scholarly journals A Study on Online Scheduling Problem of Integrated Order Picking and Delivery with Multizone Vehicle Routing Method for Online-to-Offline Supermarket

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jun Zhang ◽  
Xueyan Zhang ◽  
Yanfang Zhang
Keyword(s):  
Vehicle Routing ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Optimal Algorithm ◽  
Order Picking ◽  
Order Fulfillment ◽  
Delivery Problem ◽  
Computation Efficiency ◽  
Routing Method ◽  
Vehicle Capacity

The online order fulfillment of online-to-offline (O2O) supermarket faces the challenge in how to pick orders from thousands of products on the supermarket shelves and deliver them to customers in different zones and locations by a vehicle routing method within the lowest cost and shortest time. It is critical to integrate the order picking and delivery processes and schedule them jointly with a coordinated manner. Thus, in this paper, we study the online integrated order picking and delivery problem with multizone routing method (IOPDP-MR) to minimize both the maximum delivery completion time and the total delivery cost. The online algorithm A is presented to solve the online problem and is proved to be 2 1 + Q v -competitive, where Q v is the vehicle capacity. Since it is difficult to get a lower competitive ratio theoretically, the numerical experiments are proposed to analyze the gaps by comparing the values of algorithm A with the ones of offline optimal algorithm A∗ under different situations. It can be inferred that the competitive ratio is less than 2.5 and the average flow time for customer orders is less than 30 minutes, which verifies the good performance in both computation efficiency and customer satisfaction of algorithm A.

scholarly journals A review on the electric vehicle routing problems: Variants and algorithms

2021 ◽  
Author(s):  
Hu Qin ◽  
Xinxin Su ◽  
Teng Ren ◽  
Zhixing Luo
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problems ◽  
Location Routing Problem ◽  
Routing Problems ◽  
Routing Problem ◽  
Delivery Problem ◽  
Pickup And Delivery Problem ◽  
The Past ◽  
Location Routing ◽  
Comprehensive Survey

AbstractOver the past decade, electric vehicles (EVs) have been considered in a growing number of models and methods for vehicle routing problems (VRPs). This study presents a comprehensive survey of EV routing problems and their many variants. We only consider the problems in which each vehicle may visit multiple vertices and be recharged during the trip. The related literature can be roughly divided into nine classes: Electric traveling salesman problem, green VRP, electric VRP, mixed electric VRP, electric location routing problem, hybrid electric VRP, electric dial-a-ride problem, electric two-echelon VRP, and electric pickup and delivery problem. For each of these nine classes, we focus on reviewing the settings of problem variants and the algorithms used to obtain their solutions.

scholarly journals Online Makespan Scheduling with Job Migration on Uniform Machines

Algorithmica ◽  
2021 ◽  
Author(s):  
Matthias Englert ◽  
David Mezlaf ◽  
Matthias Westermann
Keyword(s):  
Competitive Ratio ◽  
Online Algorithm ◽  
Parallel Machines ◽  
Scheduling Algorithm ◽  
Input Sequence ◽  
Job Migration ◽  
Average Completion Time ◽  
Uniform Machine ◽  
Uniform Machines ◽  
Completion Times

AbstractIn the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to change the assignment of up to k jobs at the end for some limited number k. For m identical machines, Albers and Hellwig (Algorithmica 79(2):598–623, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and $$\approx 1.4659$$ ≈ 1.4659 . They show that $$k = O(m)$$ k = O ( m ) is sufficient to achieve this bound and no $$k = o(n)$$ k = o ( n ) can result in a better bound. We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a $$\delta = \varTheta (1)$$ δ = Θ ( 1 ) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than $$1.4659 + \delta $$ 1.4659 + δ with $$k = o(n)$$ k = o ( n ) . We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and $$\approx 1.7992$$ ≈ 1.7992 with $$k = O(m)$$ k = O ( m ) . We also show that $$k = \varOmega (m)$$ k = Ω ( m ) is necessary to achieve a competitive ratio below 2. Our algorithm is based on maintaining a specific imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines.

scholarly journals Integration of order picking and vehicle routing in a B2C e-commerce context

2017 ◽  
Vol 30 (4) ◽  
pp. 813-843 ◽  
Author(s):  
Stef Moons ◽  
Katrien Ramaekers ◽  
An Caris ◽  
Yasemin Arda
Keyword(s):  
Vehicle Routing ◽  
Order Picking

A BEST POSSIBLE ONLINE ALGORITHM FOR SCHEDULING TO MINIMIZE MAXIMUM FLOW-TIME ON BOUNDED BATCH MACHINES

2014 ◽  
Vol 31 (04) ◽  
pp. 1450030 ◽  
Author(s):  
CHENGWEN JIAO ◽  
WENHUA LI ◽  
JINJIANG YUAN
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Unit Length ◽  
Maximum Flow ◽  
Flow Time ◽  
Release Time ◽  
Batch Machine ◽  
The Difference ◽  
Over Time

We consider online scheduling of unit length jobs on m identical parallel-batch machines. Jobs arrive over time. The objective is to minimize maximum flow-time, with the flow-time of a job being the difference of its completion time and its release time. A parallel-batch machine can handle up to b jobs simultaneously as a batch. Here, the batch capacity is bounded, that is b < ∞. In this paper, we provide a best possible online algorithm for the problem with a competitive ratio of [Formula: see text].

SEMI-ONLINE MACHINE COVERING

2007 ◽  
Vol 24 (03) ◽  
pp. 373-382 ◽  
Author(s):  
SHENG-YI CAI
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Parallel Machines ◽  
Identical Parallel Machines ◽  
Processing Times ◽  
First Case ◽  
Machine Covering

This paper investigates two different semi-online versions of the machine covering, which is the problem of assigning a set of jobs to a system of m(m ≥ 3) identical parallel machines so as to maximize the earliest machine completion time. In the first case, we assume that the largest processing times is known in advance. In the second case, we assume that the total processing times of all jobs is known in advance. For each version we propose a semi-online algorithm and investigate its competitive ratio. The competitive ratio of each algorithm is [Formula: see text], which is shown to be the best possible competitive ratio for each semi-online problem.

Online Assortment Optimization with Reusable Resources

2021 ◽  
Author(s):  
Xiao-Yue Gong ◽  
Vineet Goyal ◽  
Garud N. Iyengar ◽  
David Simchi-Levi ◽  
Rajan Udwani ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Online Algorithm ◽  
Random Number ◽  
Optimal Algorithm ◽  
User Preference ◽  
Substitutable Products ◽  
Assortment Optimization ◽  
Myopic Policy ◽  
Expected Revenue ◽  
And Performance

We consider an online assortment optimization problem where we have n substitutable products with fixed reusable capacities [Formula: see text]. In each period t, a user with some preferences (potentially adversarially chosen) who offers a subset of products, St, from the set of available products arrives at the seller’s platform. The user selects product [Formula: see text] with probability given by the preference model and uses it for a random number of periods, [Formula: see text], that is distributed i.i.d. according to some distribution that depends only on j generating a revenue [Formula: see text] for the seller. The goal of the seller is to find a policy that maximizes the expected cumulative revenue over a finite horizon T. Our main contribution is to show that a simple myopic policy (where we offer the myopically optimal assortment from the available products to each user) provides a good approximation for the problem. In particular, we show that the myopic policy is 1/2-competitive, that is, the expected cumulative revenue of the myopic policy is at least half the expected revenue of the optimal policy with full information about the sequence of user preference models and the distribution of random usage times of all the products. In contrast, the myopic policy does not require any information about future arrivals or the distribution of random usage times. The analysis is based on a coupling argument that allows us to bound the expected revenue of the optimal algorithm in terms of the expected revenue of the myopic policy. We also consider the setting where usage time distributions can depend on the type of each user and show that in this more general case there is no online algorithm with a nontrivial competitive ratio guarantee. Finally, we perform numerical experiments to compare the robustness and performance of myopic policy with other natural policies. This paper was accepted by Gabriel Weintraub, revenue management and analytics.

scholarly journals Online Clique Clustering

Algorithmica ◽  
2019 ◽  
Vol 82 (4) ◽  
pp. 938-965
Author(s):  
Marek Chrobak ◽  
Christoph Dürr ◽  
Aleksander Fabijan ◽  
Bengt J. Nilsson
Keyword(s):  
Objective Function ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Optimal Solution ◽  
Deterministic Algorithm ◽  
Input Graph ◽  
Online Clustering ◽  
Objective Value ◽  
Asymptotic Competitive Ratio ◽  
Better Than

Abstract Clique clustering is the problem of partitioning the vertices of a graph into disjoint clusters, where each cluster forms a clique in the graph, while optimizing some objective function. In online clustering, the input graph is given one vertex at a time, and any vertices that have previously been clustered together are not allowed to be separated. The goal is to maintain a clustering with an objective value close to the optimal solution. For the variant where we want to maximize the number of edges in the clusters, we propose an online algorithm based on the doubling technique. It has an asymptotic competitive ratio at most 15.646 and a strict competitive ratio at most 22.641. We also show that no deterministic algorithm can have an asymptotic competitive ratio better than 6. For the variant where we want to minimize the number of edges between clusters, we show that the deterministic competitive ratio of the problem is $$n-\omega (1)$$n-ω(1), where n is the number of vertices in the graph.

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