Northwest Corner Rule Research Articles

Maximal Pearson’s correlation coefficient between Likert items from the viewpoint of Hitchcock’s transportation problem

AbstractWhen two variables are Likert-type items and their marginal distributions differ, the coefficient values of $$\pm \,$$ ± 1 in Pearson’s product-moment correlation are untenable. To address this issue, this study proposes a new method for estimating the maximal and minimal Pearson’s correlations between two Likert items whose numbers of categories are $$R$$ R and $$C$$ C when their marginal distributions are fixed. First, we demonstrate that the maximizing/minimizing correlation problem is identical to Hitchcock’s transportation problem, which is a classic linear programming problem. Second, we prove the necessary and sufficient condition under which the northwest corner rule, which is frequently used to find an initial solution to the transportation problem, provides the optimal solution to the correlation problem. Finally, the results of two simulation studies conducted with $$5\times 5$$ 5 × 5 and $$5\times 7$$ 5 × 7 contingency tables reveal the extent to which the range of Pearson’s correlation shrinks.

Implementation of the North West Corner Rule and Loop Construction Method to Minimize Material Distribution Cost on Ameroro Dam Access Road Project (Package II)

Construction projects consist of several work items and require resources to achieve the success of project work including materials and costs. The material required in large quantities in the implementation cannot always be fulfilled by one material source alone, therefore several material sources are needed so that the material demand needs can be met. Especially if it consists of several project locations and must be fulfilled by several material sources. This study aims to minimize the distribution cost of class A LPA material from the source of material collection, namely in Konaweha, Pondidaha and Moramo to the Ameroro Dam Access Road project site (Package II), namely the Entrance to the Dam Segment 1, Segment 2 and Segment 3. The results obtained by implementing the North West Corner Rule and Loop Construction methods can minimize the cost of material distribution from the initial solution of Rp. 1,887,700,000, - to Rp. 1,849,500,000, - so that the difference in cost reduction is Rp. 38,200,000, - with a minimum cost percentage of 2.02%.

A Proposed Method for Finding Initial Solutions to Transportation Problems

The Transportation Model (TM) in the application of Linear Programming (LP) is very useful in optimal distribution of goods. This paper focuses on finding Initial Basic Feasible Solutions (IBFS) to TMs hence, proposing a Demand-Based Allocation Method (DBAM) to solve the problem. This unprecedented proposal goes in contrast to the Cost-Based Resource Allocations (CBRA) associated with existing methods (including North-west Corner Rule, Least Cost Method and Vogel’s Approximation Method) which make cost cell (i.e. decision variable) selections before choosing demand and supply constraints. The proposed ‘DBAM’ on page 4 is implemented in MATLAB and has the ability to solve large-scale transportation problems to meet industrial needs. A sample of five (5) examples are presented to evaluate efficiency of the method. Initial Basic Feasible Solutions drawn from the study (according to DBAM) represent the optimal with higher accuracy, in comparison to the existing methods. Results from the study qualify the DBAM as one of the best methods to solve industrial transportation problems.

An initial basic feasible transportation solution based on the north-west corner rule programming in c

Transportation is one of the most important problems in operations research because it is involved in our daily activities and is primarily concerned with logistics. It is a very important class of linear programming model that deals with the condition of transporting commodities or resources from sources to destinations. The problem's primary goal is to save transportation time and steps by using minimal transformation costs. The solution to this problem is classified into two types: the Initial Basic Feasible Solution (IBFS) and the Optimal Solution (OS). The purpose of this research is to develop a programme that employs the North West Corner Rule to determine the Initial Basic Feasible solution to the transportation problem (NWCR). This programme was written in C# and can handle both balanced and unbalanced situations. Furthermore, the North West Corner Rule has a broader application than other methods for solving transportation problems. Finally, the proposed programme is more useful for decision makers who deal with unbalanced supply and demand quantities on a regular basis.

COMPARISON OF METHODS OF SOLVING TRANSPORTATION PROBLEMS (TP) AND RESOLVING THE ASSOCIATED VARIATIONS

Purpose: Transportation Problem is a Linear Programming application to physical distribution of goods and services from various origins to several destinations at a minimum cost.
 Methodology: In this study, five different methods were employed to solve transportation problems arising from unequal demand and supply of goods and variations. The methods considered were in terms of North West Corner Rule, Least Cost Method, Vogel’s Approximation Method, Row Minima Method and Column Minima Method were compared. Unbalanced transportation problems were resolved using Vogel’s Approximation Method (VAM) and Modified Distribution (MODI) methods.
 Findings: The methods compared produced different results with VAM generating the least transportation cost and better solution. With the MODI method, economic values were generated for the dual variables, uis and vjs associated with the source and demand points respectively.

Corner Rules Method of Solving Transportation Problem

Several approaches have been advanced for solving transportation problems. The most prominent of them in various text being, North West Corner Rule(NWCR), Least Cost Method(LCM), and Vogel's Approximation Method(VAM). This paper considered three additional corner rules, which are North East Corner Rule(NECR), South West Corner Rule(SWCR) and South East Corner Rule(SECR). Algorithms ware provided for obtaining initial feasible solution to Transportation Problems. Three test examples were considered using the rules. The results revealed that the NECR and SWCR have equal result. While NWCR and SECR also produce the same result. NECR and SWCR however, better minimize transportation cost. The two methods are therefore recommended for use in any business organization requiring shipment of products.

APPLICATION OF TRANSPORTATION MODEL FOR OPTIMAL PRODUCT DISTRIBUTION CHAIN MANAGEMENT

Many business organizations are operating at an unacceptable high distribution chain costs even as industrial competition continues to pose as a major challenge to business success. Linear programming devices can help organizations achieve efficiency. This research aims at establishing the impact of Transportation algorithm in optimal product distribution and scheduling of business organizations. In a field study of NOWAS Oil and Gas, data was significantly secondary sourced, resulting from indepth analysis of existing documented content materials on the subject. Practical application of the least cost method scheduling and North West Corner Rule method of an initial basic feasible solution was imminent. Revising that solution using the stepping stone method translated to an optimal distribution schedule and a minimum cost profit in yearly distribution schedule of Nowas Oil and Gas, Enugu. It is recommended that business organizations carryout careful analysis of their supply and demand constraints in materials and products distribution for cost minimization and overall resource optimization.
 Keywords: Application, Transportation Model, Basic Feasible Solution, Optimality, Distribution Chain, Management.

A Comprehensive Method for Arriving at Initial Feasible Solution for Optimization Problems in Engineering with Illustrative Examples

Two methods have been used extensively for arriving at initial basic feasible solution (IBF). One of them is Northwest corner rule and the other on is Russell method (Hillier & Lieberman, 2005.) Both methods have drawbacks. The IBF obtained is either far from optimal solution or does not have adequate number of entries to initiate transportation simplex algorithm. The Northwest Corner rule gives an initial feasible solution that is far from optimal while the IBF solution obtained using Russell method doesn’t give enough number of entries to start the transportation simplex algorithm. Hence, there is a need for developing a method for arriving at initial basic feasible solution with adequate number of entries needed to initiate transportation simplex algorithm, which can then be used to get an optimal solution. A computer software has been developed based on the new proposed method for this purpose. The proposed new method has been validated through four simple but illustrative examples.

A Note on Zero Suffix Method for the Optimal Solution of the Transportation Problems

Classical methods of finding the optimal solution of a transportation problem requires, initial basic feasible solution using any of the appropriate method like north-west corner rule, least cost method, Vogel’s approximation method etc. This obtained solution is improved towards the optimal solution by checking the optimality criteria using any of the existing methods, e.g., the modified distribution method, stepping-stone method etc. But Sudhakar et al. (Eur J Sci Res 68:254–257, 2012) suggested an approach called the zero suffix method that gives the optimal solution for transportation problems directly, i.e., without finding the initial basic feasible solution initially.

Improvement for enhancing effectiveness of universal power system (UPS) continuous testing process

This experiment aims to enhance the effectiveness of the Universal Power System (UPS) continuous testing process of the Electrical and Electronic Institute by applying work scheduling and time study methods. Initially, the standard time of testing process has not been considered that results of unaccurate testing target and also time wasting has been observed. As monitoring and reducing waste time for improving the efficiency of testing process, Yamazumi chart and job scheduling theory (North West Corner Rule) were applied to develop new work process. After the improvements, the overall efficiency of the process possibly increased from 52.8% to 65.6% or 12.7%. Moreover, the waste time could reduce from 828.3 minutes to 653.6 minutes or 21%, while testing units per batch could increase from 3 to 4 units. Therefore, the number of testing units would increase from 12 units up to 20 units per month that also contribute to increase of net income of UPS testing process by 72%.

Correlation Coefficients of Probabilistic Hesitant Fuzzy Elements and Their Applications to Evaluation of the Alternatives

Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making (MCDM) processes. However, some important issues related to correlation coefficient utilization within probabilistic hesitant fuzzy environments remain to be addressed. The purpose of this study is introduced a MCDM method based on correlation coefficients utilize probabilistic hesitant fuzzy information. First, the covariance and correlation coefficient between two PHFEs is introduced, the properties of the proposed covariance and correlation coefficient are discussed. In addition, the northwest corner rule to obtain the expected mean related to the multiply of two PHFEs is introduced. Second, the weighted correlation coefficient is proposed to make the proposed MCDM method more applicable. And the properties of the proposed weighted correlation coefficient are also discussed. Finally, an illustrative example is demonstrated the practicality and effectiveness of the proposed method. An illustrative example is presented to demonstrate the correlation coefficient propose in this paper lies in the interval [−1, 1], which not only consider the strength of relationship between the PHFEs but also whether the PHFEs are positively or negatively related. The advantage of this method is it can avoid the inconsistency of the decision-making result due to the loss of information.

TIGA JAWABAN PENYELESAIAN OPTIMAL DALAM PROBLEM TRANSPORTASI DENGAN VAM AND MODI METHOD

<p>The famous method to determine and solve transportation problem is the transportation model VAM and MODI method, the Northwest-Corner and Stepping-Stone method, and the Assignment method. We see how to develop an initial aolution to the transportation problem with VAM (Vogel’s Approximation Method) and MODI (Modified Distribution). VAM is not quite as simple as the Northwest Corner approach. But it facilitates a very good initial solution, as a matter of fact, one that is often the optimal solution.</p><p>VAM method trackles the problem of finding a good initial solution by taking into account the cost the costs associated with each route alternative. This is something that Northwest Corner Rules does not do. To apply VAM, we first compute for each row and column the penalty faced if we should ship over the second-best route instead of the least-cost route. After the initial of VAM solution has been found, you should evaluate it with either the Stepping-Stone method or the MODI method. The MODI (Modified Distribution) method allows us to compute improvement indices quickly for each unused square without drawing all of the closed paths. Because of this, it can often provide considerable time savings over the Stepping-Stone method for solving transportation problems. If there is a negative index indicating an imporovemet can be made, then only one Stepping-Stone path must be found. This is used as it was before to determine what changes should be made to obtain the improved solution.</p><p>In the Northwest-corner rule, the largest possible allocation is made to the cell in the upper left-hand corner of the tableau, followed by allocations to adjacent feasible celss. While the Stepping-stone method is an interactive technique for moving from an initial feasible solution to an optimal feasible solution, and continues will until the optimal solution is reached. The Stepping-stone path method is used to calculate improvement indices for the empty cells. Improved solutions are developed using a Stepping-stone path.</p><p>The assignment method, which is simple and faster to solve the transportation problem by reducing the numbers (cost) in the table/tableau until a series of zeros is found, or zero opportunity costs, which mean that we will reach the optimal cost allocations. Once we have reached the optimal cost allocations, we the allocate each sources or supply according to some point of demand (destinations). Assignment Method is a specialized form of optimization linear programming model that attempts to assign limited capacity to various demand points in a way that minimizes costs.</p><p>The special cases of transportation problem included degeneracy (a condition that occurs when the number of occupied squares in any solution is less than the number of rows plus the number of columns minus 1 in a transportation table), unbalanced problems, and multiple optimal solutions. We will see how the VAM and MODI method may be viewed as a special case of solving the multiple optimal solutions of the transportation problem.</p><p>Keywords : transportation, VAM and MODI</p>

PERBANDINGAN PEMECAHAN MASALAH TRANSPORTASI ANTARA METODE NORTHWEST-CORNER RULE DAN STEPPING-STONE METHOD DENGAN ASSIGNMENT METHOD

<p>The famous methods to determine and solve transportation problem are the Northwest-corner rule/method and the Stepping-stone Method. In the Northwest-Corner Rule, the largest possible allocation is made to the cell in the upper left-hand corner of the tableau, followerd by allocations to adjacent feasible cells; while the Stepping-Stone Method is an iterative technique for moving from an initial feasible solution to an optimum feasible solution which continues untul the optimum solution is reached. However, inn some cases, sometimes we have been facing some difficulties to solve transportation problem with these two methods, therefore we intoduce the <strong>Assignment Method, </strong>which is simpler and faster in solving the transportation problem by reducing the numbers (cost) in the table/tableau until a series of zeros is found, or zero opportunity costs, which means that will reach the optimum cost allocations. Once reach the optimum cost allocations, the next step is to allocate each source or supply according to some points of demand (destinations). <strong>Assignment Method </strong>is a specialized form of optimization linear programming model that attempts to assign limited capacitiy to various demand points in a way that minimizes costs.</p><p>Keywords :</p><p>assignment method, linear programming, lowest opportunity cost, minimize time required</p>

DUA HASIL OPTIMAL DALAM PENYELESAIAN PERSOALAN TRANSPORTASI DENGAN ASSIGNMENT METHOD, VAM AND MODI, NORTHWEST CORNER AND STEPPING-STONE

<p>The famous method to determine and solve transportation problem is the transportation model and the assignment model. We see how to develop an initial solution to the transportation problem with VAM (Vogel’s Approximation Method) and MODI (Modified Distribution) and Northwest Corner rule and the Stepping-Stone method. VAM is not quite as simple as the Northwest Corner approach, but it facilitates a very good initial solution, as a matter of fact, one that is often the optimal solution. The Assignment method, which is simple and faster to solve the transportation problem by reducing the numbers (cost) in the table/tableau until a series of zeros is found, or zero opportunity costs, which means that we will reach the optimal cost allocations. Once we have reached the optimal cost allocations, we then allocate each sources or supply according to some points of demand (destinations). Assignment Method is a specialized form of optimization linear programming model that attempts to assign limited capacity to various demand points in a way that minimizes costs. The special cases of transportation problem included degeneracy (a condition that occurs when the number of occupied squares in any solution is less than the number of rows plus the number of columns minus 1 in a transportation table), unbalanced problems, and multiple optimal solutions. At this opportunity, we would like to demonstrate the multiple optimal solutions. We will see how the Assignment method may be viewed as a special case of solving the transportation problem.</p><p> </p><p>Keywords : Assignment method, VAM and MODI, Northwest Corner and Stepping-Stone.</p>

Importance Rearrangement within Education, Economy and Natural Protection Ministries for Armenian Composite Supportive Progress (ACASP)

Sustainable Development is an innovative concept characterized as Composite Appraising Supportive Progress of Armenia (ACASP). Biodiversity concept is another topic having a vast power on public management and employment. Social, economic and environmental impacts optimize sequences within Education (S3), Economy (E5), Air (N3) & Land (N1) Ministries. Seven (7) phases of Operation Research (OR) studies correspond to nine (9) procedures of composite progressive indicators. Two (2) techniques are applied as decision making of utility function and transportation tasks. North-West Corner Rule (NWCR) and Low Cost Cell Rule (LCCR) are applied to manage public employment as per Education (S3), Economy (E5), Land (N1) and Air (N3) magnitudes of ACASP. A motivating approach is pertained not only to pick the order of significance as per biodiversity concept, but also to characterize the process of decision making through operation research techniques, particularly transportation assignments as per origins and destinations with supply and demand applications. The resulting sequence is revealed by sustenance of biodiversity concept with public employment of Armenian CASP.

Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem

Obtaining an initial basic feasible solution to a transport problem – or a corner point in the convex polytope region – is extremely important in terms of reaching the optimal solution to the problem in the shortest time. When a transport problem is basically accepted as a linear programming problem, a degenerated solution is caused by the structure of the simplex method used when modelling with linear programming and located in a corner point sometimes at the optimal solution itself but mostly in close proximity to the optimal solution vector. One of the ways to eliminate this degenerated solution is to employ approximation methods. The main aim of this paper is to introduce Tuncay Can’s approximation method, which was developed as an alternative to the approximation methods in the literature for a balanced transport problem. Tuncay Can’s approximation method usually has less iterations than other approximation methods. In this paper, the Tuncay Can approximation method is introduced as an alternative to The North West Corner Rule, Minimum Cost Method, and the RAM and VAM methods.

Programming Development on Transportation Problem using c++ and Stepping Stone for Evaluation

The aim of this research is to develop a programm for three methods of solving transportation problems. C++ was used to write the programm on initial feasible solution and optimal solution using North West Corner Rule, Least Cost Rule and Vogel Approximation Method. Stepping stone is used to obtain the optimal solution. From the result of the analysis, we discovered that the Programming on Vogel Approximation Method gives the same result at optimal solution and at low number of iterations. Hence we conclude that programming on Vogel Approximation Method is the best method of finding initial feasible solution, optimal solution and for distribution of good. Keywords: Optimal, Initial, Feasible, Cost and Solution.

OCRM: Optimal Cost Region Matching Similarity Measure for Region Based Image Retrieval

Content Based Image Retrieval (CBIR) has been the most significant area in the applications of Pattern recognition and Computer Vision for the last three decades. However, there are many open problems left unresolved. Among these, one of the current problems of CBIR is to obtain an effective Similarity Measure. The CBIR systems make use of Integrated Region Matching (IRM) to match segmented images which is computationally economic, but it is not a metric distance whereas systems that use Minimum Cost Region Matching (MiCRoM) as a similarity measure is a metric distance, but computationally expensive. In order to address the above problem, this paper has developed the Optimal Cost Region Matching (OCRM) similarity measure for region based image retrieval. The proposed OCRM uses the north-west corner rule of the Transportation problem that fulfills the monge property. The experiment carried out on 1000 color images taken from the Corel database that are compared with IRM, and MiCRoM similarity measures.

A computational study on the number of iterations to solve the transportation problem

The Transportation Problem is one of the classical problems in Operations Research. The development of more powerful personal computers in the past years made it possible to solve larger problems, creating huge opportunities of applications. The MODI method is the most cited method in the literature to solve the Transportation Problem. This method requires an initial basic feasible solution and for this purpose the literature often presents the Northwest Corner Rule, the Lest Cost Method and the Vogel Method. This paper aims to study these three different methods and analyze the number of iterations necessary to reach the optimal solution when they are used.

Faster strongly polynomial algorithms for the unbalanced transportation problem and assignment problem with monge costs

AbstractWe consider a transportation problem where the cost matrix satisfies the Monge property. The problem has supply nodes N1(|N1| = n1), demand nodes N2(|N2| = n2), supply si ≥ 0 for i∈N1, and demand dj ≥ 0 for j∈N2(n = n1 + n2,m = n1n2). When the total supply is equal to the total demand, the problem can be solved in O(n) time using the northwest corner rule (Hoffman [10]). This algorithm and run‐time, however, do not extend to the unbalanced case, where the total supply is not equal to the total demand. The fastest strongly polynomial run‐time for the unbalanced transportation problem with Monge costs is O(nlog n(m + nlog n)), and for the unbalanced assignment problem (unit supplies and demands) with Monge costs is O(n(m + nlog n)). In this article, we describe a simple algorithm that solves the unbalanced transportation problem with Monge costs in O(mn1) time and the unbalanced assignment problem with Monge costs in O(m) time using elementary data structures. We also develop a faster implementation of the algorithm that utilizes a heap, a self‐balancing binary search tree, and dynamic trees, and solves the transportation problem with Monge costs in O(mlog n1) time. Our algorithms improve the run‐times for: (i) the unbalanced transportation problem with Monge costs by a factor of nlog n/log n1 or better and (ii) the unbalanced assignment problem with Monge costs by a factor of n or better. © 2013 Wiley Periodicals, Inc. NETWORKS, 2013