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CMA Intermediate · Operations Management and Strategic Management

Job Evaluation and Assignment Problem for CMA Inter

Job evaluation rates the worth of a job; merit rating rates the performance of the person doing it. The assignment problem matches n jobs to n workers, one each, at least total cost. You solve it with the Hungarian method: reduce rows, reduce columns, cover zeros with minimum lines, adjust, and assign.

What this chapter covers

This chapter has two parts that look unrelated but share one idea: putting the right person on the right job. The first part is descriptive. Job evaluation ranks jobs by their relative worth so that pay can be fair. Merit rating assesses how well an employee performs the job. You must know the methods, the purpose and the difference between the two.

The second part is numerical. The assignment problem is a special case of the transportation problem. Each worker gets exactly one job and each job goes to exactly one worker. The aim is to minimise total cost or time, or to maximise profit or output. The Hungarian method is the standard way to solve it.

In Paper 9, this chapter sits in the operations side of the syllabus, alongside other decision techniques. The descriptive part also links to human resource and organisation topics in the strategic management side. The numerical part gives you a short, rule-based sum that can be scored with step marks if your layout is clean.

The assignment problem follows a fixed algorithm, so a well-prepared student can score full marks on it in a 14-mark question or answer an MCQ on it in under two minutes. The theory on job evaluation and merit rating is easy to learn and suits MCQs and short notes. Because the chapter is small and rule-driven, the effort you put in returns marks more reliably than in many longer chapters. The risk is carelessness: one wrong subtraction ruins the whole matrix, so practice matters more than reading.

Job Evaluation, Job Allocation - Assignment: topics in the order to study them

  1. 1Job Evaluation and Merit RatingStart with the theory: it is short, sets the context of matching people to jobs, and is needed for MCQs and short notes.
  2. 2Job Allocation and Assignment Problem BasicsLearn the problem structure, the cost matrix and the one-job-per-worker rule before any algorithm.
  3. 3Hungarian Method for Minimisation ProblemsThis is the core algorithm; every later variation is built on it, so master it on balanced minimisation first.
  4. 4Maximisation and Unbalanced Assignment ProblemsThese are conversions: you turn the problem into a balanced minimisation one and then reuse the same method.
  5. 5Special Cases: Restrictions and Multiple Optimal SolutionsStudy this last because it needs the full method: you block cells with a very large cost and spot alternative assignments.

How to prepare Job Evaluation, Job Allocation - Assignment

Split your time: about one sitting for theory and the rest for practising sums by hand. Do not just read solved examples.

  1. Learn the definitions of job evaluation and merit rating, and write a two-column comparison of purpose, subject assessed and use.
  2. List the methods of job evaluation and the common merit rating methods in your own words, with one line on how each works.
  3. Write the Hungarian method as a numbered checklist from memory: row reduction, column reduction, minimum lines to cover all zeros, adjust, repeat, assign.
  4. Solve at least five balanced minimisation problems of size 3x3 and 4x4, checking that the number of lines equals the matrix size before assigning.
  5. Practise conversions: for maximisation, subtract every entry from the largest entry; for unbalanced problems, add a dummy row or column of zeros.
  6. Solve problems with a restriction, where a worker cannot do a job, and ones with ties, where you list every optimal assignment.
  7. Finish by checking your final answer: add the original costs of the chosen cells, never the reduced ones, and write the assignment pairs clearly.

Common mistakes in Job Evaluation, Job Allocation - Assignment

  • Mixing up job evaluation and merit rating

    Fix: Remember: job evaluation is about the job, merit rating is about the person doing it. Write this as the first line of any answer.

  • Assigning before the minimum number of covering lines equals the matrix size

    Fix: Always draw the minimum lines and count them. Assign only when the count equals n; otherwise adjust and repeat.

  • Drawing more lines than necessary

    Fix: Cover zeros using the fewest lines, starting with the row or column holding the most zeros, and recheck for waste.

  • Computing the final cost from the reduced matrix

    Fix: Take the chosen cells back to the original cost matrix and add those values. For maximisation, use the original profit matrix.

  • Forgetting to balance an unbalanced problem

    Fix: Check the matrix is square first. If not, add a dummy row or column of zeros, and note that a job or worker paired with the dummy is left unassigned.

  • Ignoring alternative optimal solutions

    Fix: If the question asks for all solutions, or the zeros allow a different valid selection, list each one and confirm that the total cost is the same.

Last-day revision: Job Evaluation, Job Allocation - Assignment

  • Job evaluation rates the job; merit rating rates the employee.
  • Job evaluation helps fix fair relative pay for jobs.
  • Merit rating assesses an employee's performance and is used for things like promotion and increments.
  • Assignment problem: n workers, n jobs, one job per worker, one worker per job.
  • It is a special case of the transportation problem where every supply and demand is 1.
  • Hungarian steps: subtract row minimum, subtract column minimum, cover zeros with the fewest lines.
  • If the minimum number of lines equals n, an optimal assignment exists among the zeros.
  • If lines are fewer than n, subtract the smallest uncovered value from uncovered cells and add it to cells at line intersections.
  • Maximisation: subtract every entry from the largest entry, then minimise.
  • Unbalanced matrix: add a dummy row or column with zero costs to make it square.
  • Restricted assignment: put a very large cost in the prohibited cell.
  • Report total cost from the original matrix; several zero choices may give alternative optimal solutions with the same total.

Job Evaluation, Job Allocation - Assignment practice questions

Job Evaluation, Job Allocation - Assignment in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Job Evaluation, Job Allocation - Assignment: frequently asked questions

What is the difference between job evaluation and merit rating?

Job evaluation measures the relative worth of a job, regardless of who does it. Merit rating measures how well an individual performs in that job. The first guides the pay structure; the second guides increments, promotions and training.

How do I solve an assignment problem in the exam?

Make the matrix square, convert maximisation to minimisation if needed, then reduce rows and columns. Cover all zeros with the fewest lines, adjust until the lines equal n, and assign. Show each matrix so you earn step marks.

How do I handle a maximisation assignment problem?

Subtract every entry from the largest entry in the matrix to get an opportunity-loss matrix. Solve it as a minimisation problem. Then add up the original profits of the chosen cells for the answer.

What do I do if a worker cannot be given a particular job?

Put a very large cost, usually written as M, in that cell so it will never be chosen in a minimisation problem. Then solve in the usual way and check that the final assignment avoids that cell.