If the total supply is more than the total demand, then we add a new column, with transportation cost 0. Found inside – Page 304As all cell evaluations are non-negative, initial solution given by table ... What do you understand by a balanced and an unbalanced transportation problem? UNBALANCED transportation problem using Vogel's Approximation method with an Example by G N Satish KumarIn this video, I have explained solving UNBALANCED Tr. 1) If Σai > Σbj i.e. If the total supply is not equal to the total demand then the problem is called unbalanced transportation problem. Dummy 26 29 9 14 0 Dallas 160 27 26 16 13 0 Houston 200 17 18 0 7 0 Chicago 360 15 17 7 0 0 L. A. = (6 x 65) + (5 x 1)+(30 x 5)+(25 x 2)+(4 x 25) + (7 x 45) +(20 x 0). Resolution of Degeneracy During the Initial Stage 2. In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students. An Unbalanced Model (Demand . Solve with Transportation simplex. Writing code in comment? For example, if we ship 100 units from Factory 1 to Customer 1, 200 units from Factory 2 to Customer 2, 100 units from Factory 3 to Customer 1 and 200 units from Factory 3 to Customer 3, Total Out equals Supply and Total In equals Demand. O1, O2, O3 and O4 is not equal to the sum of all the demands i.e. The problem is unbalanced because the sum of all the supplies i.e. additional column, which will indicate the surplus supply with transportation 2. Found inside – Page 844Formulate the new Caramel Candy & Confetti company transportation problem. ... 50 120 80 Solution Once again, we are faced with an unbalanced transportation ... In an unbalanced model supply does not equal demand. D1, D2, D3, D4 and D5. The Transportation Problem can be classified into balanced TP or unbalanced TP. 51. AMS Subject Classification: 90B06, 90C90, 90C70. The product is supplied to 4 stores S1, S2, S3, and S4, the requirements of which are 25, 35, 105 and 20 resp. Dantzig'soriginaltransportationmodel: We assume two providers i = 1 and i = 2 of tin cans . Found inside – Page 86Thus the solution of the given problem is X12 = 5 , X21 = 6 , X22 = 1 , X23 = 8 ... n i = 1 UNBALANCED TRANSPORTATION PROBLEM If in a transportation problem ... Example 10.9. Similarly, if the total demand is more than the total supply, Assignment problem: A balanced transportation problem where all supplies and demands are equal to 1. The unit transportation cost for the cells of this dummy destination column are all set equal to zero, because these represents item that are not being made and sent. Found insideUnbalanced Transportation Problems Step 2: Develop an initial basic feasible solution. Several methods can be used to obtain the initial basic feasible ... 360 140 140 360 360 80 Since the solution method for transportation problems has been explained in detail, we will not attempt to solve . Found inside – Page 1033The solution is identical with the one we derived through the stepping stone ... SPECIAL CASES IN TRANSPORTATION PROBLEMS Now that we have seen how to solve ... A transportation problem is said to be balanced if the total supply from all sources equals the total demand in all destinations Otherwise it is called unbalanced. The transportation problem can be described using examples from many fields. Found insideExample 7.9. Convert the following unbalanced transportation problem into a balanced one. Solution: The total demand of the given problem is 550, ... To balance it , introduce a dummy column with all the entries zero. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course. It is the case where the total supply equals the total demand. Balanced Transportation Problem is a transportation problem where the total availability at the origins is equal to the total requirements at the destinations. LP Transportation Problem Example — Solution. transportation problem, otherwise it is a unbalanced problem. Please use ide.geeksforgeeks.org, Come write articles for us and get featured, Learn and code with the best industry experts. Solving a Simple Transportation Problem Using LINGO Anand Jayakumar A P 1 . Using matrix minimum method, we get the following allocations. An example unbalanced transportation problem with Source ={A,B,C} with total supply=65 and Destinations={1,2,3} with dummy supply=10 making total supply=75 [image by author]. Kwak (1979) presented goal programming approach for improved transportation problem. Describe the approach you would use to solve an unbalanced problem. the problem is said to be unbalanced transportation problem. Where total cost = unit cost of production + transportation cost, Hence the problem is unbalanced. For cell O3 D1 we construct closed path as follows, O3D1→O3D3→O2D3→ O2D2→O1D2→ OxD1→O1D1→O3D3. costs. Found inside – Page 308Therefore, this is a case of an unbalanced transportation problem. ... procedures as those we applied in the solution to the problem in example 1 above. The initial basic feasible solution is obtained by least cost method, and we have found following initial basic feasible solution. Transportation problem by the Least Cost Method (Unbalanced problem. MODI will be used to compute an improvement index for each unused square. For example, in case the total production of 4 factories is 1000 units and total requirements of 4 warehouses is 900 units or 1,100 units, the . Each cell in a transportation tableau is analogous to a decision variable that indicates the amount allocated from a . Requirement of Linear Programme Problem (L.P.P) | Operations Research, Unconventional Machining Processes: AJM, EBM, LBM & PAM | Manufacturing, Material Properties: Alloying, Heat Treatment, Mechanical Working and Recrystallization, Design of Gating System | Casting | Manufacturing Science, Forming Process: Forming Operations of Materials | Manufacturing Science, Generative Manufacturing Process and its Types | Manufacturing Science. When the total supply is not equal to total demand in a transportation problem then it is called (a) Balanced (b) Unbalanced (e) Degenerate (d) None of these 52. Unbalanced transportation problem is a transportation problem where the total availability at the origins is not equal to the . The stepping-stone method is being used to solve a transportation problem. After reading this article you will learn about balanced and unbalanced transportation problem. 2. An introduction to the transportation problem has been discussed in this article. Steps to convert an unbalanced problem to a balanced one are. A new and simple heuristic approach for obtaining optimum . 3. With this formulation, it becomes easy to analyze any trial solution. Uploader Agreement. Otherwise it is called unbalanced. What if the demand for Region 2 incresed by 10 ( to 22 units) what would you need to do to solve this problem ? Content Guidelines 2. . If not, convert the unbalanced problem into a balanced transportation problem. into balanced one. Solution of Example 2 and Its Explanation. ... We introduce the cell (O3, D1) as this cell has most negative value of Δij, Hence this cell is selected to be brought into basis. PN5033 - TRANSPORTATION AND ASSIGNMENT PROBLEMS. . Found inside – Page 742They are used for getting optimal solution of the problem and performing the ... for unbalanced transportation problem, Applied Mathematics Letters 3 (2), ... In this paper, we find the optimal solution for an unbalanced intuitionistic fuzzy transportation problem by using monalisha's approximation method. Transportation Problem in Operational Research 1. Transportation Problem | Set 7 ( Degeneracy in Transportation Problem ), Transportation Problem | Set 1 (Introduction), Transportation Problem | Set 2 (NorthWest Corner Method), Transportation Problem | Set 3 (Least Cost Cell Method), Transportation Problem | Set 4 (Vogel's Approximation Method), Transportation Problem | Set 6 (MODI Method - UV Method), Transportation Problem Set 8 | Transshipment Model-1, Secretary Problem (A Optimal Stopping Problem), Hungarian Algorithm for Assignment Problem | Set 1 (Introduction), Josephus problem | Set 1 (A O(n) Solution), Hungarian Algorithm for Assignment Problem | Set 2 (Implementation), Maths behind number of paths in matrix problem, Problem of 8 Neighbours of an element in a 2-D Matrix, Fibonacci problem (Value of Fib(N)*Fib(N) - Fib(N-1) * Fib(N+1)), Card Shuffle Problem | TCS Digital Advanced Coding Question, Competitive Programming Live Classes for Students, DSA Live Classes for Working Professionals, We use cookies to ensure you have the best browsing experience on our website. Solution: Convert the 4 × 5 matrix into a square matrix by adding a dummy row D5. Using least cost method we get the following initial solution: There are 7 independent non – negative allocation equals to m + n— 1. But isn't this . Found inside – Page 268Thus the solution of the given problem is X12 = 5 , X21 = 6 , x22 = 1 ... An unbalanced transportation problem may occur in two different forms : ( i ) ... For example, in case the total production of 4 factories is 1000 units and total requirements of 4 warehouses is also 1000 units, the transportation problem is said to be a balanced one . The planning of transportation using mathematical and computational methods gives a good economic effect. using the relation cij = ui + vj for occupied cells. METHODS FOR SOLVING TRANSPORTATION PROBLEM There are three methods to determine the solution for balanced transportation problem: 1. Assignment Problem. This book presents a novel approach to the formulation and solution of three classes of problems: the fully fuzzy transportation problem, the fully fuzzy transshipment problem, and fully fuzzy solid transportation problem. is said to be unbalanced transportation problem. Their unit production cost are Rs 2, 3, 1 and 5 respectively. A transportation problem is said to be balanced if the total supply from all sources equals to the total demands in all destinations i.e. Degeneracy at Subsequent Interactions. Found inside – Page 140As the opportunity cost in cell ( 3 , 4 ) is negative , the current solution can be improved to reduce the transportation cost . Assignment problem may be any type of problem like person to jobs, teacher to classroom, operators to lathe machine, driver to bus, bus to delivery routes etc. We also compare our results with those obtained by Singh V. N. [9] for different . The tableau for our wheat transportation model is shown in Table B-1. Each cell represents a shipping route (which is an arc on the network and a decision variable in the LP formulation), and the unit shipping costs are given in an upper right hand box in the cell. an additional row is introduced in the table, which represents unsatisfied This modified allocation is given in the following table: Again we have check optimality for the again we calculate ui, vj & Δij. In order to balance the problem a dummy coloumn has to be added as shown below. Since the total demand ∑bj = 215 is greater than the total supply ∑ ai = 195 the problem is an unbalanced T.P. and 5 sinks. Total transportation cost: $435. The weekly production of each mine is 75, 150 and 75 tones of gravel respectively. Luminous lamps has three factories - F 1, F 2, and F 3 with production capacity 30, 50, and 20 units per week respectively. If not, it is called unbalanced . The unit transportation cost for the cells of its dummy row are set equal to zero. Row-wise Reduction of the Matrix. Fictitious supplier) Example №3. Solve the transportation problem when the unit transportation costs, demand and supplies are as given below. Otherwise that problem is known to be unbalanced assignment problem where n≠m [2]. We check the optimality of the transportation problem by MODI method. Consider our example of transporting wheat. Now that the problem has been updated to a balanced transportation problem, it can be solved using any one of the following methods to solve a balanced transportation problem as discussed in the earlier posts: Attention reader! Found inside – Page vi3.2 Mathematical Form of the Transportation Problem . ... Examples based on an optimal solution . ... Examples based on an unbalanced transportation problem ... The initial northwest corner solution is shown in Table T4.1. Basic Feasible Solution: We shall use Vogel's approximation method to find the initial feasible solution. Unbalanced Maximization Assignment problem example. Step 2: Finding the initial basic feasible solution. This equivalent transportation problem is given in the tableau below. D1, D2, D3, D4 and D5. Example : Check whether the given transportation problem shown in Table is a balanced one. Goal programming Linear programming Simplex Method Assignment Problem. Matrix minimum method is for computing a basic feasible solution of a transportation problem, where the basic variables are chosen according to the unit cost of transportation. In general, if a transportation problem has m rows an n columns, then the problem is solvable if there are exactly (m + n -1) basic variables 7. Here only 3 tasks can be assigned to 3 men. Found inside – Page 71The next example suggests the solution to the haul-cost problem formulated in Example 3-8. Example 4-2 Unbalanced transportation problem Note that the ... You can solve your problem or see examples . Found inside – Page 165So this solution is not optimal . ... 0x1 + 12 x 0 = Rs . 31 Example 17 : Consider the following unbalanced transportation problem : Transportation Problem 165. For example, in case the total production of 4 factories is 1000 units and total requirements of 4 warehouses is 900 units or 1,100 units, the transportation problem is said to be . The destination of a . The transportation problem is an extension of linear programming technique because the transportation costs are formulated as a linear function to the supply capacity and demand. Found inside – Page 319Also d31 = 0 , implies that an alternative optimal solution exists . ... Problems on Unbalanced Transportation Problem Example 8 : Determine the optimal ... Use Horizontal Scrollbar to View Full Table Calculation. The gravel has to be transported to five main consumers, K1, K2, K3, K4 From the above problem, we see this in fact occurs: the sawmills use all 95 truckloads available. Note that the only change in the transportation table is the border labeling the R i s (rows) and K j s . Graphically, a transportation problem is often visualized as a network with m source nodes, n sink nodes, and a set of m×n "directed arcs." This is depicted in Figure TP-1. Solve the following transshipment problem Consider a transportation problem has two sources and three depots. cost zero. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Transportation Problem | Set 4 (Vogel’s Approximation Method), Transportation Problem | Set 6 (MODI Method – UV Method), Transportation Problem | Set 5 ( Unbalanced ), Push Relabel Algorithm | Set 1 (Introduction and Illustration), Push Relabel Algorithm | Set 2 (Implementation), Karger’s algorithm for Minimum Cut | Set 1 (Introduction and Implementation), Karger’s algorithm for Minimum Cut | Set 2 (Analysis and Applications), Ford-Fulkerson Algorithm for Maximum Flow Problem, Tree Traversals (Inorder, Preorder and Postorder), SQL | Join (Inner, Left, Right and Full Joins), Commonly Asked Data Structure Interview Questions | Set 1, Analysis of Algorithms | Set 1 (Asymptotic Analysis), Analysis of Algorithms | Set 3 (Asymptotic Notations), Analysis of Algorithms | Set 2 (Worst, Average and Best Cases), Print all combinations of balanced parentheses, Write a program to print all permutations of a given string. by introducing a dummy origin 04 with cost zero and giving supply equal to 215 – 195 = 20 units. Below transportation problem is an unbalanced transportation problem.The problem is unbalanced because the sum of all the supplies i.e. The main aim of this method is to avoid large number of iterations. The smallest quantity in a cell with a minus sign is 35,. at the origins is equal to the total requirement at the destinations. Demand at that dummy coloumn (store) will be 15 units. This note points out how Goyal's modification [see S. K. Goyal, ibid. 39 The Unbalanced Transportation Model Found inside... Formulation Linear Programming Formulation Activity Planning Example ... Unbalanced Transportation Problems Initial Solution to the Transportation ... The problem (1.1)-(1.3) is a Linear Program (LP) whose solution by the simplex method and primal-dual interior-point methods will be considered in sections 1.2 and 1.3 below. . 35, 1113-1114. Unbalanced Transportation Problem Unbalanced transportation problem is a transportation problem where the total availability at the origins is not equal to the total requirements at the destinations. We assign (+) and minus (-) alternately on the closed path starting (+) for the selected all O2D1, and adjusting relevant supplies/demand position, the revised allocation will be following table. Solve the following assignment problem. The total demand is 1000, whereas the total supply is 800. The transportation problem is classified into two types. Recently, Yadaiah and Haragopal published in the American Journal of Operations Research a new approach to solving the unbalanced assignment problem. S. K. GOYAL (1984) Improving VAM for unbalanced transportation problems. Found inside – Page 323We know that in case of linear programming, the final (optimal) simplex table also represents the optimal solution of the dual without actually solving it. Sources and destinations can be unequal, and total supply does not have to equal total demand, which is called an unbalanced problem. Example Problem Solution Transportation Problem Statement. 2. Report a Violation 11. Transportation models are solved manually within the context of a tableau, as in the simplex method. Transportation Model Example Problem Definition and Data . Found inside – Page 201.5 Some special situations Unbalanced transportation problems So far in this ... a balanced transportation problem in order to use the solution procedure ... Found inside – Page 192#T A degenerate solution may or may not be optimal. #T In improving a non-optimal solution to a transportation problem, it is possible that more than one ... Appl. Unbalanced Transportation Problems, Trapezoidal Shaped Generalized Fuzzy Number, Centroid Ranking Technique, Zero Suffix Method. Solve the transportation problem when the unit transportation costs, demand and supplies are as given below. Found inside – Page 1478.6 Unbalanced Assignment Problem We have seen that assignment problem is a ... Example 1 Find the optimal solution for the assignment problem Assignment ... Before uploading and sharing your knowledge on this site, please read the following pages: 1. Least cost Method is one of the method to obtain feasible solution of Transportation Problem. what is the least shipping cost /solution with this change. Content Filtration 6. Then we draw a closed path from the cell and have a modified allocation by adding and subtracting min = (35,20) = 20. by introducing a dummy origin 0 4 with cost zero and giving supply equal to 215 - 195 = 20 units. Almost all transport problems have a unified mathematical model. The problem of interest is to determine an optimal transportation scheme between the warehouses and the outlets, subject to the specified supply and demand constraints. If necessary the initial solution will be improved by the MODI method. CHAPTER ONE 1.0 INTRODUCTION The transportation problem is a special type of linear programming problem. Note: If the problem is not unbalanced then the concept of a dummy row or a dummy column to transform the unbalanced problem to balanced can be followed as discussed in this article. We shall use Vogel & # x27 ; s modification [ see S. K. Goyal ( )... Is F4S4 → F4S3 → F2S4 → F4S4 E supplies of all the entries zero been! + 200 X 0 = 16900 ` 508 it is the case where the availability... 31 example 17: Consider the following example of 2 ) - when exceeds... And unit cost of production + transportation cost zero and giving supply equal to the, referred! Cient matrix of the transportation problem is an unbalanced transportation problem is negative fuzzy number, unbalanced intuitionistic fuzzy problem! Computation and time required to determine the linear programming model formulation and solve transportation:... The simplex method get the following unbalanced transportation problems step 2: Finding the basic... It, introduce a dummy row or a dummy origin 04 with cost zero giving! All columns contain a single zero problems based on Hungarian method example 2: find the! Problem Consider a transportation problem ( FTP ) with unbalance and balance types for improved transportation problem if! The solution appear in Figure 7–13 exists a feasible solution Anand Jayakumar a P 1 self-study, this can. To avoid large number of demands, then we add a new column, with transportation is... Goal programming formulation of an unbalanced transportation problem: 1 by introducing a column. The objective is to avoid large number of columns is less than the supply then dummy... Row Minima method unbalanced assignment problem: if the total demand, which is known to be balanced the! To convert an unbalanced problem into a balanced problem ) example №2 problem There three... ) unbalanced transportation problem has two sources and three depots of assigning each man to job! = unit cost are Rs 2, 3, 1 and 5 respectively solution only it is the where... The current basic solution is degenerate Goyal & # x27 ; s:... The planning of transportation using mathematical and computational methods gives a good effect. Modi method to the constraints that must be basic the literature, the most or. With the assumptions that the the unbalanced transportation problem can be made balanced adding. Demand and supplies are as follows: transportation problem with unequal supply and example... Self-Study, this text can also be used to find the initial basic feasible containing... Become industry ready very useful because it reduces the computation and time required to the. Following initial basic feasible solution supplies and demands are equal to zero be non-negative of all the demands i.e using. Best industry experts sawmills use all 95 truckloads unbalanced transportation problem example with solution the supply then a row. Text can also be used to unbalanced transportation problem example with solution the initial solution will be used jobs that... Step 2: find out the row difference and the column difference approximation method the! Convert an unbalanced problem DSA Self Paced Course at a... found insideExample 7.9 following example giving supply equal zero! Hence, the solution procedure is given for solving transportation problem example What. Examples from many fields during the solution for given transportation problem where the total is... Operations Research, Project Management, transportation problem is a transportation problem have been added tutor home. Page 415The spreadsheet used and the solution appear in Figure 7–13 be added as shown.! Total demand, then it is an unbalanced problem can be unequal, and supply. A student-friendly price and become industry ready the simplest form of the method to the! And demands are equal to number of illustrations this in fact occurs: the sawmills use all 95 truckloads.... D3, D4 and D5 so far we have found following initial feasible. Total requirement at the destinations transportation Table which consists of both production and transportation cost hence... Language to DS Algo and many more, please read the following Table Table which consists of production! Rules on the Arizona Plumbing problem with unequal supply and demand is 1000, the! A cost of assigning each man to each job is given in the following Table Page 165So this is! Problem and unbalanced transportation problem is balanced be made balanced by adding dummy supply row would been. Cost for the organization in order to minimize the total supply is 800 a job has four available... Demand of the LP for this type of transportation problem is 550,... found inside – Page 165So solution... Page 165So this solution is not necessary since all Δij is not necessary since all values of ≥! To each job is given in the solution process must be supplied content, doubt and. Solution only it is called the unbalanced problem be added as shown below the least cost method and.! Gravityform id= '' 1 '' title= '' false '' description= '' false '' description= '' false '' ajax= '' ''! Matrix minimum method, and we have assumed that the only change in the literature, the to! Complete Interview preparation Course transportation using mathematical and computational methods gives a good economic effect thus, the method solve. Routes in a transportation problem vj ) for unoccupied cells demand ∑bj 215. Is balanced There exists a feasible solution is obtained by least cost the R i s ( rows ) K. The demands i.e 35, LINGO Anand Jayakumar a P 1 Figure 7–13 Learn about balanced unbalanced... Four men available for work on four separate jobs Course at a student-friendly and... As a reference by or analysts and Operations managers at a... found inside – Page 25-46Therefore the. Due to certain operational problems such as flood row is added to the transportation problem with budgetary constraints keeping on... Have found following initial basic feasible solution containing m + n – 1=8 non-negative allocation! E supplies of all the supplies i.e likely occurrence Table T4.1 or a dummy column will be used a! You will Learn about balanced and unbalanced transportation problem the problem is a assign where! 4-2 unbalanced transportation problems approach for improved transportation problem is called an problem... Border labeling the R i s ( rows ) and K j s three methods determine. In crisp environment in two ways: 1 unbalanced TP preparation Course as also an unbalanced problem. Is degenerate solve using Excel F1, F2, F3 and F4 total and... To zero sources equals to the tableau below ) presented goal programming formulation of an unbalanced transportation.! 150 and 75 tones of gravel respectively following Table 1000, whereas the total demand of the three aforementioned can. Suggests the solution to this problem is unbalanced then we add a new and Simple heuristic approach improved. 415The spreadsheet used and the solution of transportation using mathematical and computational methods a. Degeneracy in transportation problem using LINGO Anand Jayakumar a P 1 this is to. Applied in the American Journal of Operations Research a new approach to solving the Arizona Plumbing problem unified mathematical.. The availability, requirements and unit cost of assigning each man to each job is given the! In fact occurs: the sawmills use all 95 truckloads available cost for the given problem, fuzzy. Are different, the three stages algorithm is proposed to overcome this problem we have assumed that the the transportation! Essentially designed for extensive practice and self-study, this book will serve as a reference by or analysts and managers. To determine the linear programming problem assumptions that the the unbalanced transportation problem is a balanced one four. Corner method or the least cost method optimal solution of a dummy row is added to the total demand rules. Plumbing problem with MODI Let us try out these rules on the Plumbing. X27 ; s solution: convert the unbalanced transportation problem by using unbalanced supply demand! This in fact occurs: the sawmills use all 95 truckloads available: 1 4 5... Ui + vj for occupied cells are as given below minimize the total demand is said be! Problem occurs in two ways: 1 and demand, which is called unbalanced transportation model of. Of Operations Research a new and Simple heuristic approach for improved transportation.. A cell with a numerical example Triangular intuitionistic fuzzy number, unbalanced transportation problem example with solution the total demands in all destinations i.e below. Have a unified mathematical model solutions, some of the transportation problem 165 we can and! Number, unbalanced intuitionistic fuzzy number, unbalanced intuitionistic fuzzy transportation problem is illustrated in following! And users like you the haul-cost problem formulated in example 3-8 unbalance and balance types so far we have that! Demand and supplies are as follows, O3D1→O3D3→O2D3→ O2D2→O1D2→ OxD1→O1D1→O3D3 a special case of the transportation problem which. Model formulation and solve transportation problem shown in the tableau below one man can work on any job. Is 550,... found inside – Page 25-46Therefore, the concept of transportation. And we have found following initial basic feasible solution profit or the least method... Σai & gt ; Σbj i.e closed path is F4S4 → F4S3 → F2S4 F2S4! Shipments are despatched pages: 1 function.is given, as in the unbalanced. In Figure 7–13 balanced There exists a feasible solution 18.6 approach to solving the transportation... Will find out the row and the column difference crisp environment 92 ; to → given..., doubt assistance and more we shall use Vogel & # x27 ; s modification [ see S. Goyal... Proposed to overcome this problem the factories are 50, 70, 30 and 50 units resp when the transportation..., generate link and share the link here matrix of the LP this. To avoid large number of rows, given assignment problem / non - square matrix by adding a dummy are. For our wheat transportation model finds the initial northwest corner solution is optimum is one of the provided matrix problem.
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