scholarly journals A Hybrid Dynamic Programming for Solving Fixed Cost Transportation with Discounted Mechanism

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Farhad Ghassemi Tari
Keyword(s):  
Dynamic Programming ◽  
Programming Model ◽  
Transportation Network ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Transportation Cost ◽  
Solution Algorithm ◽  
Transportation Costs ◽  
Programming Algorithm ◽  
Fixed Cost

The problem of allocating different types of vehicles for transporting a set of products from a manufacturer to its depots/cross docks, in an existing transportation network, to minimize the total transportation costs, is considered. The distribution network involves a heterogeneous fleet of vehicles, with a variable transportation cost and a fixed cost in which a discount mechanism is applied on the fixed part of the transportation costs. It is assumed that the number of available vehicles is limited for some types. A mathematical programming model in the form of the discrete nonlinear optimization model is proposed. A hybrid dynamic programming algorithm is developed for finding the optimal solution. To increase the computational efficiency of the solution algorithm, several concepts and routines, such as the imbedded state routine, surrogate constraint concept, and bounding schemes, are incorporated in the dynamic programming algorithm. A real world case problem is selected and solved by the proposed solution algorithm, and the optimal solution is obtained.

scholarly journals The dynamic programming approach to long term production planning in agriculture

2011 ◽  
Vol 59 (2) ◽  
pp. 129-136 ◽  
Author(s):  
Jitka Janová
Keyword(s):  
Dynamic Programming ◽  
Production Planning ◽  
Programming Model ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Goal Function ◽  
Programming Algorithm ◽  
Programming Approach ◽  
Model Case ◽  
Local Character

The production planning in agriculture is one of the most important decision problems of the farmer. Although some decision support tools based mainly on linear programming and addressed to agriculture authorities were presented, their direct application by a farmer is not possible. This is mainly due to the local character of the models developed for particular agricultural conditions and also due to the complexness of underlying mathematical programming models.This paper aims to develop dynamic programming model for the long run crop plan optimization covering the typical conditions of Czech farms, which could serve as a platform for further enlargements and changes according to needs and conditions of particular farm. The dynamic programming algorithm is developed in detail for model case of four areas to be planted by four crops each year. The possibility of covering different constraints by generating the state space is discussed, and the generating procedure for crop rotation rules is shown. The goal function reflects the farmers objective of profit maximization and it is defined with respect to harvests’ randomness. The case study is solved for the data from South Moravian agriculture cooperative and the optimal solution is presented and discussed.

scholarly journals Multidimensional Dynamic Programming Algorithm forN-Level Batching with Hierarchical Clustering Structure

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Seung-Kil Lim ◽  
June-Young Bang ◽  
Jae-Gon Kim
Keyword(s):  
Dynamic Programming ◽  
Hierarchical Clustering ◽  
Programming Model ◽  
Dynamic Programming Algorithm ◽  
Nonlinear Integer Programming ◽  
Batch Size ◽  
Programming Algorithm ◽  
Processing Cost ◽  
Level 1 ◽  
Item Types

This study focuses on theN-level batching problem with a hierarchical clustering structure. Clustering is the task of grouping a set of item types in such a way that item types in the same cluster are more similar (in some sense or another) to each other than to those in other clusters. In hierarchical clustering structure, more and more different item types are clustered together as the level of the hierarchy increases.N-level batching is the process by which items with different types are grouped into several batches passed from level 1 to levelNsequentially for given hierarchical clustering structure such that batches in each level should satisfy the maximum and minimum batch size requirements of the level. We consider two types of processing costs of the batches: unit processing cost and batch processing cost. We formulate theN-level batching problem with a hierarchical clustering structure as a nonlinear integer programming model with the objective of minimizing the total processing cost. To solve the problem optimally, we propose a multidimensional dynamic programming algorithm with an example.

scholarly journals Comparison of Dynamic Programming Algorithm and Greedy Algorithm on Integer Knapsack Problem in Freight Transportation

2018 ◽  
Vol 5 (1) ◽  
pp. 49 ◽  
Author(s):  
Global Ilham Sampurno ◽  
Endang Sugiharti ◽  
Alamsyah Alamsyah
Keyword(s):  
Dynamic Programming ◽  
Greedy Algorithm ◽  
Knapsack Problem ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Freight Transportation ◽  
Total Weight ◽  
Knapsack Problems ◽  
Programming Algorithm ◽  
Selection Of

At this time the delivery of goods to be familiar because the use of delivery of goods services greatly facilitate customers. PT Post Indonesia is one of the delivery of goods. On the delivery of goods, we often encounter the selection of goods which entered first into the transportation and  held from the delivery. At the time of the selection, there are Knapsack problems that require optimal selection of solutions. Knapsack is a place used as a means of storing or inserting an object. The purpose of this research is to know how to get optimal solution result in solving Integer Knapsack problem on freight transportation by using Dynamic Programming Algorithm and Greedy Algorithm at PT Post Indonesia Semarang. This also knowing the results of the implementation of Greedy Algorithm with Dynamic Programming Algorithm on Integer Knapsack problems on the selection of goods transport in PT Post Indonesia Semarang by applying on the mobile application. The results of this research are made from the results obtained by the Dynamic Programming Algorithm with total weight 5022 kg in 7 days. While the calculation result obtained by Greedy Algorithm, that is total weight of delivery equal to 4496 kg in 7 days. It can be concluded that the calculation results obtained by Dynamic Programming Algorithm in 7 days has a total weight of 526 kg is greater when compared with Greedy Algorithm.

Supply Chain Scheduling with Transportation Cost on a Single Machine

2011 ◽  
Vol 382 ◽  
pp. 106-109
Author(s):  
Jing Fan
Keyword(s):  
Supply Chain ◽  
Single Machine ◽  
System Integration ◽  
Production Cost ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Transportation Cost ◽  
Programming Algorithm ◽  
Scheduling Problem ◽  
Supply Chain Scheduling

Supply chain scheduling problem is raised from modern manufacturing system integration, in which manufacturers not only process orders but also transport products to customer’s location. Therefore, the system ought to consider how to appropriately send finished jobs in batches to reduce transportation costs while considering the processing sequence of jobs to reduce production cost. This paper studies such a supply chain scheduling problem that one manufacturer produces with a single machine and deliveries jobs within limited transportation times to one customer. The objective function is to minimize the total sum of production cost and transportation cost. The NP hard property of the problem is proved in the simpler way, and the pseudo-dynamic programming algorithm in the literature is modified as the MDP algorithm to get the optimal solution which is associated with the total processing times of jobs.

scholarly journals Dynamic Programming and Heuristic for Stochastic Uncapacitated Lot-Sizing Problems with Incremental Quantity Discount

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yuli Zhang ◽  
Shiji Song ◽  
Cheng Wu ◽  
Wenjun Yin
Keyword(s):  
Dynamic Programming ◽  
Lot Sizing ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Programming Algorithm ◽  
Quantity Discount ◽  
Path Property ◽  
Commercial Solver

The stochastic uncapacitated lot-sizing problems with incremental quantity discount have been studied in this paper. First, a multistage stochastic mixed integer model is established by the scenario analysis approach and an equivalent reformulation is obtained through proper relaxation under the decreasing unit order price assumption. The proposed reformulation allows us to extend the production-path property to this framework, and furthermore we provide a more accurate characterization of the optimal solution. Then, a backward dynamic programming algorithm is developed to obtain the optimal solution and considering its exponential computation complexity in term of time stages, we design a new rolling horizon heuristic based on the proposed property. Comparisons with the commercial solver CPLEX and other heuristics indicate better performance of our proposed algorithms in both quality of solution and run time.

Optimal Bus Stop Spacing Through Dynamic Programming and Geographic Modeling

2000 ◽  
Vol 1731 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Peter G. Furth ◽  
Adam B. Rahbee
Keyword(s):  
Dynamic Programming ◽  
Operating Cost ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Programming Algorithm ◽  
Demand Distribution ◽  
Bus Stop ◽  
Geographic Modeling ◽  
Bus Stop Spacing ◽  
Stop Spacing

A discrete approach was used to model the impacts of changing bus-stop spacing on a bus route. Among the impacts were delays to through riders, increased operating cost because of stopping delays, and shorter walking times perpendicular to the route. Every intersection along the route was treated as a candidate stop location. A simple geographic model was used to distribute the demand observed at existing stops to cross-streets and parallel streets in the route service area, resulting in a demand distribution that included concentrated and distributed demands. An efficient, dynamic programming algorithm was used to determine the optimal bus-stop locations. The model was compared with the continuum approach used in previous studies. A bus route in Boston was modeled, in which the optimal solution was an average stop spacing of 400 m (4 stops/mi), in sharp contrast to the existing average spacing of 200 m (8 stops/mi). The model may also be used to evaluate the impacts of adding, removing, or relocating selected stops.

scholarly journals Diversity of Solutions: An Exploration Through the Lens of Fixed-Parameter Tractability Theory

2020 ◽  
Author(s):  
Julien Baste ◽  
Michael R. Fellows ◽  
Lars Jaffke ◽  
Tomáš Masařík ◽  
Mateus de Oliveira Oliveira ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Practical Interest ◽  
Optimal Solution ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Point Of View ◽  
Programming Algorithm ◽  
Fixed Parameter Tractability ◽  
Fixed Parameter

When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good solutions. In this work we initiate a systematic study of diversity from the point of view of fixed-parameter tractability theory. We consider an intuitive notion of diversity of a collection of solutions which suits a large variety of combinatorial problems of practical interest. Our main contribution is an algorithmic framework which --automatically-- converts a tree-decomposition-based dynamic programming algorithm for a given combinatorial problem X into a dynamic programming algorithm for the diverse version of X. Surprisingly, our algorithm has a polynomial dependence on the diversity parameter.

scholarly journals An improved heuristic-dynamic programming algorithm for rectangular cutting problem

2020 ◽  
Vol 17 (3) ◽  
pp. 717-735
Author(s):  
Aihua Yin ◽  
Chong Chen ◽  
Dongping Hu ◽  
Jianghai Huang ◽  
Fan Yang
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Computation Time ◽  
Programming Algorithm ◽  
Recursive Method ◽  
Two Dimensional ◽  
One Dimensional ◽  
Block Width ◽  
Cutting Problem

In this paper, the two-dimensional cutting problem with defects is discussed. The objective is to cut some rectangles in a given shape and direction without overlapping the defects from the rectangular plate and maximize some profit associated. An Improved Heuristic-Dynamic Program (IHDP) is presented to solve the problem. In this algorithm, the discrete set contains not only the solution of one-dimensional knapsack problem with small rectangular block width and height, but also the cutting positions of one unit outside four boundaries of each defect. In addition, the denormalization recursive method is used to further decompose the sub problem with defects. The algorithm computes thousands of typical instances. The computational experimental results show that IHDP obtains most of the optimal solution of these instances, and its computation time is less than that of the latest literature algorithms.

scholarly journals Global Optimization for Bus Line Timetable Setting Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Qun Chen
Keyword(s):  
Dynamic Programming ◽  
Global Optimization ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Programming Algorithm ◽  
Computational Time ◽  
Global Optimal Solution ◽  
Time Period ◽  
Flow Intensity ◽  
Global Optimal

This paper defines bus timetables setting problem during each time period divided in terms of passenger flow intensity; it is supposed that passengers evenly arrive and bus runs are set evenly; the problem is to determine bus runs assignment in each time period to minimize the total waiting time of passengers on platforms if the number of the total runs is known. For such a multistage decision problem, this paper designed a dynamic programming algorithm to solve it. Global optimization procedures using dynamic programming are developed. A numerical example about bus runs assignment optimization of a single line is given to demonstrate the efficiency of the proposed methodology, showing that optimizing buses’ departure time using dynamic programming can save computational time and find the global optimal solution.

Structural Join Algorithm of XML Query Based on Exhaustive Dynamic Programming

2012 ◽  
Vol 198-199 ◽  
pp. 1527-1530
Author(s):  
Xue Min Zhang ◽  
Xiao Wen Chen ◽  
Jia Lin Jiao
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Search Space ◽  
Programming Algorithm ◽  
Structural Join ◽  
Join Algorithm ◽  
Local Optimal Solution ◽  
Global Optimal ◽  
Basic Ideas

Using the advantages of exhaustive dynamic programming algorithm, on the basic ideas of the global optimal solution is derived based on local optimal solution, this paper propose a new structural selection join algorithm. The algorithm connects to the sub-tree, and then connects to the structure of the whole. Though not guaranteed optimal solution, this algorithm can improve much in the time complexity, reduce the search space and improve efficiency.

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