wright's saving algorithm and later the customers have been prioritized on assigning optimal route using Analytic Hierarchy Process (AHP) as a Multi Criteria Decision Making (MCDM) tool. The highlight of this research is to diminish the total transportation cost without violating the vehicle capacity and ultimately improve the customer satisfaction.

Energy Saving from Cloud Resources for a Sustainable Green Cloud Computing Environment

Cloud computing services are proliferation. The Cloud computing resources face major pitfall in energy consumes. The prime of energy consumption in cloud computing is by means of client computational devices, server computational devices, network computational devices and power required to cool the IT load. The cloud resources contribute high operational energy cost and emit more carbon emission to the environment. Therefore the cloud services providers need green cloud environment resolution to decrease the operational energy cost along with environmental impact. The most important objective of this effort is to trim down the energy from utilized and unutilized (idle) cloud resources and save the energy in cloud resources efficiently. To achieve the sustainable green cloud environment from an Energy Saving Algorithm used to choose the appropriate virtual services so that the power at the client, server, and network recourses can be reduced.

Mathematical Formulation and Comparison of Solution Approaches for the Vehicle Routing Problem with Access Time Windows

The application of the principles of sustainability to the implementation of urban freight policies requires the estimation of all the costs and externalities involved. We focus here on the case of access time windows, which ban the access of freight vehicles to central urban areas in many European cities. Even though this measure seeks to reduce congestion and emissions in the most crowded periods of the day, it also imposes additional costs for carriers and results in higher emissions and energy consumption. We present here a mathematical model for the Vehicle Routing Problem with Access Time Windows, a variant of the VRP suitable for planning delivery routes in a city subject to this type of accessibility restriction. We use the model to find exact solutions to small problem instances based on a case study and then compare the performance over larger instances of a modified savings algorithm, a genetic algorithm, and a tabu search procedure, with the results showing no clear prevalence of any of them, but confirming the significance of those additional costs and externalities.

A critical analysis of the “improved Clarke and Wright savings algorithm”

AbstractIn their paper “An improved Clarke and Wright savings algorithm for the capacitated vehicle routing problem,” published in ScienceAsia (38, 3, 307–318, 2012), Pichpibul and Kawtummachai developed a simple stochastic extension of the well‐known Clarke and Wright savings heuristic for the capacitated vehicle routing problem. Notwithstanding the simplicity of the heuristic, which they call the “improved Clarke and Wright savings algorithm” (ICW), the reported results are among the best heuristics ever developed for this problem. Through a careful reimplementation, we demonstrate that the results published in the paper could not have been produced by the ICW heuristic. Studying the reasons how this paper could have passed the peer review process to be published in an ISI‐ranked journal, we have to conclude that the necessary conditions for a thorough examination of a typical paper in the field of optimization are generally lacking. We investigate how this can be improved and come to the conclusion that disclosing source code to reviewers should become a prerequisite for publication.

Parallel space saving on multi‐ and many‐core processors

SummaryGiven an array of n elements and a value 2≤k≤n, a frequent item or k‐majority element is an element occurring in more than n/k times. The k‐majority problem requires finding all of the k‐majority elements. In this paper, we deal with parallel shared‐memory algorithms for frequent items; we present a shared‐memory version of the Space Saving algorithm, and we study its behavior with regard to accuracy and performance on many and multi‐core processors, including the Intel Phi accelerator. We also investigate a hybrid MPI/OpenMP version against a pure MPI‐based version. Through extensive experimental results, we prove that the MPI/OpenMP parallel version of the algorithm significantly enhances the performance of the earlier pure MPI version of the same algorithm. Results also prove that for this algorithm the Intel Phi accelerator does not introduce any improvement with respect to the Xeon octa–core processor.

Developing decision support system for heterogeneous fleet vehicle routing problem using hybrid heuristic

In the last few years, there has been an increasing use of optimisation packages and decision support system (DSS) for the efficient and effective decision making. A significant variant of vehicle routing problem (VRP) arises when a fleet of vehicles is characterised by different capacities and operating costs, which is known as heterogeneous fleet vehicle routing problem (HFVRP). This paper aims at determining the optimal composition of fleet and set of routes to be accomplished by a fleet of heterogeneous vehicles for serving a given set of customers with the objective of minimising the total routing cost. To obtain the solution of the HFVRP, implementations of construction heuristics (savings algorithm, nearest neighbour, branch and cut) and improvement heuristics (2-opt and or-opt) are achieved through development of a DSS which eventually leads to proposal of a hybrid heuristic for route optimisation.

Developing decision support system for heterogeneous fleet vehicle routing problem using hybrid heuristic

In the last few years, there has been an increasing use of optimisation packages and decision support system (DSS) for the efficient and effective decision making. A significant variant of vehicle routing problem (VRP) arises when a fleet of vehicles is characterised by different capacities and operating costs, which is known as heterogeneous fleet vehicle routing problem (HFVRP). This paper aims at determining the optimal composition of fleet and set of routes to be accomplished by a fleet of heterogeneous vehicles for serving a given set of customers with the objective of minimising the total routing cost. To obtain the solution of the HFVRP, implementations of construction heuristics (savings algorithm, nearest neighbour, branch and cut) and improvement heuristics (2-opt and or-opt) are achieved through development of a DSS which eventually leads to proposal of a hybrid heuristic for route optimisation.

On Frequency Estimation and Detection of Frequent Items in Time Faded Streams

We deal with the problem of detecting frequent items in a stream under the constraint that items are weighted, and recent items must be weighted more than older ones. This kind of problem naturally arises in a wide class of applications in which recent data is considered more useful and valuable with regard to older, stale data. The weight assigned to an item is, therefore, a function of its arrival timestamp. As a consequence, whilst in traditional frequent item mining applications we need to estimate frequency counts, we are instead required to estimate decayed counts . These applications are said to work in the time fading model. Two sketch-based algorithms for processing time-decayed streams have been recently published independently near the end of 2016. The Filtered Space Saving with Quasi-Heap (FSSQ) algorithm, besides a sketch, also uses an additional data structure called quasi-heap to maintain frequent items. Forward Decay Count-Min Space Saving (FDCMSS), our algorithm, cleverly combines key ideas borrowed from forward decay, the Count-Min sketch and the Space Saving algorithm. Therefore, it makes sense to compare and contrast the two algorithms in order to fully understand their strengths and weaknesses. We show, through extensive experimental results, that FSSQ is better for detecting frequent items than for frequency estimation. The use of the quasi-heap data structure slows down the algorithm owing to the huge number of maintenance operations. Therefore, FSSQ may not be able to cope with high-speed data streams. FDCMSS is better suitable for frequency estimation; moreover, it is extremely fast and can be used in the context of high-speed data streams and for the detection of frequent items as well, since its recall is always greater than 99%, even when using an extremely tiny amount of space. Therefore, FDCMSS proves to be an overall good choice when considering jointly the recall, precision, average relative error and the speed.

Mining frequent items in the time fading model

We present FDCMSS, a new sketch-based algorithm for mining frequent items in data streams. The algorithm cleverly combines key ideas borrowed from forward decay, the Count-Min and the Space Saving algorithms. It works in the time fading model, mining data streams according to the cash register model. We formally prove its correctness and show, through extensive experimental results, that our algorithm outperforms λ-HCount, a recently developed algorithm, with regard to speed, space used, precision attained and error committed on both synthetic and real datasets.

A route-selecting order batching model with the S-shape routes in a parallel-aisle order picking system

This paper introduces a route-selecting order batching model with the S-shape routing method in parallel-aisle order picking (SRSB). Order pickers in a wide-aisle system prefer the S-shape route taking a u-turn at the last aisle to shorten the travel distance. Although u-turns improve operations, they actually increase computational complexity in order batching. Our study defines a route-set for the S-shape routes and composites a best fit route for batches from the predefined S-shape routes while partitioning orders into batches. The large-scale extension of the SRSB obtains near-optimal solutions by the tight lower bound of the by identifying the route-selection based relaxed batching model. A comparison of the heuristics solution and its pairing lower bound shows 3.5–6.8 percent optimal gaps on average in a six-aisle parallel-aisle system over a 200–500 orders time-window, which outperforms an available best large-scale algorithm with a 9.9 percent shorter travel distance on average. Using the identified lower bound, we evaluate other large-scale batching algorithms in the published literature. We find that a popular savings algorithm shows 8.3–19.8 percent optimal gaps over a variety of large-scale simulation cases.

Research on Distribution of Hobbing Machine Spare Parts with Time Limits

Distribution of hobbing machine spare parts is a key factor to improve the efficiency of service-oriented spare part allocation. In order to minimize the distribution route, the distribution model of hobbing machine spare parts with time limits was put forward. The modified savings algorithm was adopted to solve the model. To improve the loading rate of classic savings algorithm, the modified savings algorithm allowed the split delivery according to customers' requirements. A case study verified that the application of modified savings algorithm ensured the shortest distribution route and improved the vehicle loading rate.

A parallel space saving algorithm for frequent items and the Hurwitz zeta distribution

We present a message-passing based parallel version of the Space Saving algorithm designed to solve the k–majority problem. The algorithm determines in parallel frequent items, i.e., those whose frequency is greater than a given threshold, and is therefore useful for iceberg queries and many other different contexts. We apply our algorithm to the detection of frequent items in both real and synthetic datasets whose probability distribution functions are a Hurwitz and a Zipf distribution respectively. Also, we compare its parallel performances and accuracy against a parallel algorithm recently proposed for merging summaries derived by the Space Saving or Frequent algorithms.

An Energy Saving Algorithm to Prolong the Lifetime of Wireless Sensor Network

This paper considers a heterogeneous network of energy constrained sensors deployed over a region. Each Normal sensor node in a network is systematically gathering and transmitting sensed data to the clusterhead, and then cluster head sending data to a base station (via intermediate cluster- heads). This paper focuses on reducing the energy consumption and hence improving lifetime of wireless sensor Networks. Clustering sensor node is an effective topology for the energy constrained networks. So energy saving algorithm has been developed in which clusters are formed considering a subset of high energy nodes as a cluster-head and another subset of powerful nodes is ask to go to sleep. When Cluster heads deplete their energy another subset of nodes becomes active and acts as a cluster head. Proposed approach is implemented in MATLAB, Simulation results shows that it can prolong the network lifetime than LEACH protocol, and achieves better performance than the existing clustering algorithms such as LEACH.

Aggregation of Order Picking System Using Order Batching

The objective of this project is to know about the Order Picking System (OPS) in the warehouse management system (WMS). Order picking is a continuous process in distribution center. Before the picking process being carried out for a large set of orders, batching of customer orders can accelerate the order picking process. Hence in this project the OPS are carried out using order batching, the order picking is done by picker to parts method. This picker to part method is being done using various routing strategies, which is performed by heuristic algorithm. The order batching is performed using the savings algorithm. The order picking process is done for various routing strategies with batching and without batching. The comparison of routing strategies with batching and without batching is done for multiple cross aisle. The routing strategies are done using the interactive warehouse. The optimization using Vehicle Routing Problem (VRP) will reduce the warehouse operating cost and time taken to pick the orders.

以太无源光网络中面向多播业务的节能算法

以太无源光网络中面向多播业务的节能算法

The application of design criteria for locating a hub configured supply chain for a restaurant cluster in the Stellenbosch area

Restaurants, in general, utilise numerous suppliers. Normally they deliver on different days in the week and at different times during the day, logistically not an optimum approach. Not only does the current practice cause frequent interruptions, but by segregating the food supply chain unnecessary traffic is generated. This article investigated the need for developing a third party supplier hub, the best positioning of that hub and the most economical routes to the customers. With the aim of providing non-franchised restaurants with the necessary leverage to become market leaders, the hub is planned to only service the restaurants within the vicinity of the Stellenbosch area. In such a hub-configured supply chain, the suppliers would be delivering to the proposed hub, from where once-off deliveries to all the restaurants may be made on days and/or times determined by them. In order to investigate the benefits of providing such a hub structure, a systematic implementation approach was used. The first step was to do market research in order to establish the need for such a hub. That is, the viability of the hub from a restaurant’s perspective was established. The next step entailed the investigation of the design criteria needed in determining a favourable hub location. Four possible hub locations were identified. The Clark and Wright’s savings algorithm was then used to determine the optimal hub location and the feasibility of the results was verified with the aid of a global positioning system (GPS) device. The last steps followed involved the determination of an effective hub floor plan that may be utilised, possible products that can be supplied to the restaurants and the necessary assets needed to provide the hub’s service. Finally, by incorporating all these facets, a cost analysis was done to determine the hub’s profitability.