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Quizzes > Mathematics > Advanced Math

Optimization Techniques Quiz: Test Your Transportation Problem Skills

Take this transportation problem methods quiz to sharpen your optimization techniques!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for a quiz on optimization techniques and transportation problem methods on teal background.

Ready to take your skills to the next level? Our free Optimization Techniques Quiz invites logistics enthusiasts, operations buffs, and data-driven pros to explore a transportation problem methods quiz designed to sharpen your route planning prowess. Tackle the North-West Corner method test, refine allocations with MODI method practice, and optimize expenses in the Least Cost Method assessment. Whether you're tackling solving optimization problems quiz or testing your smarts with transportation trivia , you'll gain the confidence to streamline real-world supply chains. Ready to prove yourself? Take the Optimization Techniques Quiz now!

What is the primary objective of the transportation problem in operations research?
Minimize total transportation cost
Maximize number of routes used
Maximize total supply shipped
Minimize the number of supply locations
The transportation problem seeks to distribute goods from multiple sources to multiple destinations while minimizing the sum of shipping costs. It is a specialized linear programming problem focusing on cost efficiency. Other objectives like maximizing routes or supply shipped are not the focus of its classic formulation. Source
Which initial solution method starts allocations at the top-left cell of the cost matrix regardless of costs?
North-West Corner Method
Least Cost Method
Vogel’s Approximation Method
MODI Method
The North-West Corner Method always begins allocation at the (1,1) position (top-left) and moves either right or down based on remaining supply and demand. It ignores the costs in its initial allocation step. This simplicity often leads to a suboptimal starting solution but is easy to implement. Source
In the context of the transportation problem, what does MODI stand for?
Modified Distribution Method
Minimum Opportunity Distribution Inference
Modal Optimization of Distribution Indices
Matrix of Optimal Distribution Iterations
MODI stands for the Modified Distribution Method, which is a technique used to optimize an existing feasible solution for the transportation problem. It calculates dual variables and opportunity costs to test for optimality and identify improvements. This method iteratively adjusts allocations to minimize total cost. Source
Which rule does the Least Cost Method use to determine its first allocation?
Select the cell with the smallest unit transportation cost
Select the top-left cell in the matrix
Select the row with the highest supply
Select the column with the highest demand
The Least Cost Method chooses the cell with the lowest shipping cost first for initial allocation, aiming to reduce overall expense from the start. It then adjusts supply and demand before moving to the next least costly cell. This often yields a better initial solution than the North-West Corner Method. Source
In a balanced transportation problem with m supply sources and n demand destinations, how many basic variables are required for a basic feasible solution?
m + n - 1
m + n
m * n
m + n + 1
A balanced transportation problem requires exactly m + n – 1 basic variables to form a non-degenerate basic feasible solution. This ensures the system of supply and demand equations remains independent. Using more or fewer allocations would either overconstrain or leave the solution underdetermined. Source
What condition defines degeneracy in a transportation problem solution?
Number of allocations is less than m + n - 1
Number of allocations equals m + n - 1
Number of allocations exceeds m + n - 1
All supply or demand are zero
Degeneracy occurs when the count of basic allocations falls below m + n – 1, causing the solution to fail in spanning the full solution space. This can lead to zero loops and makes the computation of dual variables ambiguous. To correct it, an artificial zero allocation is introduced in a non-basic cell. Source
What is the main purpose of calculating the dual variables u_i and v_j in the MODI method?
To compute opportunity costs for unused cells
To determine supply and demand values directly
To identify the pivot element for allocation
To balance the transportation matrix
The dual variables u_i and v_j represent the potential values for source i and destination j respectively. By computing u_i + v_j, you can find the opportunity cost for each unused cell (c_{ij} – (u_i + v_j)). These opportunity costs indicate whether the current solution can be improved. Source
Which initial solution method usually yields a lower total cost than the North-West Corner Method?
Least Cost Method
Row Minima Method
Column Maxima Method
North-East Corner Method
The Least Cost Method often produces a better (lower-cost) initial solution than the North-West Corner Method because it allocates shipments based on the minimum cost entries first. This targeted approach generally reduces overall transportation expense from the outset. However, it may require more computation than simpler rules. Source
In the MODI method, an unused cell has an opportunity cost calculated as c_ij ? (u_i + v_j). What does a negative value imply?
The current solution can be improved by introducing this cell
The current solution is already optimal
This cell must be removed from consideration
The problem is degenerate
A negative opportunity cost means that shifting allocation into this unused cell will reduce total transportation cost. Therefore, the existing solution is not optimal. You form a closed loop with this cell and adjust allocations to improve cost. Repeating until no negatives remain yields the optimal solution. Source
What defines a closed loop (cycle) used in adjusting allocations during the MODI method?
A path of horizontal and vertical moves that returns to the starting cell
Any contiguous block of filled cells
A diagonal chain of unused cells
A set of cells all in the same row
A closed loop in the transportation tableau is a series of alternating horizontal and vertical moves through allocated cells that begins and ends at the entering cell. This loop is used to adjust shipments by adding and subtracting quantities alternately along the path. It preserves supply and demand constraints while improving the solution. Source
How is degeneracy corrected when the number of basic variables is less than m + n – 1?
Introduce a zero allocation in an unoccupied cell
Remove one allocation from the basis
Combine two supply nodes into one
Increase the demand of one destination by one unit
When degeneracy arises (basic allocations < m + n – 1), a zero allocation is temporarily assigned to an unused cell to restore the count of basic variables. This artificial entry prevents loops of zero length and preserves the solution structure. It does not affect the cost but allows proper calculation of dual variables. Source
If multiple cells have negative opportunity costs in the MODI method, which one should be selected first to enter the basis for improvement?
The cell with the most negative opportunity cost
The cell with the least negative opportunity cost
Any of the negative-cost cells at random
The cell with the highest supply
When multiple unused cells exhibit negative opportunity costs, selecting the most negative cost cell leads to the greatest immediate reduction in total transportation cost. This approach speeds convergence to the optimal solution. Other negative-cost cells can be tested in subsequent iterations. Source
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Study Outcomes

  1. Apply the North-West Corner Method -

    Use the North-West Corner method test to generate initial feasible solutions for transportation problem scenarios in the Optimization Techniques Quiz.

  2. Analyze Cost Allocations with the Least Cost Method -

    Employ the Least Cost Method assessment to identify minimum-cost allocations and refine your decision-making in cost matrix challenges.

  3. Evaluate Optimality Using the MODI Method -

    Perform MODI method practice to calculate opportunity costs, adjust allocations, and confirm optimal transportation solutions.

  4. Solve Transportation Problem Scenarios -

    Tackle diverse transportation problem methods quiz questions to sharpen your problem-solving skills and method application.

  5. Interpret Cost Matrices and Constraints -

    Understand supply, demand, and cost matrix structures to accurately model and solve optimization problems.

  6. Enhance Decision-Making in Optimization -

    Integrate insights from multiple methods to select the best solution and develop robust optimization strategies.

Cheat Sheet

  1. Formulating a Balanced Transportation Table -

    Start by listing all sources (suppliers) and destinations (consumers) in a matrix where total supply equals total demand; if they differ, introduce a dummy row or column as per standard operations research practices. Label each cell with its transportation cost to create the basis for your Optimization Techniques Quiz. Remember the phrase "Balance Before Solve" to lock in this critical setup step.

  2. North-West Corner Method Initialization -

    Allocate as much as possible to the top-left (north-west) cell, then exhaust either its row supply or column demand before moving right or down. Continue this "greedy" allocation without considering cost, which provides a quick feasible solution often tested in a North-West Corner method test. This simple algorithm is covered extensively in MIT OpenCourseWare's OR syllabus.

  3. Least Cost Method for Better Feasible Solution -

    Select the cell with the lowest unit cost and allocate the maximum possible supply or demand, then cross out the satisfied row or column and repeat. This method tends to yield a lower initial transportation cost compared to the north-west approach, making it a staple in any Least Cost Method assessment. It's highlighted in many university textbooks for its practical efficiency.

  4. MODI Method (UV Method) for Optimality -

    Compute dual variables (u and v) for rows and columns, then calculate opportunity costs (Δij = cij - ui - vj) to check if all are non-negative. If any Δij is negative, adjust allocations along the identified closed path to improve the solution - this key step appears in most MODI method practice problems. This technique is a cornerstone of linear programming optimization in academic journals.

  5. Stepping-Stone Analysis and Handling Degeneracy -

    Use the stepping-stone method to trace loops from unused cells and quantify the net cost change for potential reallocations, ensuring you choose moves that reduce total cost. Be alert for degeneracy when the number of allocations < m + n - 1; introduce a zero-allocation (a "ghost" shipment) to maintain feasibility, a nuance covered in professional OR certifications. This final check guarantees your solution is truly optimal for transportation problem methods quizzes.

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