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Assignment Method

Published on :

21 Aug, 2024

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Dheeraj Vaidya

What Is The Assignment Method?

The assignment method is a strategic approach to allocating organizational resources, including tasks and jobs to various departments like people, machines, or teams. It aims to minimize total costs or completion time and gain maximum efficiency, by assigning resources to corresponding units.

The assignment procedure's importance stems from its capacity to optimize resource allocation procedures in a business. Organizations may guarantee that resources are used optimally, reducing waste and increasing productivity by implementing a systematic method. It facilitates the decision-making process for the efficient and economical use of resources by helping to make well-informed choices.

Table of contents

Assignment method explained, methodology, advantages & disadvantages, frequently asked questions (faqs), recommended articles.

• The assignment method strategically allocates resources to tasks, jobs or teams to minimize costs or completion time. It optimizes resource utilization, reduces waste, and improves operational efficiency.
• It involves using methods like complete enumeration, simplex, transportation, or the Hungarian method. It involves using the assignment method of linear programming .
• The   Hungarian assignment method efficiently solves assignment problems by determining optimal assignments using a cost matrix.
• Advantages include structured resource allocation, enhanced resource utilization, and improved operational effectiveness. Limitations include data accuracy requirements and limited flexibility for dynamic changes.

The assignment method in operation research is a strategy for allocating organizational resources to tasks to increase profit via efficiency gains, cost reductions , and improved handling of operations that might create bottlenecks . It is an operations management tool that, by allocating jobs to the appropriate individual, minimizes expenses , time, and effort.

The technique is an essential tool for project management and cost accounting . It assists in allocating indirect expenses , such as overhead, to objects or cost centers according to predetermined standards, such as direct labor hours or required machine hours. The method helps determine the overall cost of every good or service, which helps with pricing, output, and resource distribution decisions. It also guarantees effective work allocation, on-time project completion, and economical use of resources. In short, it solves assignment problems.

Assignment problems involve assigning workers to specific roles, such as office workers or trucks on delivery routes, or determining which machines or products should be used in a plant during a specific period. Transportation problems involve distributing empty freight cars or assigning orders to factories. Allocation problems also involve determining which machines or products should be used to produce a given product or set of products. Unit costs or returns can be independent or interdependent, and if allocations affect subsequent periods, the problem is dynamic, requiring consideration of time in its solution.

The assignment problem can be solved using four methods: The complete enumeration method, the simplex method, the transportation method, and the Hungarian method.

The complete enumeration approach generates a list of potential assignments between resources and activities, from which the best option is chosen based on factors like cost, distance, time, or optimum profit. If the minimum cost, time, or distance for two or more assignments is the same, then this approach offers numerous optimal solutions. However If there are a lot of assignments, it is no longer appropriate for manual calculations. Assignment method calculators, if reliable, can be used for the same.

The simplex method can be solved as a linear programming problem using the simplex algorithm. The transportation method is a special case of the assignment problem. The method is, however, computationally inefficient for solving the assignment problem due to the solution's degeneracy problem.

The Hungarian assignment method problem, developed by mathematician D. Konig, is a faster and more efficient approach to solving assignment problems. It involves determining the cost of making all possible assignments using a matrix. Each problem has a row representing the objects to be assigned and columns representing assigned tasks. The cost matrix is square, and the optimum solution is to have only one assignment in a row or column. This method is a variation of the transportation problem, with the cost matrix being square and the optimum solution being one assignment in a row or column of the cost matrix.

Let us look into a few examples to understand the concept better.

TechLogistics Solutions, an imaginary delivery company, employs the assignment method to optimize the distribution of its delivery trucks. They meticulously consider distance, traffic conditions, and delivery schedules. TechLogistics efficiently allocates trucks to routes through strategic assignments, effectively reducing fuel costs and ensuring punctual deliveries. This method significantly enhances the company's operational efficiency and optimizes the utilization of its delivery resources.

Suppose XYZ Inc., a manufacturing company, is challenged to efficiently assign tasks to its machines (A, B, and C). Using the assignment method, XYZ calculates the cost matrix, reflecting the cost associated with each task assigned to each machine. Leveraging advanced algorithms like the Hungarian method, the company identifies optimal task-machine assignments, minimizing overall costs. This approach enables XYZ to streamline its production processes and enhance cost-effectiveness in manufacturing operations .

Advantages of the assignment method include:

• Resource allocation is carried out in a structured and organized manner.
• Enhancement of resource utilization to achieve optimal outcomes.
• Facilitation of efficient distribution of tasks.
• Improvement in operational effectiveness and productivity.
• Economical allocation of resources.
• Reduction in project completion time.
• Consideration of multiple factors and constraints for informed decision-making.

The disadvantages of the assignment method are as follows:

• Dependence on accurate and up-to-date data for effective decision-making.
• Complexity when dealing with resource allocation on a large scale.
• Subjectivity is involved in assigning values to the resource-requirement matrix.
• Limited flexibility in accommodating dynamic changes or unforeseen circumstances.
• Applicable primarily to quantitative tasks, with limitations in addressing qualitative aspects.

Johnson's rule is an operations research method that aims to estimate the optimal sequence of jobs in two work centers to reduce makespan. It optimizes the overall efficiency of the process. In contrast, the assignment method is useful for resource allocation, matching resources to specific tasks or requirements to optimize efficiency.

The study assignment method refers to the process of allocating students to specific courses or study programs based on their preferences, skills etc. It involves matching students with appropriate courses or programs to ensure optimal utilization of educational resources and meet individual student needs.

The assignment method is frequently employed when there is a requirement to allocate restricted resources like personnel, equipment, or budget to particular tasks or projects. It aids in enhancing resource utilization operational efficiency, and enables informed decision-making regarding resource allocation considering various factors and constraints.

This article has been a guide to what is Assignment Method. Here, we explain its methodologies, examples, advantages, & disadvantages. You may also find some useful articles here -

• Cost Allocation Methods
• Propensity Score Matching
• Regression Discontinuity Design

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Picture Fuzzy Linear Assignment Method and Its Application to Selection of Pest House Location

Fatma kutlu gundogdu.

Industrial Engineering Department, National Defence University, Turkish Air Force Academy, 34149 Istanbul, Turkey

The theory of picture fuzzy sets is useful for handling uncertainty in multiple attribute decision making problems by considering membership, non-membership and indeterminacy degrees independently for each element. In this paper, by extending the classical linear assignment method, we propose a novel method which is called picture fuzzy linear assignment method (PF-LAM) for solving multiple criteria group decision-making problems with picture fuzzy sets. A ranking procedure consisting of aggregation functions, score functions, accuracy functions, and weighted rank frequency and a binary mathematical model are presented to determine the priority order of various alternatives. The applicability and validity of the proposed method is shown through the selection of pest house locations. The proposed method helps managers to find the best location to construct the pest house based on the determined criteria.

Introduction

Fuzzy Sets theory, developed by Zadeh [ 1 ], is a useful and appropriate approach in order to deal with imprecise and uncertain information in vague situations. After the introduction of fuzzy sets, they have been very popular in almost all branches of science [ 2 ]. Many researchers [ 2 – 14 ] have introduced many extensions of ordinary fuzzy sets in the literature. These extensions have been utilized by numerous researchers in recent years in the solution of multi-attribute decision-making problems [ 2 ]. One of the latest extensions is Picture fuzzy sets (PFS). Picture Fuzzy Sets (PFS) were developed by Cuong [ 14 ] and it is a direct extension of intuitionistic fuzzy sets (IFS) that can model uncertainty using membership degree, non-membership degree, and hesitant degree independently.

Wang and Li [ 15 ] introduced the theory of picture hesitant fuzzy set based on the picture fuzzy sets and the hesitant fuzzy set. Sarwar Sindhu et al. [ 16 ] proposed a linear programming model in order to find exact weights and construct a modified distance based on similarity measure under picture fuzzy environment. Liang et al. [ 17 ] presented a MCDM method which is a combination of TODIM method with the ELECTRE method in a picture fuzzy environment. Thao [ 18 ] developed the entropy measure for PFS and proposed the similarity measures for MCDM problems in order to select suppliers. Tian et al. [ 19 ] proposed a picture fuzzy MCDM method and introduced weighted picture fuzzy power Choquet ordered geometric operator and a weighted picture fuzzy power Shapley Choquet ordered geometric operator.

The linear assignment method (LAM) was proposed by Bernardo and Blin [ 20 ], inspiring from assignment problem in linear programming for multi-attribute decision-making [ 21 ]. The basic idea of the LAM is that the combination of the criteria-wise rankings into an overall preference ranking that produces an optimal compromise among the several component rankings. Developing an extended linear assignment method to solve multi-criteria decision-making (MCDM) problems under Pythagorean fuzzy environment was the aim of [ 22 ]. In addition, Liang et al. [ 23 ] developed the linear assignment method for interval-valued Pythagorean fuzzy sets. By extending the traditional linear assignment method, Chen [ 24 ] developed an efficient method for solving MCDM problems in the interval-valued intuitionistic fuzzy environment.

To the best of our knowledge, there is no research about extension and application of linear assignment method in picture fuzzy environment. Therefore, the aim of this paper is to develop a novel multi-attribute decision-making method based on linear assignment approach with picture fuzzy sets and also show the useful application to site selection of pest house. The proposed algorithm has the following contributions. First, judgment values are given as picture linguistic terms, which can consider the hesitancy degree of decision makers’ comments about alternatives and criteria. Second, linear assignment method has been employed to rank alternatives to avoid the effect of subjectivity.

In Sect.  2 , the definitions of Picture fuzzy sets are presented. In Sect.  3 , the Picture fuzzy linear assignment method are detailed step by step. In Sect.  4 , an application is given and in Sect.  5 , the conclusion is given.

Picture Fuzzy Sets: Preliminaries

There are some definitions about PFS is given as follows with related equations.

Definition 2.1:

Definition 2.2:

Basic operators for Single-valued picture fuzzy sets;

Definition 2.3:

Definition 2.4:

Score functions and Accuracy functions of sorting picture fuzzy numbers are defined by;

Picture Fuzzy Linear Assignment Method

Table 1.

Picture fuzzy linguistic terms [ 25 ]

Collect the decision-makers’ evaluations for the alternatives and criteria based on Table  1 .

Aggregate the individual decision matrices based on PFWA operator as given in Eq. ( 7 ).

Compute the elements of scored decision matrix by utilizing the picture fuzzy score function (Eq.  8 ).

An Application to Pest House Location Selection

In this section, a numerical example is presented to illustrate feasibility and practical advantages of new proposed method. Nowadays, Coronavirus Disease (COVID-19) has emerged as a global problem since spread of the disease to March 2020, more than one million people have been infected by COVID-19 virus. The disease is quickly spreading between people during close contact. In the future, existing hospitals will not be enough for the patients who are suffering from Coronavirus or similar dangerous viruses. Each country has to establish pet houses. The aim of this problem is to select the best site location in order to establish pest house in Turkey. The mostly preferred five locations (X1: Ankara, X2: Izmir, X3: Istanbul-Atatürk Airport, X4: Istanbul-Sancaktepe, and X5: Bursa) are evaluated as alternatives. Four criteria have been determined in order to evaluate these alternatives. Criteria are logistic support opportunities to settlements (C1), economical situations (C2), population density (C3), and proximity to settlements (C4). Three decision makers who have different significance levels such as 0.3, 0.5, 0.2, are going to evaluate the above five possible alternatives according to four criteria based on picture linguistic terms as presented in Table  2 .

Table 2.

Assessments of decision-makers

Table 3.

Aggregated decision matrix

Calculate the score value of each alternative based on each criterion using Eq. ( 8 ). The results are shown in Table  4 .

Table 4.

The score value of each alternative

Table 5.

The linear assignment model is constructed as follows. The objective function of this binary mathematical model tries to maximize the sum of the weights of alternatives by choosing the optimal order of them.

In the recent years, picture fuzzy sets have been very widespread in almost all branches. Picture fuzzy sets are another extension of the ordinary fuzzy sets. PFS should satisfy the condition that the sum of membership degree and non-membership degree and hesitancy degree should be equal to or less than one. In this study, the classical linear assignment model is extended to picture fuzzy linear assignment model and the novel method is applied to site selection problem for pest house. It has been successfully solved by picture fuzzy linear assignment model. The proposed PF-LAM method is performed to get the optimal preference ranking of the alternatives according to a set of criteria-wise rankings within the context of PFS.

For future studies, the proposed method can be applied to several decision support systems and the illustrative example can be extended by real data.

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Operations Management

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Chapter Questions

Use the assignment method to determine the best way to assign workers to jobs, given the following cost information. Compute the total cost for your assignment plan. $$ \begin{array}{|c|c|c|c|c|} \hline & & {3}{|c|}{\text { JOB }} \\ \hline & & \text { A } & \text { B } & \text { C } \\ \hline & 1 & 5 & 8 & 6 \\ \hline [t]{2}{*}{\text { Worker }} & 2 & 6 & 7 & g \\ \hline & 3 & 4 & 5 & 3 \\ \hline \end{array} $$

Rework Problem 1, treating the numbers in the table as profits instead of costs. Compute the total profit.

Assign trucks to delivery routes so that total costs are minimized, given the cost data shown. What is the total cost? $$ \begin{array}{ll|rrrrr} {7}{c}{\text { ROUTE }} \\ { 3 - 7 } & & {6}{c}{} \\ & & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\ { 3 - 7 } & \mathbf{1} & 4 & 5 & 9 & 8 & 7 \\ & 2 & 6 & 4 & 8 & 3 & 5 \\ \text { Truck } & 3 & 7 & 3 & 10 & 4 & 6 \\ & 4 & 5 & 2 & 5 & 5 & 8 \\ & \mathbf{5} & 6 & 5 & 3 & 4 & 9 \end{array} $$

Develop an assignment plan that will minimize processing costs, given the information shown, and interpret your answer. $$ \begin{array}{cc|rrr} {1}{c}{} & {3}{c}{\text { WORKER }} \\ { 3 - 5 } & & \text { A } & \text { B } & \text { C } \\ { 3 - 5 } & & 8 & 11 \\ { 3 - 5 } \text { Job } & 1 & 12 & 10 & 8 \\ & 2 & 13 & 10 & 14 \\ & 3 & 14 & 9 & 12 \end{array} $$

Use the assignment method to obtain a plan that will minimize the processing costs in the following table under these conditions: a. The combination 2-D is undesirable. b. The combinations 1-A and 2-D are undesirable $$ \begin{aligned} &\text { WORKER }\\ &\begin{array}{cc|ccccc} { 3 - 6 } & & \mathbf{A} & \mathbf{B} & \mathbf{C} & \mathbf{D} & \mathbf{E} \\ { 3 - 6 } & \mathbf{1} & 14 & 18 & 20 & 17 & 18 \\ \text { Job } & \mathbf{2} & 14 & 15 & 19 & 16 & 17 \\ & 3 & 12 & 16 & 15 & 14 & 17 \\ & 4 & 11 & 13 & 14 & 12 & 14 \\ & \mathbf{5} & 10 & 16 & 15 & 14 & 13 \end{array} \end{aligned} $$

The following table contains information concerning four jobs that are awaiting processing at a work center. $$ \begin{array}{ccc} \text { Job } & \begin{array}{c} \text { Job Time } \\ \text { (days) } \end{array} & \begin{array}{c} \text { Due Date } \\ \text { (days) } \end{array} \\ \hline \text { A } & 14 & 20 \\ \text { B } & 10 & 16 \\ \text { C } & 7 & 15 \\ \text { D } & 6 & 17 \end{array} $$ a. Sequence the jobs using (1) FCFS, (2) SPT, (3) EDD, and (4) CR. Assume the list is by order of arrival. b. For each of the methods in part $a$, determine (1) the average job flow time, (2) the average tardiness, and (3) the average number of jobs at the work center. c. Is one method superior to the others? Explain.

Using the information presented in the following table, identify the processing sequence that would result using (1) FCFS, (2) SPT, (3) EDD, and (4) CR. For each method, determine (1) average job flow time, (2) average job tardiness, and (3) average number of jobs in the system. Jobs are listed in order of arrival. (Hint: First determine the total job time for each job by computing the total processing time for the job and then adding in the setup time. All times and due dates are in hours.)$$ \begin{array}{ccccr} \text { Job } & \begin{array}{c} \text { Processing } \\ \text { Time per Unit } \end{array} & \begin{array}{c} \text { Units } \\ \text { per Job } \end{array} & \begin{array}{c} \text { Setup } \\ \text { Time } \end{array} & \begin{array}{c} \text { Due } \\ \text { Date } \end{array} \\ \hline \text { a } & .14 & 45 & 0.7 & 4 \\ \text { b } & .25 & 14 & 0.5 & 10 \\ \text { c } & .10 & 18 & 0.2 & 12 \\ \text { d } & .25 & 40 & 1.0 & 20 \\ \text { e } & .10 & 75 & 0.5 & 15 \end{array} $$

The following table shows orders to be processed at a machine shop as of 8:00 a.m. Monday. The jobs have different operations they must go through. Processing times are in days. Jobs are listed in order of arrival. a. Determine the processing sequence at the first work center using each of these rules: (1) FCFS, (2) S/O. b. Compute the effectiveness of each rule using each of these measures: (1) average flow time, (2) average number of jobs at the work center. $$ \begin{array}{cccc} \text { Job } & \begin{array}{c} \text { Processing } \\ \text { Time } \\ \text { (days) } \end{array} & \begin{array}{c} \text { Due } \\ \text { Date } \\ \text { (days) } \end{array} & \begin{array}{c} \text { Remaining } \\ \text { Number of } \\ \text { Operations } \end{array} \\ \hline \text { A } & 8 & 20 & 2 \\ \text { B } & 10 & 18 & 4 \\ \text { C } & 5 & 25 & 5 \\ \text { D } & 11 & 17 & 3 \\ \text { E } & 9 & 35 & 4 \end{array} $$

A wholesale grocery distribution center uses a two-step process to fill orders. Tomorrow’s work will consist of filling the seven orders shown. Determine a job sequence that will minimize the time required to fill the orders. $$ \begin{aligned} &\text { TIME (hours) }\\ &\begin{array}{ccc} { 2 - 3 } \text { Order } & \text { Step 1 } & \text { Step 2 } \\ \hline \text { A } & 1.20 & 1.40 \\ \text { B } & 0.90 & 1.30 \\ \text { C } & 2.00 & 0.80 \\ \text { D } & 1.70 & 1.50 \\ \text { E } & 1.60 & 1.80 \\ \text { F } & 2.20 & 1.75 \\ \text { G } & 1.30 & 1.40 \end{array} \end{aligned} $$

The times required to complete each of eight jobs in a two-machine flow shop are shown in the table that follows. Each job must follow the same sequence, beginning with machine A and moving to machine B. a. Determine a sequence that will minimize makespan time. b. Construct a chart of the resulting sequence, and find machine B’s idle time. c. For the sequence determined in part a, how much would machine B’s idle time be reduced by splitting the last two jobs in half? $$ \begin{aligned} &\text { TIME (hours) }\\ &\begin{array}{ccc} { 2 - 3 } \text { Job } & \text { Machine A } & \text { Machine B } \\ \hline \text { a } & 16 & 5 \\ \text { b } & 3 & 13 \\ \text { c } & 9 & 6 \\ \text { d } & 8 & 7 \\ \text { e } & 2 & 14 \\ \text { f } & 12 & 4 \\ \text { g } & 18 & 14 \\ \text { h } & 20 & 11 \end{array} \end{aligned} $$

Given the operation times provided: a. Develop a job sequence that minimizes idle time at the two work centers. b. Construct a chart of the activities at the two centers, and determine each one’s idle time, assuming no other activities are involved. $$ \begin{aligned} &\text { JOB TIMES (minutes) }\\ &\begin{array}{lcccccc} & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\ \hline \text { Center 1 } & 20 & 16 & 43 & 60 & 35 & 42 \\ \text { Center 2 } & 27 & 30 & 51 & 12 & 28 & 24 \end{array} \end{aligned} $$

A shoe repair operation uses a two-step sequence that all jobs in a certain category follow. All jobs can be split in half at both stations. For the group of jobs listed, a. Find the sequence that will minimize total completion time. b. Determine the amount of idle time for workstation B. c. What jobs are candidates for splitting? Why? If they were split, how much would idle time and makespan time be reduced? $$ \begin{array}{lccccc} & {4}{c}{\text { JOB TIMES (minutes) }} \\ { 2 - 6 } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\ \hline \text { Workstation A } & 27 & 18 & 70 & 26 & 15 \\ \text { Workstation B } & 45 & 33 & 30 & 24 & 10 \end{array} $$

The following schedule was prepared by the production manager of Marymount Metal Shop: Determine a schedule that will result in earliest completion of all jobs on this list. $$ \begin{array}{cccccc} & {2}{c}{\text { CUTTING }} & & {2}{c}{\text { POLISHING }} \\ { 2 - 3 } { 5 - 6 } \text { Job } & \text { Start } & \text { Finish } & & \text { Start } & \text { Finish } \\ \hline \text { A } & 0 & 2 & & 2 & 5 \\ \text { B } & 2 & 6 & & 6 & 9 \\ \text { C } & 6 & 11 & & 11 & 13 \\ \text { D } & 11 & 15 & & 15 & 20 \\ \text { E } & 15 & 17 & & 20 & 23 \\ \text { F } & 17 & 20 & & 23 & 24 \\ \text { G } & 20 & 21 & & 24 & 28 \end{array} $$

The production manager must determine the processing sequence for seven jobs through the grinding and deburring departments. The same sequence will be followed in both departments. The manager’s goal is to move the jobs through the two departments as quickly as possible. The foreman of the deburring department wants the SPT rule to be used to minimize the work-in- process inventory in his department. $$ \begin{array}{ccc} &{2}{c}{\begin{array}{c} \text { PROCESSING TIME } \\ \text { (hours) } \end{array}} \\ { 2 - 3 } \text { Job } & \text { Grinding } & \text { Deburring } \\ \hline \text { A } & 3 & 6 \\ \text { B } & 2 & 4 \\ \text { C } & 1 & 5 \\ \text { D } & 4 & 3 \\ \text { E } & 9 & 4 \\ \text { F } & 8 & 7 \\ \text { G } & 6 & 2 \end{array} $$ a. Prepare a schedule using SPT for the grinding department. b. What is the flow time in the grinding department for the SPT sequence? What is the total time needed to process the seven jobs in both the grinding and deburring departments? c. Determine a sequence that will minimize the total time needed to process the jobs in both departments. What flow time will result for the grinding department? d. Discuss the trade-offs between the two alternative sequencing arrangements. At what point would the production manager be indifferent concerning the choice of sequences?

A foreman has determined processing times at a work center for a set of jobs and now wants to sequence them. Given the information shown, do the following: a. Determine the processing sequence using (1) FCFS, (2) SPT, (3) EDD, and (4) CR. For each sequence, compute the average job tardiness, the average flow time, and the average number of jobs at the work center. The list is in FCFS order. b. Using the results of your calculations in part a, show that the ratio of average flow time and the average number of jobs measures are equivalent for all four sequencing rules. c. Determine the processing sequence that would result using the S/O rule. $$ \begin{array}{cccc} \text { Job } & \begin{array}{c} \text { Job Time } \\ \text { (days) } \end{array} & \begin{array}{c} \text { Due } \\ \text { Date } \end{array} & \begin{array}{c} \text { Operations } \\ \text { Remaining } \end{array} \\ \hline \text { a } & 4.5 & 10 & 3 \\ \text { b } & 6.0 & 17 & 4 \\ \text { c } & 5.2 & 12 & 3 \\ \text { d } & 1.6 & 27 & 5 \\ \text { e } & 2.8 & 18 & 3 \\ \text { f } & 3.3 & 19 & 1 \end{array} $$

Given the information in the following table, determine the processing sequence that would result using the S/O rule. $$ \begin{array}{cccc} \text { Job } & \begin{array}{c} \text { Remaining } \\ \text { Processing } \\ \text { Time (days) } \end{array} & \begin{array}{c} \text { Due } \\ \text { Date } \end{array} & \begin{array}{c} \text { Remaining } \\ \text { Number of } \\ \text { 0perations } \end{array} \\ \hline \text { a } & 5 & 8 & 2 \\ \text { b } & 6 & 5 & 4 \\ \text { c } & 9 & 10 & 4 \\ \text { d } & 7 & 12 & 3 \\ \text { e } & 8 & 10 & 2 \end{array} $$

Given the following information on job times and due dates, determine the optimal processing sequence using (1) FCFS, (2) SPT, (3) EDD, and (4) CR. For each method, find the average job flow time and the average job tardiness. Jobs are listed in order of arrival. $$ \begin{array}{ccc} \text { Job } & \begin{array}{c} \text { Job Time } \\ \text { (hours) } \end{array} & \begin{array}{c} \text { Due Date } \\ \text { (hours) } \end{array} \\ \hline \text { a } & 3.5 & 7 \\ \text { b } & 2.0 & 6 \\ \text { c } & 4.5 & 18 \\ \text { d } & 5.0 & 22 \\ \text { e } & 2.5 & 4 \\ \text { f } & 6.0 & 20 \end{array} $$

The Budd Gear Co. specializes in heat-treating gears for automobile companies. At 8:00 a.m., when Budd's shop opened today, five orders (listed in order of arrival) were waiting to be processed. $$ \begin{array}{cccc} \text { Order } & \begin{array}{c} \text { Order Size } \\ \text { (units) } \end{array} & \begin{array}{c} \text { Per Unit Time in } \\ \text { Heat Treatment } \\ \text { (minutes/unit) } \end{array} & \begin{array}{c} \text { Due Date } \\ \text { (min. from now) } \end{array} \\ \hline \text { A } & 16 & 4 & 160 \\ \text { B } & 6 & 12 & 200 \\ \text { C } & 10 & 3 & 180 \\ \text { D } & 8 & 10 & 190 \\ \text { E } & 4 & 1 & 220 \end{array} $$

The following table contains order-dependent setup times for three jobs. Which processing sequence will minimize the total setup time? $$ \begin{array}{lccccc} & & &{2}{c}{\begin{array}{c} \text { Following Job's } \\ \text { Setup Time (hrs.) } \end{array}} \\ & & \begin{array}{c} \text { Setup } \\ \text { Time (hrs.) } \end{array} & \text { A } & \text { B } & \text { C } \\ \hline \text { Preceding } & \text { A } & 2 & - & 3 & 5 \\ \text { Job } & \text { B } & 3 & 8 & - & 2 \\ & \text { C } & 2 & 4 & 3 & - \end{array} $$

The following table contains order-dependent setup times for three jobs. Which processing sequence will minimize the total setup time? $$ \begin{array}{|c|c|c|c|c|c|} \hline & & [b]{2}{*}{\begin{array}{c} \text { Setup } \\ \text { Time (hrs.) } \end{array}} & {3}{|c|}{\begin{array}{l} \text { Following Job's Setup } \\ \text { Time (hrs.) } \end{array}} \\ \hline {4}{*}{\begin{array}{l} \text { Preceding } \\ \text { Job } \end{array}} & & & \text { A } & \text { B } & \text { C } \\ \hline & \text { A } & 2.4 & - & 1.8 & 2.2 \\ \hline & \text { B } & 3.2 & 0.8 & - & \\ \hline & \text { C } & 2.0 & 2.6 & 1.3 & \\ \hline \end{array} $$

The following table contains order-dependent setup times for four jobs. For safety reasons, job C cannot follow job A, nor can job A follow job C. Determine the processing sequence that will minimize the total setup time. ( Hint: There are 12 alternatives.) $$ \begin{array}{|c|c|c|c|c|c|c|} \hline & & [b]{2}{*}{\begin{array}{c} \text { Setup } \\ \text { Time (hrs.) } \end{array}} & {4}{|c|}{\begin{array}{l} \text { Following Job's } \\ \text { Setup Time (hrs.) } \end{array}} \\ \hline & & & \text { A } & \text { B } & \text { C } & \text { D } \\ \hline & \text { A } & 2 & - & 5 & x & 4 \\ \hline \text { Preceding } & \text { B } & 1 & 7 & - & 3 & 2 \\ \hline [t]{2}{*}{\text { Job }} & \text { C } & 3 & x & 2 & \text { - } & 2 \\ \hline & \text { D } & 2 & 4 & 3 & 6 & - \\ \hline \end{array} $$

Given this information on planned and actual inputs and outputs for a service center, determine the work backlog for each period. The beginning backlog is 12 hours of work. The figures shown are standard hours of work. $$ \begin{aligned} &\text { PERIOD }\\ &\begin{array}{|l|l|c|c|c|c|c|} \hline {4}{*}{\text { Input }} & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} \\ { 2 - 7 } & \text { Planned } & 24 & 24 & 24 & 24 & 20 \\ \hline \text { Actual } & 25 & 27 & 20 & 22 & 24 \\ \hline \end{array}\\ &\begin{array}{|c|c|c|c|c|c|c|} \hline [t]{2}{*}{\text { Output }} & \text { Planned } & 24 & 24 & 24 & 24 & 23 \\ \hline & \text { Actual } & 24 & 22 & 23 & 24 & 24 \\ \hline \end{array} \end{aligned} $$

Given the following data on inputs and outputs at a work center, determine the cumulative deviation and the backlog for each time period. The beginning backlog is 7. $$ \begin{aligned} &\text { PERIOD }\\ &\begin{array}{|l|c|c|c|c|c|c|} \hline & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} \\ \hline \text { Planned } & 200 & 200 & 180 & 190 & 190 & 200 \\ \hline \text { Actual } & 210 & 200 & 179 & 195 & 193 & 194 \\ \hline \end{array} \end{aligned} $$ $$ \begin{array}{|l|l|c|c|c|c|c|c|} \hline & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} \\ \hline {2}{*}{\text { Output }} & \text { Planned } & 200 & 200 & 180 & 190 & 190 & 200 \\ { 2 - 7 } & \text { Actual } & 205 & 194 & 177 & 195 & 193 & 200 \\ { 2 - 7 } & & & & & & & \end{array} $$

Determine the minimum number of workers needed, and a schedule for the following staffing requirements, giving workers two consecutive days off per cycle (not including Sunday). $$ \begin{array}{lcccccc} \text { Day } & \text { Mon } & \text { Tue } & \text { Wed } & \text { Thu } & \text { Fri } & \text { Sat } \\ \hline \text { Staff needed } & 2 & 3 & 1 & 2 & 4 & 3 \end{array} $$

Determine the minimum number of workers needed, and a schedule for the following staffing requirements, giving workers two consecutive days off per cycle (not including Sunday). $$ \begin{array}{lcccccr} \text { Day } & \text { Mon } & \text { Tue } & \text { Wed } & \text { Thu } & \text { Fri } & \text { Sat } \\ \hline \text { Staff needed } & 3 & 4 & 2 & 3 & 4 & 5 \end{array} $$

Determine the minimum number of workers needed, and a schedule for the following staffing requirements, giving workers two consecutive days off per cycle (not including Sunday)$$ \begin{array}{lcccccc} \text { Day } & \text { Mon } & \text { Tue } & \text { Wed } & \text { Thu } & \text { Fri } & \text { Sat } \\ \hline \text { Staff needed } & 4 & 4 & 5 & 6 & 7 & 8 \end{array} $$

• DOI: 10.1007/978-3-030-51156-2_13
• Corpus ID: 220496820

Picture Fuzzy Linear Assignment Method and Its Application to Selection of Pest House Location

• Fatma Kutlu Gundogdu
• Published in Intelligent and Fuzzy… 10 June 2020
• Mathematics
• Intelligent and Fuzzy Techniques: Smart and Innovative Solutions

6 Citations

Evaluating public transport service quality using picture fuzzy analytic hierarchy process and linear assignment model, perfect score function in picture fuzzy set and its applications in decision-making problems, on laplacian energy of picture fuzzy graphs in site selection problem, topological data analysis of m-polar spherical fuzzy information with lam and sir models, developing a fuzzy optimized model for selecting a maintenance strategy in the paper industry: an integrated fgp-anp-fmea approach, a non-linear mathematical approach for solving matrix games with picture fuzzy payoffs with application to cyberterrorism attacks, 27 references, a bi-objective score-variance based linear assignment method for group decision making with hesitant fuzzy linguistic term sets, picture hesitant fuzzy set and its application to multiple criteria decision-making, the extended linear assignment method for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets, partitioned fuzzy measure-based linear assignment method for pythagorean fuzzy multi-criteria decision-making with a new likelihood, modeling of linear programming and extended topsis in decision making problem under the framework of picture fuzzy sets, weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems, an extended picture fuzzy vikor approach for sustainable supplier management and its application in the beef industry, similarity measures of picture fuzzy sets based on entropy and their application in mcdm, performance evaluation of green mine using a combined multi-criteria decision making method with picture fuzzy information, the linear assignment method for multicriteria group decision making based on interval‐valued pythagorean fuzzy bonferroni mean, related papers.

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Creative Assignments: Teaching with Images – Part 1

by Cosette Bruhns | Dec 17, 2019 | Instructional design , Services | 1 comment

Photo by Christopher Flynn on Unsplash

Images (e.g. photographs, illustrations, and visual metaphors) can facilitate student engagement and understanding in classroom assignments by making abstract concepts tangible and providing a different way of illustrating arguments to students. Instructors can assign images as submission requirements in order to encourage students to draw connections across boundaries and disciplines through a visual lens. Used with care, images can also support inclusive teaching practices by inviting students to engage with course content through different points of view, facilitating student access to remote objects or collections, and increasing opportunities for students who excel at visual learning to participate fully in assignments. In these cases, images serve as a portal for engaging with course material through a different framework (i.e., not text- or audio-based). Finally, using images in assignments can invite students to exercise different aspects of critical thinking skills, like visual literacy and lateral thinking, by encouraging students to develop an argument about or relating to some aspect of an image.

A Few Examples

Here are some examples of how images can be incorporated into student assignments to help you get started. The assignment types are listed in order of shallow to steep learning curve.

Image Discussion Board Posts

Discussion board posts are often assigned by instructors in order to invite students to expand their thoughts on a course reading or discussion. One way instructors can continue to broaden student learning about a topic outside of the classroom creatively is by assigning an image submission in a discussion board. By assigning an image as a submission requirement instead of text, instructors can stimulate student imagination and facilitate student ability to make visual connections between different ideas.

For example, in a literature course on Ovid’s Metamorphoses , an instructor could assign an image submission as a way to invite students to think about how to visualize an allegorical theme or passage from the text. Students could submit images in response to the selected theme or passage, along with a short one- to two-sentence explanation for why the image is related to the original theme. When the class next meets, instructors can draw on their image responses to engage students visually and creatively by asking students to further explain their reasons for submitting their image and why they think it is related to the original theme or passage.

For this type of assignment, Canvas-supported tools like Discussion Board can help achieve this goal. Follow the instructions on the Canvas resource page for more on how to create assignments using Canvas Discussion Board.

Tip: When creating a discussion post, remember to select “Allow threaded replies” under Options, in order to let students respond to each other’s comments.

Image Annotation

Image annotation is the ability to mark up an image with text or visual symbols in order to highlight some aspect within the image. Applied to an assignment, instructors can use the idea of image annotation to introduce skills like visual literacy or visual analysis, by asking students to annotate images in order to make an argument about or pertaining to an image based on close analysis of an object or aspect of the original image. By emphasizing a specific aspect of an image, instructors can encourage students to think critically about the relationship between the image and concepts or themes addressed in class.

For example, in a class addressing early modern Italian art, an instructor could ask students to individually or collaboratively annotate an image of Duccio’s Maestà in order to analyze different historical, political, and theological themes represented in the painting. The instructor could create an assignment asking students to isolate specific elements of the painting, using annotation methods, in order to identify main themes to explore further through individual projects or in-class discussion, strengthening the relationship between the assignment and the course. It might be a useful exercise to create a working list of objects, ideas, or concepts identified through the image annotation assignment that students can build on during the course. In a course that examines multiple images, instructors could return to that set of student-produced themes to see how they are represented in other images representing the Madonna. By drawing connections between concepts and images, instructors can begin to introduce students to skills like visual literacy, which is important for interpreting, understanding, and making meaning from images.

There are a number of easy-to-use tools for image annotation that are readily available. Google Jamboard is an interactive whiteboard that can be shared with multiple students. Features of Google Jamboard include real-time collaboration and a number of creative drawing tools for visualizing ideas. In an image annotation assignment, students could share a Google Jamboard file with the class that creatively isolates an aspect of the original image in order to share an observation or build an argument about that image.

Ex. Duccio di Buoninsegna, Maestà , c. 1308-1311. Google Jamboard can be used to add simple mark-ups to an image as an assignment or in real-time. The bottom tool in the tool bar is a digital laser pointer that can be used during a presentation to highlight an aspect of an image. As part of the Google Suite, Google Jamboard files can be easily shared with multiple collaborators.

Where to To Find Image Resources

A number of images are available for use in teaching and student assignments through fair use laws. There is a list of resources for finding fair use images on the UChicago wiki tools page . Many images are also easily searchable on databases such as LUNA , the University of Chicago’s image collections database, the Getty Search Gateway , and the Met Collection , to name a few. Several museums participate in open access policies, allowing their public domain images to be downloaded, used, and reproduced for scholarly and educational purposes. For further information on fair use policies, reach out to the University of Chicago’s Copyright Information Center , or the Visual Resource Center , which provides support in researching images or digitizing and developing a collection of images for research and teaching.

Getting Help and Next Steps

If you are interested in using image exercises in your classroom or as assignments, contact Academic Technology Solutions for help. ATS instructional designers can help you create exercises that support your broader learning objectives and select the appropriate software tools to use in your class.

Stay tuned for Part 2, in which we will discuss digital exhibitions!

Thanks, Cosette, this is great. Take a look at WeVu for this too. Images and pdfs, with group annotation, with private and public replies to annotations. Can be used for whole-class dialogue about parts of images, or for assignments where students’ annotations are only seen by instructors.

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The Assignment Method: Definition, Applications, and Implementation Strategies

Last updated 03/15/2024 by

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Understanding the assignment method

Optimized resource utilization, enhanced production efficiency, maximized profitability, applications of the assignment method, workforce allocation, production planning, sales territory management, resource budgeting.

• Optimizes resource utilization
• Enhances production efficiency
• Maximizes profitability
• Requires thorough analysis of past performance and market conditions
• Potential for misallocation of resources if not executed properly

Frequently asked questions

How does the assignment method differ from other resource allocation methods, what factors should organizations consider when implementing the assignment method, can the assignment method be applied to non-profit organizations or public sector agencies, what role does technology play in implementing the assignment method, are there any ethical considerations associated with the assignment method, key takeaways.

• The assignment method optimizes resource allocation to enhance efficiency and profitability.
• Applications include workforce allocation, production planning, sales territory management, and resource budgeting.
• Effective implementation requires thorough analysis of past performance and market conditions.
• Strategic allocation of resources can drive overall performance and revenue growth.

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Assignment Method: Examples of How Resources Are Allocated

What Is the Assignment Method?

The assignment method is a way of allocating organizational resources in which each resource is assigned to a particular task. The resource could be monetary, personnel , or technological.

Understanding the Assignment Method

The assignment method is used to determine what resources are assigned to which department, machine, or center of operation in the production process. The goal is to assign resources in such a way to enhance production efficiency, control costs, and maximize profits.

The assignment method has various applications in maximizing resources, including:

• Allocating the proper number of employees to a machine or task
• Allocating a machine or a manufacturing plant and the number of jobs that a given machine or factory can produce
• Assigning a number of salespersons to a given territory or territories
• Assigning new computers, laptops, and other expensive high-tech devices to the areas that need them the most while lower priority departments would get the older models

Companies can make budgeting decisions using the assignment method since it can help determine the amount of capital or money needed for each area of the company. Allocating money or resources can be done by analyzing the past performance of an employee, project, or department to determine the most efficient approach.

Regardless of the resource being allocated or the task to be accomplished, the goal is to assign resources to maximize the profit produced by the task or project.

Example of Assignment Method

A bank is allocating its sales force to grow its mortgage lending business. The bank has over 50 branches in New York but only ten in Chicago. Each branch has a staff that is used to bring in new clients.

The bank's management team decides to perform an analysis using the assignment method to determine where their newly-hired salespeople should be allocated. Given the past performance results in the Chicago area, the bank has produced fewer new clients than in New York. The fewer new clients are the result of having a small market presence in Chicago.

As a result, the management decides to allocate the new hires to the New York region, where it has a greater market share to maximize new client growth and, ultimately, revenue.

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• Table of Contents
• Course Home
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• Scratch ActiveCode
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• Instructors Guide
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• Report A Problem
• 8.1 Two-dimensional (2D) Arrays
• 8.1.1 2D Arrays (Day 1)
• 8.1.5 Set Value(s) in a 2D Array (Day 2)
• 8.2 Traversing 2D Arrays (nested loops)
• 8.2.1 Nested Loops for 2D Arrays (Day 1)
• 8.2.5 Enhanced For-Each Loop for 2D Arrays (Day 2)
• 8.3 2D Arrays Summary
• 8.4 Mixed Up Code Practice
• 8.5 Toggle Mixed Up or Write Code Practice
• 8.6 Code Practice with 2D Arrays
• 8.7 Free Response Questions
• 8.7.1 Free Response - Gray Image A
• 8.7.2 Free Response - Gray Image B
• 8.7.3 Free Response - Route Cipher A
• 8.7.4 Free Response - Route Cipher B
• 8.8 Multiple-Choice Exercises
• 8.8.1 Easier Multiple Choice Questions
• 8.8.2 Medium Multiple Choice Questions
• 8.8.3 Hard Multiple Choice Questions
• 8.9 College Board Picture Lab and Steganography Lab for 2D Arrays
• 8.9.1 Picture Lab A1 - A3
• 8.9.2 Picture Lab A4: 2D Arrays in Java
• 8.9.3 Picture Lab A5: Modifying a Picture
• 8.9.4 Picture Lab A6: Mirroring Pictures
• 8.9.5 Picture Lab A7: Mirroring Part of a Picture
• 8.9.6 Picture Lab A8: Creating a Collage
• 8.9.7 Picture Lab A9: Simple Edge Detection
• 8.10 More Code Practice with 2D Arrays
• 8.9.2. Picture Lab A4: 2D Arrays in Java" data-toggle="tooltip">
• 8.9.4. Picture Lab A6: Mirroring Pictures' data-toggle="tooltip" >

Time estimate: 90 min.

8.9.3. Picture Lab A5: Modifying a Picture ¶

Even though digital pictures have millions of pixels, modern computers are so fast that they can process all of them quickly. You will write methods in the Picture class that modify digital pictures.

8.9.3.1. Picture Classes: UML and Inheritance ¶

The Picture class inherits attributes and methods from the SimplePicture class and the SimplePicture class implements the DigitalPicture interface as shown in the Unified Modeling Language (UML) class diagram in the figure below.

Figure 1: A UML Class diagram ¶

A UML class diagram shows classes and the relationships between the classes. Each class is shown in a box with the class name at the top. The middle area shows attributes (instance or class variables) and the bottom area shows methods. The open triangle points to the class that the connected class inherits from. The straight line links show associations between classes. Association is also called a “has-a” relationship. The numbers at the end of the association links give the number of objects associated with an object at the other end.

For example, it shows that one Pixel object has one Color object associated with it and that a Color object can have zero to many Pixel objects associated with it. You may notice that the UML class diagram doesn’t look exactly like Java code. UML isn’t language specific.

The following questions require some knowledge about inheritance which is covered in the next unit, Unit 9. You may want to come back to do these questions after Unit 9.

Click on this Picture Lab project link and click on Show files to answer the following questions.

9-11-1: Click on the Picture Lab project link and click on Show files. Open Picture.java and look for the method getPixels2D . Is it there?

• The Picture.java class does not have the getPixels2D() method defined in it but it inherits it from the class SimplePicture.
• No, but it is inherited
• Correct, this class inherits that method from the class SimplePicture.

9-11-2: Open SimplePicture.java and look for the method getPixels2D . Is it there?

• Yes, the SimplePicture class contains the method getPixels2D.
• The SimplePicture class contains the method getPixels2D.

DigitalPicture p = new DigitalPicture();

• We cannot create an object from an interface because it is abstract.
• Correct! We cannot create an object from an interface because it is abstract.

DigitalPicture p = new SimplePicture();

• Yes. The SimplePicture class implements the interface DigitalPicture which means it is a type of Digital Picture.
• The SimplePicture class implements the interface DigitalPicture which means it is a type of Digital Picture.

DigitalPicture p = new Picture();

• Yes, because Picture extends SimplePicture which implements the interface DigitalPicture.
• Picture extends SimplePicture which implements the interface DigitalPicture.

SimplePicture p = new Picture();

Picture p = new SimplePicture();

• Picture inherits from SimplePicture, but not the other way around.

Because DigitalPicture declares a getPixels2D method that returns a two-dimensional array of Pixel objects, SimplePicture implements that interface, and Picture inherits from SimplePicture, you can use the getPixels2D method on a Picture object. You can loop through all the Pixel objects in the two-dimensional array to modify the picture. You can get and set the red, green, and/or blue value for a Pixel object. You can also get and/or set the Color value for a Pixel object. For example,

8.9.3.2. Image Modification Exercises ¶

What do you think you will see if you modify the beach picture to set all the blue values to zero? Do you think you will still see a beach? Run the main method in the Picture class in the Active Code below. The body of the main method will create a Picture object named beach from the “beach.jpg” file and call the method that sets the blue values at all pixels to zero. The following code is the main method from the Picture class.

The method zeroBlue in the Picture class gets a two-dimensional array of Pixel objects from the current picture (the picture the method was called on). It then declares a variable that will refer to a Pixel object named pixelObj . It uses a nested for-each loop to loop through all the pixels in the picture. Inside the body of the nested for-each loop it sets the blue value for the current pixel to zero. Note that you cannot change the elements of an array when you use a for-each loop. If, however, the array elements are references to objects that have methods that allow changes, as they are here, you can change the internal state of objects referenced in the array.

The following code is the zeroBlue method in the Picture class.

Another option is to use for loops with indices to visit each pixel in the picture:

You may have done this exercise in the programming challenge in lesson 8.2. Using the zeroBlue method as a starting point, write the method keepOnlyBlue that will keep only the blue values, that is, it will set the red and green values to zero. Be sure to call the new test method in the main method.

You can use beach.jpg or one of the other images seen at the bottom of this lesson in the active codes below which are autograded. To use your own images, you can fork this replit.com Swing project or this alternative replit.com project (click output.jpg to see the result) or download the project files form replit to your own IDE.

Picture Lab keepOnlyBlue: Using zeroBlue() as a guide, write a method called keepOnlyBlue() that keeps only the blue values by setting the red and green values to zero. Change the method call in main from zeroBlue to keepOnlyBlue to test it. Try one of the other images below like metalLion.jpg, water.jpg, kitten.jpg, puppies.jpg, blueMotorcycle.jpg, or student.jpg.

2. Write the negate method to negate all the pixels in a picture. To negate a picture, set the red value to 255 minus the current red value (use the pixel’s getRed method), the green value to 255 minus the current green value and the blue value to 255 minus the current blue value. Be sure to call the new test method in the main method.

Picture Lab negate: Write a method called negate() that negates all the pixels in a picture by setting the red value to 255 minus the current red value (use the pixel’s getRed() method), the green value to 255 minus the current green value and the blue value to 255 minus the current blue value. Try one of the other images below like beach.jpg, metalLion.jpg, water.jpg, kitten.jpg, puppies.jpg, blueMotorcycle.jpg, or student.jpg.

3. Write the grayscale method to turn the picture into shades of gray. Set the red, green, and blue values to the average of the current red, green, and blue values (add all three values and divide by 3). Be sure to call the new test method in the main method.

Picture Lab Grayscale: Write a method called grayscale to turn the picture into shades of gray. Set the red, green, and blue values to the average of the current red, green, and blue values (add all three values and divide by 3). Try another image file from beach.jpg, metalLion.jpg, water.jpg, kitten.jpg, puppies.jpg, blueMotorcycle.jpg, student.jpg.

4. Challenge — Explore the water.jpg picture. Write a method fixUnderwater() to modify the pixel colors to make the fish easier to see. There are many ways to do this, but you could try increasing one of the colors by a certain factor. Here are some more complex algorithms for increasing the brightness and contrast of images https://ie.nitk.ac.in/blog/2020/01/19/algorithms-for-adjusting-brightness-and-contrast-of-an-image/ .

Picture Lab fix-underwater: Write a method called fixUnderwater() to modify the pixel colors to make the fish easier to see. Try increasing one of the colors by a certain factor.

Extra Challenge — This exercise is not in the original picture lab. Can you change just the t-shirt color in student.jpg? You will need to use an if statement inside the loops to look for the red t-shirt color and then change it. The red pixels probably have a high red value (for example greater than 200) and low green and blue values (for example less than 100). After changing the t-shirt color, try changing the background color or the hair color.

Can you change just the t-shirt color in student.jpg? You will need to use an if statement inside the loops to look for the red t-shirt color and then change it. The red pixels probably have a high red value (for example greater than 200) and low green and blue values (for example less than 100). After changing the t-shirt color, try changing the background color or the hair color.

Choose from these images:

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The incredible HALK: borrowing data for age assignment

Understanding age and growth are important for fisheries science and management; however, age data are not routinely collected for many populations. We propose and test a method of borrowing age–length data across increasingly broader spatiotemporal levels to create a hierarchical age–length key (HALK). We assessed this method by comparing growth and mortality metrics to those estimated from lake–year age–length keys ages using seven common freshwater fish species across the upper Midwestern United States. Levels used for data borrowing began most specifically by borrowing within lake across time and increased in breadth to include data within the Hydrologic Unit Code (HUC) 10 watershed, HUC8 watershed, Level III Ecoregion, and finally a species-wide data ALK using all available data with our study for a species. Median deviation in mean length of age-3 fish was within 1 cm for the most specific HALK levels, and median deviation in total annual mortality was close to 0 for most species when borrowing occurred within HUC10 and HUC8 watersheds. Percent error in growth curves increased with data borrowing, but plateaued—or even decreased—for some species when data borrowing expanded across spatial levels. We present the HALK as a method for gaining age information about a fishery when age data are unavailable.

Citation Information

Browse Course Material

Course info.

• Felice C. Frankel

Departments

• Chemical Engineering

As Taught In

• Engineering
• Graphic Design
• Photography
• Health and Medicine
• Teaching and Education

Learning Resource Types

Making science and engineering pictures: a practical guide to presenting your work, week 3: light.

The Greek roots of the word photography are “photos” (meaning light) and “graphé” (meaning drawing). Taken together photography means “drawing with light.” In this week, we will investigate light.

Observe difference between various light sources (LED, tungsten, fluorescent, available light) as well as the effect of bounced light, shadows, and reflective / transmitted light.

What You’ll Need

• SLR camera with interchangeable lens capacity
• 105 macro lens
• Your camera’s software and cable to view images on your computer
• An additional lighting source
• Find an image of a small object (in a magazine or online), scan or clip the image, use drawing tools to indicate on the image where you think the light sources are positioned.
• Take an image of your object in daylight and label it image 1. Then add a secondary light source and label it image 2.
• Describe the differences
• Indicate where the shadow(s) lie
• Make a determination which image is more effective and explain why

Optional Assignments

Take an image of your object with a direct light source and then use a white card to bounce the light (remember to keep exposure accurate) and take another image.

Think creatively about an unusual lighting method to photograph your object and take a picture. How did the unusual light source impact the photo? Did you learn anything about lighting?

Visual Index

Week 3 Visual Index (PDF)

Week 3 Summary (PDF)

Course Videos

Video 11: An introduction

Video 12: Fluorescence

Video 13: Use Your Imagination

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Samar Education

Assignment method of teaching, assignment method.

Assignment method as the name suggests students are assigned some tasks-theoretical as well as practical nature for being performed at their parts in the school, at the workshop or laboratory, library or at their home. They are provided necessary guidance instruction and also the specific outlines for completing their assignments in time.

Assignment is a necessary part of the teaching and learning process, helping us measure whether our students have really learned what we want them to learn. While exams and quizzes are certainly favorite and useful methods of assessment, out of class assignments (written or otherwise) can offer similar insights into our students' learning. And just as creating a reliable test takes thoughtfulness and skill, so does creating meaningful and effective assignments.

Undoubtedly, many instructors have been on the receiving end of disappointing student work, left wondering what went wrong, and often, those problems can be remedied in the future by some simple fine-tuning of the original assignment. This paper will take a look at some important elements to consider when developing assignments, and offer some easy approaches to creating a valuable assessment experience for all involved.

Features of the Assignment Method

• More emphasis is given on practical work.
• In this method all aspects of the subject matter are included.
• The teacher has to provide adequate guidance.
• Students get used to doing work on their own.
• Each student works according to his capacity.
• Students develop the habit of fulfilling their responsibilities.

Importance of Assignments

• Homework acts as a motivator of the students. This motivates the student to make maximum use of the acquired knowledge.
• Homework also saves time as it eliminates the need to re-read the lesson in class.
• Homework gives students opportunities to express their ideas through self-activity.
• Apart from the school, the home environment is also necessary to make the knowledge permanent, otherwise the ignorant will be unable to remember the absorbed knowledge.
• Properly planned homework helps in guidance.
• Through homework, students have to write their own answers to the questions. They bring books on various subjects from the library to read at home. This develops the habits of self-study in them.

Types of assignment method

1. page-by-page assignment.

This type is sometimes called the textbook assignment. It designates the number of pages to be covered. Page-by-page assignment is unsatisfactory, but recent studies have revealed that this type is still widely used in the elementary grades.

2. Problem assignment

This type of assignment gets away from the basic textbook idea. It encourages the use of references and stimulates reflective thinking. In this type the problem to be solved is the prime consideration. Special directions and suggestions are important in this type of assignment.

3. Topical assignment

In this kind of assignment the topic to be developed is the prime consideration. This is also a form of textbook assignment which is often given in social and natural science subjects.

4. Project assignment

This is a special type of assignment which is best adapted to vocational courses, to natural science subjects, and in some measure to social science subjects and other content subjects. In this type of assignment a project is considered a unit.

5. Contract assignment

This form of assignment is extensively used in individualized types of instruction with the main purpose of adjusting the task to the ability and interest of the individual.

6. Unit assignment

This type is associated with the Mastery Plan and the Cycle Plan of instruction. It is best adapted to the subjects which are divided into units. The so-called flexible assignment is used with the unit assignment plan.

7. Cooperative or group assignment

Cooperative assignment is most frequently utilized in a socialized type of recitation, or in a project method of instruction. Assignment of this type stimulates pupils to do their own thinking and to organize their materials. Here pupils also participate in determining desirable objectives and in deciding what should be done to attain them. Cooperative assignment can be utilized to advantage in many high school classes.

8. Syllabus assignment

Syllabus assignment is often utilized in the college or university. In this type of assignment, questions and references are given to guide the students. Here again guide questions and other suggestions are given to insure attention to the important points of the lesson.

9. Drill assignment

It is the purpose of this assignment to strengthen the connections formed in the process of growth in mental motor skills. Memorizing a poem or mastery of facts or simple combination facts in Arithmetic are good examples of this type of assignment. Drill assignment, like other type of assignment, should be motivated.

Merits of Assignment Method

1. Development of useful habit:- Assignment method helps in imbibing useful habits like below:

• (a) A sense of responsibility of finishing the task in hand.
• (b) Habit of self study and confidence in one's abilities.
• (c) Self dependency in action and thought.

2. Recognition of individual differences:- The assignment are alloted to the students on the basis of their mental abilities, capacities, interests and aptitudes. They are also allowed to execute their assignments according to their own pace. The brighter ones have not to wait for the slow learners as they can undertake next higher assignments after finishing the one in hand.

3. Provides freedom to work:- There is no restrictions of time both in term of starting and finishing with the assignment. The duration for the execution of the assignment depends upon the mental and physical stamina of the pupil. They may go to the library or work in the laboratory. according to their convenience.

Demerits of Assignment Method

1. Strain on the teacher:- The teacher is expected to work hard in the method for preparing the assignments, assigning these to the students individually or in groups, guiding the students at the proper time in a proper way and evaluating their work.

2. Not suitable to all types of learners:- This method does not suit student of low intelligence and also those having average capacities. Similarly, it cannot also work with the students who are irresponsible or careless and thus cannot be relied to finish their assignment properly in a specified time.

3. Provides stimulation for cheating:- Assignment method may provide temptation or compulsion to a number of students for copying the answers of the questions and results of the experiments from the readily available source or note book of their classmates. If it happens, the very purpose of these assignments is completely lost.

Precautions in the Planning of Assignments

• The selection of homework should be done keeping in view the prior knowledge of the students.
• Homework should be inspirational.
• In the planning of homework, the interests and respects of the students should be taken care of. 4. Homework should be definite and clear.
• Homework should be based on the teaching formula of 'from simple to complex'.
• There should be mutual harmony in homework.
• There should be variety in homework.
• Homework should be useful.
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• Demonstration Method of Teaching
• Discussion Method of Teaching
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