scholarly journals Fleet Size and Rebalancing Analysis of Dockless Bike-Sharing Stations Based on Markov Chain

2019 ◽  
Vol 8 (8) ◽  
pp. 334 ◽  
Author(s):  
Zhai ◽  
Liu ◽  
Du ◽  
Wu
Keyword(s):  
Linear Programming ◽  
Markov Chain ◽  
Steady State ◽  
Transition Probability ◽  
Programming Method ◽  
Linear Programming Method ◽  
Steady State Probability ◽  
Fleet Size ◽  
Analysis Experiment ◽  
Bike Sharing

In order to improve the dynamic optimization of fleet size and standardized management of dockless bike-sharing, this paper focuses on using the Markov stochastic process and linear programming method to solve the problem of bike-sharing fleet size and rebalancing. Based on the analysis of characters of bike-sharing, which are irreducible, aperiodic and positive-recurrence, we prove that the probability limits the state (steady-state) of bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then a new “Markov chain dockless bike-sharing fleet size solution” algorithm is proposed. The process includes three parts. Firstly, the irreducibility of the bike-sharing transition probability matrix is analyzed. Secondly, the rank-one updating method is used to construct the transition probability random prime matrix. Finally, an iterative method for solving the steady-state probability vector is therefore given and the convergence speed of the method is analyzed. Furthermore, we discuss the dynamic solution of the bike-sharing steady-state fleet size according to the time period, so as improving the practicality of the algorithm. To verify the efficiency of this algorithm, we adopt the linear programming method for bicycle rebalancing analysis. Experiment results show that the algorithm could be used to solve the disordered deployment of dockless bike-sharing.

scholarly journals SOLUTION TO FLEET SIZE OF DOCKLESS BIKE-SHARING STATION BASED ON MATRIX ANALYSIS

2018 ◽  
Vol IV-4 ◽  
pp. 255-262
Author(s):  
Y. Zhai ◽  
J. Liu ◽  
J. Du ◽  
J. Chen
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Sparse Matrix ◽  
Transition Probability ◽  
Limit State ◽  
Matrix Analysis ◽  
Steady State Probability ◽  
Probability Limit ◽  
Fleet Size ◽  
Bike Sharing

<p><strong>Abstract.</strong> Aiming at the problems of the lack of reasonable judgment of fleet size and non-optimization of rebalancing for dockless bike-sharing station, based on the usage characteristics of dockless bike-sharing, this paper demonstrates that the Markov chain is suitable for the analysis of the fleet size of station. It is concluded that dockless bike-sharing Markov chain probability limit state (steady-state) only exists and is independent of the initial probability distribution. On that basis, this paper analyses the difficulty of the transition probability matrix parameter statistics and the power method of the bike-sharing Markov chain, and constructs the transition probability sparse matrix in order to reduce computational complexity. Since the sparse matrices may be reducible, the rank-one updating method is used to construct the transition probability random prime matrix to meet the requirements of steady-state size calculation. An iterative method for solving the steady-state probability is therefore given and the convergence speed of the method is analysed. In order to improve the practicability of the algorithm, the paper further analyses the construction methods of the initial values of the dockless bike-sharing and the transition probability matrices at different time periods in a day. Finally, the algorithm is verified with practical and simulation data. The results of the algorithm can be used as a baseline reference data to dynamically optimize the fleet size of dockless bike-sharing station operated by bike-sharing companies for strengthening standardized management.</p>

scholarly journals MATHEMATICAL ANALYSIS OF VEHICLE DELIVERY SCALE OF BIKE-SHARING RENTAL NODES

2018 ◽  
Vol XLII-3 ◽  
pp. 2229-2235
Author(s):  
Y. Zhai ◽  
J. Liu ◽  
L. Liu
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Transition Probability ◽  
Limit State ◽  
Linear Equations ◽  
Transition Probability Matrix ◽  
State Probability ◽  
Steady State Probability ◽  
Bike Sharing ◽  
State Scale

Aiming at the lack of scientific and reasonable judgment of vehicles delivery scale and insufficient optimization of scheduling decision, based on features of the bike-sharing usage, this paper analyses the applicability of the discrete time and state of the Markov chain, and proves its properties to be irreducible, aperiodic and positive recurrent. Based on above analysis, the paper has reached to the conclusion that limit state (steady state) probability of the bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then this paper analyses the difficulty of the transition probability matrix parameter statistics and the linear equations group solution in the traditional solving algorithm of the bike-sharing Markov chain. In order to improve the feasibility, this paper proposes a "virtual two-node vehicle scale solution" algorithm which considered the all the nodes beside the node to be solved as a virtual node, offered the transition probability matrix, steady state linear equations group and the computational methods related to the steady state scale, steady state arrival time and scheduling decision of the node to be solved. Finally, the paper evaluates the rationality and accuracy of the steady state probability of the proposed algorithm by comparing with the traditional algorithm. By solving the steady state scale of the nodes one by one, the proposed algorithm is proved to have strong feasibility because it lowers the level of computational difficulty and reduces the number of statistic, which will help the bike-sharing companies to optimize the scale and scheduling of nodes.

scholarly journals Determination of Transportation Fleet Size using The Combination of Adjusted SPT Rule and Linear Programming Method

2016 ◽  
Vol 3 (3) ◽  
pp. 138
Author(s):  
Pujo Saroyo ◽  
M.P.A Wibowo
Keyword(s):  
Linear Programming ◽  
Flow Time ◽  
Programming Method ◽  
Fleet Management ◽  
Linear Programming Method ◽  
Fleet Size ◽  
Average Flow ◽  
Competitive Industry ◽  
Spt Rule

<p>In a very competitive industry, XYZ Ltd. needs to have an effective, efficient and reliable logistics fleet management. The fleets should be able to help the company serve the market demands and guarantee the distribution of its products. This research analyzed and determined the by-truck transportation fleet size of XYZ Ltd using the combination of adjusted SPT Rule and linear programming method. The results showed that the product delivery’s scheduling was arranged by operating a fleet of 13 tronton trucks and 25 trailer trucks, with the scheduling of delivery resulting in maximum makespan of 6.98 days and an average flow-time per shipment of 3.83 days. <br /><strong>Keywords</strong>: Fleet Management, Logistics Transportation, Adjusted SPT</p>

Multi-Objective Fuzzy Linear Programming for Land Allocation under Different Crops in Bhagwanpur Distributary

2019 ◽  
Vol 6 (04) ◽  
Author(s):  
ASHUTOSH UPADHYAYA
Keyword(s):  
Linear Programming ◽  
Crop Production ◽  
Fuzzy Linear Programming ◽  
Programming Method ◽  
Command Area ◽  
Linear Programming Method ◽  
Net Return ◽  
Multi Objective ◽  
Labour Requirement ◽  
Canal Command Area

A study was undertaken in Bhagwanpur distributary of Vaishali Branch Canal in Gandak Canal Command Area, Bihar to optimally allocate land area under different crops (rice and maize in kharif, wheat, lentil, potato in rabi and green gram in summer) in such a manner that maximizes net return, maximizes crop production and minimizes labour requirement employing simplex linear programming method and Multi-Objective Fuzzy Linear Programming (MOFLP) method. Maximum net return, maximum agricultural production, and minimum labour required under defined constraints (including 10% affinity level of farmers to rice and wheat crops) as obtained employing Simplex method were ` 3.7 × 108, 5.06 × 107 Kg and 66,092 man-days, respectively, whereas Multi-Objective Fuzzy Linear Programming (MOFLP) method yielded compromised solution with net return, crop production and labour required as ` 2.4 × 108, 3.3 × 107Kg and 1,79,313 man-days, respectively. As the affinity level of farmers to rice and wheat crops increased from 10% to 40%, maximum net return and maximum production as obtained from simplex linear programming method and MOFLP followed a decreasing trend and minimum labour required followed an increasing trend. MOFLP may be considered as one of the best capable ways of providing a compromised solution, which can fulfill all the objectives at a time.

scholarly journals Optimal Recycling of Steel Scrap and Alloying Elements: Input-Output based Linear Programming Method with Its Application to End-of-Life Vehicles in Japan

2017 ◽  
Vol 51 (22) ◽  
pp. 13086-13094 ◽  
Author(s):  
Hajime Ohno ◽  
Kazuyo Matsubae ◽  
Kenichi Nakajima ◽  
Yasushi Kondo ◽  
Shinichiro Nakamura ◽  
...  
Keyword(s):  
Linear Programming ◽  
End Of Life ◽  
Programming Method ◽  
Alloying Elements ◽  
Steel Scrap ◽  
Input Output ◽  
Linear Programming Method

scholarly journals FORECASTING VOLUMES OF SALES GOODS BY LINEAR PROGRAMMING METHOD (ON MATERIALS NEMIROV BPC, NEMIROV VINNITSYA REGION)

2021 ◽  
Author(s):  
Tayisa Vozniuk ◽  
Olga Mazur
Keyword(s):  
Linear Programming ◽  
Raw Materials ◽  
Decomposition Methods ◽  
Point Of View ◽  
Programming Method ◽  
Bakery Products ◽  
Economic Activities ◽  
Linear Programming Method ◽  
Material Resources ◽  
Decision Tasks

In this article reveals an example of forecasting the volumes of sales goods through ways of implement optimization analysis, that is by linear programming method. For example, volume of production goods for realization her consumers no must to exceed of determined out maximum or to be lower by minimum, what can to foreseeing in this task. For decision tasks of linear programming with a large number of variables and constraints, decomposition methods are used, which allow instead of the original problem to solve tasks of little volume. In general methodology of linear programming together with simplex-method is considered on the example Nemyriv bakery, where determined out profit on unit bakery products, obtained through the optimal ratio of material resources and costs incurred. In analysis and treatment of economic activities the each enterprises, particularly at composition forecast as to volumes of sales goods with aim of receiving profit, linear programming maybe successfully used out for decision tasks with optimization of development and organization trade processes upon regarding the sale of its products. With point of view management a tasks of linear programming – this tasks of optimal using resources. In each event planning of production goods necessity have on attention, which different productions resources (workforce, raw, materials, means of production) are limited, and also which known norm of costs these resources on different kinds goods, or possible are multiples variants to separating production resources. In our work, we ascertained that in analysis, compliance is checked of demand for bakery products to stocks of most-important kinds raw and materials together with costs as most important conditions for receive profit on enterprises and avoiding of excessive and unforeseen losses. With aim of rise efficiency of enterprises activities necessary and further to look at question of renewing assortment goods and increase quality her, increasing volumes of production, maximum of loading production powers equipment, efficiency using of available resources.

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