disadvantages of assignment problem in operational research

Assignment Problem: Meaning, Methods and Variations | Operations Research

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

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Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

How to Solve the Assignment Problem: A Complete Guide

Table of Contents

Assignment problem is a special type of linear programming problem that deals with assigning a number of resources to an equal number of tasks in the most efficient way. The goal is to minimize the total cost of assignments while ensuring that each task is assigned to only one resource and each resource is assigned to only one task. In this blog, we will discuss the solution of the assignment problem using the Hungarian method, which is a popular algorithm for solving the problem.

Understanding the Assignment Problem

Before we dive into the solution, it is important to understand the problem itself. In the assignment problem, we have a matrix of costs, where each row represents a resource and each column represents a task. The objective is to assign each resource to a task in such a way that the total cost of assignments is minimized. However, there are certain constraints that need to be satisfied – each resource can be assigned to only one task and each task can be assigned to only one resource.

Solving the Assignment Problem

There are various methods for solving the assignment problem, including the Hungarian method, the brute force method, and the auction algorithm. Here, we will focus on the steps involved in solving the assignment problem using the Hungarian method, which is the most commonly used and efficient method.

Step 1: Set up the cost matrix

The first step in solving the assignment problem is to set up the cost matrix, which represents the cost of assigning a task to an agent. The matrix should be square and have the same number of rows and columns as the number of tasks and agents, respectively.

Step 2: Subtract the smallest element from each row and column

To simplify the calculations, we need to reduce the size of the cost matrix by subtracting the smallest element from each row and column. This step is called matrix reduction.

Step 3: Cover all zeros with the minimum number of lines

The next step is to cover all zeros in the matrix with the minimum number of horizontal and vertical lines. This step is called matrix covering.

Step 4: Test for optimality and adjust the matrix

To test for optimality, we need to calculate the minimum number of lines required to cover all zeros in the matrix. If the number of lines equals the number of rows or columns, the solution is optimal. If not, we need to adjust the matrix and repeat steps 3 and 4 until we get an optimal solution.

Step 5: Assign the tasks to the agents

The final step is to assign the tasks to the agents based on the optimal solution obtained in step 4. This will give us the most cost-effective or profit-maximizing assignment.

Solution of the Assignment Problem using the Hungarian Method

The Hungarian method is an algorithm that uses a step-by-step approach to find the optimal assignment. The algorithm consists of the following steps:

• Subtract the smallest entry in each row from all the entries of the row.
• Subtract the smallest entry in each column from all the entries of the column.
• Draw the minimum number of lines to cover all zeros in the matrix. If the number of lines drawn is equal to the number of rows, we have an optimal solution. If not, go to step 4.
• Determine the smallest entry not covered by any line. Subtract it from all uncovered entries and add it to all entries covered by two lines. Go to step 3.

The above steps are repeated until an optimal solution is obtained. The optimal solution will have all zeros covered by the minimum number of lines. The assignments can be made by selecting the rows and columns with a single zero in the final matrix.

Applications of the Assignment Problem

The assignment problem has various applications in different fields, including computer science, economics, logistics, and management. In this section, we will provide some examples of how the assignment problem is used in real-life situations.

Applications in Computer Science

The assignment problem can be used in computer science to allocate resources to different tasks, such as allocating memory to processes or assigning threads to processors.

Applications in Economics

The assignment problem can be used in economics to allocate resources to different agents, such as allocating workers to jobs or assigning projects to contractors.

Applications in Logistics

The assignment problem can be used in logistics to allocate resources to different activities, such as allocating vehicles to routes or assigning warehouses to customers.

Applications in Management

The assignment problem can be used in management to allocate resources to different projects, such as allocating employees to tasks or assigning budgets to departments.

Let’s consider the following scenario: a manager needs to assign three employees to three different tasks. Each employee has different skills, and each task requires specific skills. The manager wants to minimize the total time it takes to complete all the tasks. The skills and the time required for each task are given in the table below:

The assignment problem is to determine which employee should be assigned to which task to minimize the total time required. To solve this problem, we can use the Hungarian method, which we discussed in the previous blog.

Using the Hungarian method, we first subtract the smallest entry in each row from all the entries of the row:

Next, we subtract the smallest entry in each column from all the entries of the column:

We draw the minimum number of lines to cover all the zeros in the matrix, which in this case is three:

Since the number of lines is equal to the number of rows, we have an optimal solution. The assignments can be made by selecting the rows and columns with a single zero in the final matrix. In this case, the optimal assignments are:

• Emp 1 to Task 3
• Emp 2 to Task 2
• Emp 3 to Task 1

This assignment results in a total time of 9 units.

I hope this example helps you better understand the assignment problem and how to solve it using the Hungarian method.

Solving the assignment problem may seem daunting, but with the right approach, it can be a straightforward process. By following the steps outlined in this guide, you can confidently tackle any assignment problem that comes your way.

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Operations Research

1 Operations Research-An Overview

• History of O.R.
• Approach, Techniques and Tools
• Phases and Processes of O.R. Study
• Typical Applications of O.R
• Limitations of Operations Research
• Models in Operations Research
• O.R. in real world

2 Linear Programming: Formulation and Graphical Method

• General formulation of Linear Programming Problem
• Optimisation Models
• Basics of Graphic Method
• Important steps to draw graph
• Multiple, Unbounded Solution and Infeasible Problems
• Solving Linear Programming Graphically Using Computer
• Application of Linear Programming in Business and Industry

3 Linear Programming-Simplex Method

• Principle of Simplex Method
• Computational aspect of Simplex Method
• Simplex Method with several Decision Variables
• Two Phase and M-method
• Multiple Solution, Unbounded Solution and Infeasible Problem
• Sensitivity Analysis
• Dual Linear Programming Problem

4 Transportation Problem

• Basic Feasible Solution of a Transportation Problem
• Modified Distribution Method
• Stepping Stone Method
• Unbalanced Transportation Problem
• Degenerate Transportation Problem
• Transhipment Problem
• Maximisation in a Transportation Problem

5 Assignment Problem

• Solution of the Assignment Problem
• Unbalanced Assignment Problem
• Problem with some Infeasible Assignments
• Maximisation in an Assignment Problem
• Crew Assignment Problem

6 Application of Excel Solver to Solve LPP

• Building Excel model for solving LP: An Illustrative Example

7 Goal Programming

• Concepts of goal programming
• Goal programming model formulation
• Graphical method of goal programming
• The simplex method of goal programming
• Using Excel Solver to Solve Goal Programming Models
• Application areas of goal programming

8 Integer Programming

• Some Integer Programming Formulation Techniques
• Binary Representation of General Integer Variables
• Unimodularity
• Cutting Plane Method
• Branch and Bound Method
• Solver Solution

9 Dynamic Programming

• Dynamic Programming Methodology: An Example
• Definitions and Notations
• Dynamic Programming Applications

10 Non-Linear Programming

• Solution of a Non-linear Programming Problem
• Convex and Concave Functions
• Kuhn-Tucker Conditions for Constrained Optimisation
• Quadratic Programming
• Separable Programming
• NLP Models with Solver

11 Introduction to game theory and its Applications

• Important terms in Game Theory
• Saddle points
• Mixed strategies: Games without saddle points
• 2 x n games
• Exploiting an opponent’s mistakes

12 Monte Carlo Simulation

• Reasons for using simulation
• Monte Carlo simulation
• Limitations of simulation
• Steps in the simulation process
• Some practical applications of simulation
• Two typical examples of hand-computed simulation
• Computer simulation

13 Queueing Models

• Characteristics of a queueing model
• Notations and Symbols
• Statistical methods in queueing
• The M/M/I System
• The M/M/C System
• The M/Ek/I System
• Decision problems in queueing

Assignment Problem

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The problem of optimally assigning m individuals to m jobs, so that each individual is assigned to one job, and each job is filled by one individual. The problem can be formulated as a linear-programming problem with the objective function measuring the (linear) utility of the assignment as follows:

The problem is a special form of the transportation problem and, as such,...

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Burkard, R., Dell’Amico, M., & Marterllo, S. (2009). Assignment problems . Philadelphia: SIAM.

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Kuhn, H. W. (1995). The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2 , 83–97.

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Robert H. Smith School of Business, University of Maryland, College Park, MD, USA

Saul I. Gass

Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, MD, USA

Michael C. Fu

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(2013). Assignment Problem. In: Gass, S.I., Fu, M.C. (eds) Encyclopedia of Operations Research and Management Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1153-7_200965

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Operational research as implementation science: definitions, challenges and research priorities

• Thomas Monks 1  

Implementation Science volume  11 , Article number:  81 ( 2015 ) Cite this article

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Operational research (OR) is the discipline of using models, either quantitative or qualitative, to aid decision-making in complex implementation problems. The methods of OR have been used in healthcare since the 1950s in diverse areas such as emergency medicine and the interface between acute and community care; hospital performance; scheduling and management of patient home visits; scheduling of patient appointments; and many other complex implementation problems of an operational or logistical nature.

To date, there has been limited debate about the role that operational research should take within implementation science. I detail three such roles for OR all grounded in upfront system thinking: structuring implementation problems, prospective evaluation of improvement interventions, and strategic reconfiguration. Case studies from mental health, emergency medicine, and stroke care are used to illustrate each role. I then describe the challenges for applied OR within implementation science at the organisational, interventional, and disciplinary levels. Two key challenges include the difficulty faced in achieving a position of mutual understanding between implementation scientists and research users and a stark lack of evaluation of OR interventions. To address these challenges, I propose a research agenda to evaluate applied OR through the lens of implementation science, the liberation of OR from the specialist research and consultancy environment, and co-design of models with service users.

Operational research is a mature discipline that has developed a significant volume of methodology to improve health services. OR offers implementation scientists the opportunity to do more upfront system thinking before committing resources or taking risks. OR has three roles within implementation science: structuring an implementation problem, prospective evaluation of implementation problems, and a tool for strategic reconfiguration of health services. Challenges facing OR as implementation science include limited evidence and evaluation of impact, limited service user involvement, a lack of managerial awareness, effective communication between research users and OR modellers, and availability of healthcare data. To progress the science, a focus is needed in three key areas: evaluation of OR interventions, embedding the knowledge of OR in health services, and educating OR modellers about the aims and benefits of service user involvement.

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Operational research (OR) is the discipline of using models, either quantitative or qualitative, to aid decision-making in complex problems [ 1 ]. The practice of applied healthcare OR distinguishes itself from other model-based disciplines such as health economics as it is action research based where operational researchers participate collaboratively with those that work in or use the system to define, develop, and find ways to sustain solutions to live implementation problems [ 2 ]. The methods of OR have been used in healthcare since the 1950s [ 3 ] to analyse implementation problems in diverse areas such as emergency departments [ 4 – 6 ] and management policies for ambulance fleet [ 7 ]; acute stroke care [ 8 – 11 ], outpatient clinic waiting times [ 12 ], and locations [ 13 ]; cardiac surgery capacity planning [ 14 ]; the interface between acute and community care [ 15 ]; hospital performance [ 16 ]; scheduling and routing of nurse visits [ 17 ]; scheduling of patient appointments [ 18 ]; and many other complex implementation problems of an operational or logistical nature.

Implementation science is the study of methods to increase the uptake of research findings in healthcare [ 19 ]. Given the volume of OR research in healthcare implementation problems, it is remarkable that limited discussion of the discipline has occurred within the implementation science literature. A rare example of debate is given by Atkinson and colleagues [ 20 ] who introduce the notion of system science approaches for use in public health policy decisions. Their argument focused on two modelling methods, system dynamics and agent-based simulation, and the potential benefits they bring for disinvestment decisions in public health. To complement and extend this debate, I define the overlap between implementation science and OR. I have focused on the upfront role that OR takes when used as an implementation science tool. Although some detail of method is given, the full breath of OR is beyond the scope of this article; a detailed overview of all the methods can be found elsewhere [ 21 ]. I describe three roles for OR within implementation science: structuring an implementation problem, prospective evaluation of an intervention, and strategic reconfiguration of services. For each role, I provide a case study to illustrate the concepts described. I then describe the challenges for OR within implementation science at the organisational, interventional, and disciplinary levels. Given these challenges, I derive a research agenda for implementation science and OR.

OR to structure an implementation problem

The first role for OR in implementation science is to provide a mechanism for structuring an implementation problem. Within OR, problem structuring methods provide participatory modelling approaches to support stakeholders in addressing problems of high complexity and uncertainty [ 22 ]. These complex situations are often poorly defined and contain multiple actors with multiple perspectives and conflicting interests [ 23 ]. As such, they are unsuitable for quantitative approaches. Problem structuring methods aim to develop models that enable stakeholders to reach a shared understanding of their problem situation and commit to action(s) that resolve it [ 23 ]. Approaches might serve as a way to clearly define objectives for a quantitative modelling study [ 24 ], systematically identify the areas to intervene within a system [ 25 ], or may be an intervention to improve a system in its own right.

A case example—understanding patient flow in the mental health system

A mental health service provider in the UK provided treatment to patients via several specialist workforces. Here, I focus on two: psychology and psychiatric talking therapies (PPT) and recovering independent life (RIL) teams. Waiting times to begin treatment under these services were high (e.g. for RIL team median = 55 days, inter-quartile range = 40–95 days), and treatment could last many years once it had begun. The trust’s management team were eager to implement new procedures to help staff manage case load and hence reduce waiting times to prevent service users, here defined as patients, their families, and carers, from entering a crisis state due to diminishing health without treatment. Management believed that reasons for delays were more complex than lack of staff, but the exact details were unclear and there was much disagreement between the senior management. The implementation science intervention I detail was conducted as an OR problem structuring exercise.

A system dynamics (SD) model was constructed to aid management target their interventions. SD is a subset of system thinking—the process of understanding how things within a system influence one another within the whole. SD models can be either qualitative or quantitative. In this case, a purely qualitative model was created. Figure  1 illustrates stock and flow notation that is commonly used in SD. The example is the concept of a simple waiting list for a (generic) treatment. It can be explained as follows. General practitioners (GPs) refer service users to a waiting list at an average daily rate, while specialist clinicians treat according to how much daily treatment capacity they have. The variable waiting list is represented as a rectangular stock: an accumulation of patients. The waiting list stock is either depleted or fed by rate variables, referring and treating, represented as flows (pipes with valves) entering and leaving the stock. Figure  1 also contains two feedback loops that are illustrated by the curved lines. The first loop is related to the GP reluctance to refer to a service with a long waiting time. As the waiting list for a service increases in number, so does the average waiting time of service users and so does the pressure for GPs to consider an alternative service (lowering the daily referral rate). The second loop is related to specialist clinicians reacting to long waiting lists by creating a small amount of additional treatment capacity and increasing admission rates.

Example system thinking for a waiting list—stock and flow notation. Notation guide. Rectangles represent stocks which are acculations of quantity of interest; Pipes with valves represent flows which feed or deplete stocks; arrows represent how one aspect of a system positively or negatively influences another

A preliminary version of the SD model was created using a series of interviews with clinicians and managers from the three services. This was followed by a group model building workshop that involved all senior management. Group model building is a structured process that aims to create a shared mental model of a problem [ 26 ]. The workshop began with a nominal group exercise. The group were asked to individually write down what they believed were the key factors that affected patient waiting times. The group were specifically asked to focus on strategic issues as opposed to detailed process-based problems. After all individual results had been shared, the group were asked to (i) hypothesise how these factors influenced each other and (ii) propose any missing variables that may mediate influence. For example, available treatment capacity is reduced by non-clinical workload. Non-clinical workload is increased by several other factors (discussed below in results) and so on.

Figure  2 illustrates one of the qualitative SD models developed in collaboration with the mental health trust. It uses the same stock and flow notation illustrated in Fig.  1 . The model shown is focussed on the RIL teams. Several insights were gained in its construction. First, it was clear to all parties that that this was not a simple demand and treatment capacity problem. For example, a great deal of non-core work takes place due to monitoring of ‘discharged’ service users within social care. The fraction of service users who undergo monitoring is determined by the degree of trust between clinicians and social care teams. When trust is low, the fraction of service users monitored increases and vice versa. A similar soft issue can be found in the discharge of complex patients, i.e. those that require a combination of medication, management by GPs in the community, and social care input. In this case, there is a delay while GPs build confidence that it is appropriate for a patient to be discharged into their care. While this negotiation takes place, a patient still requires regular monitoring by a mental health clinician. Other systemic issues are also visible. For example, the long delays in beginning treatment lead to clinicians spending time contacting patients by phone before they were admitted. This all takes time and reinforces the delay cycle.

A simplified version of the RIL team patient flow model

The results of the modelling were used to inform where interventions could be targeted. For example, a more detailed qualitative SD study to identify the trust issues between clinicians, social services, and general practitioners.

OR as a tool for prospective evaluation

The second role of OR within implementation science is as a prospective evaluation tool. That is, to provide a formal assessment and appraisal of competing implementation options or choices before any actual implementation effort, commitment of resources or disinvestment takes place. Informally, this approach is often called what-if analysis [ 21 ]. A mathematical or computational model of a healthcare system is developed that predicts one or more measures of performance, for example, service waiting times, patients successfully treated, avoided mortality, or operating costs. The model can be set up to test and compare complex interventions to the status-quo. For example, decision makers may wish to compare the number of delayed transfers of care in a rehabilitation pathway before and after investment in services to prevent hospital admissions and disinvestment in rehabilitation in-patient beds. The approach has been applied widely in the areas outlined in the introduction to this article.

A case example—emergency medicine capacity planning

As a simple case example of prospective evaluation, consider the emergency department (ED) overcrowding problems faced by the United Kingdom’s (UK) National Health Service (NHS). The performance of NHS EDs is (very publically) monitored by recording the proportion of patients who can be seen and discharged from an ED within 4 hours of their arrival. The UK government has set a target that 95 % of service users must be processed in this time. In recent years, many NHS EDs have not achieved this benchmark. The reasons for this are complex and are not confined to the department [ 27 ] or even the hospital [ 15 ]. However, given the high public interest, many EDs are attempting to manage the demands placed on them by implementing initiatives to reduce waiting times and optimise their own processes.

Our case study took place at a large ‘underperforming’ hospital in the UK. The management team were divided in their view about how to reduce waiting times. One option was to implement a clinical decision-making unit (CDU). A CDU is a ward linked to the ED that provides more time for ED clinicians to make decisions about service users with complex needs. However, at times of high pressure, a CDU can also serve as buffer capacity between the ED and the main hospital. That is, a CDU provides space for service users at risk of breaching the 4-h target once admitted; service users are no longer at risk of breach. The question at hand was if a CDU were implemented, how many beds are required in order for the ED to achieve the 95 % benchmark?

Figure  3 illustrates the logic of a computer simulation model that was developed to evaluate the implementation of a CDU on ED waiting times. A computer simulation model is a simplified dynamic representation of the real system that in most cases is accompanied by an animation to help understanding. In this case, the simulation mimicked the flow of patients into an ED, their assessment, and treatment by clinicians and then flow out to different parts of the hospital or to leave the hospital entirely. The scope of the modelling included the hospital’s Acute Medical Unit (AMU) that admits medical patients from the ED. In Fig.  3 , the rectangular boxes represent processes, for example, assessment and treatment in the ED. The partitioned rectangles represent queues, for example, patient waiting for admission to the AMU. The model was set up to only admit patients to the CDU who had been in ED longer than 3.5 h and only then if there was a free bed. Once a patient’s CDU stay was complete, they would continue on their hospital journey as normal, i.e. discharged home, admitted to the AMU or admitted to another in-patient ward.

Emergency department and clinical decision-making unit model. Notation guide. Rectangles represent processes; partitioned rectangles represent queues; ellipses represent start and end points; arrows represent the direction of patient flow

In the model, the various departments and wards are conceptualised as stochastic queuing systems subject to constraints. This means that the variability we see in service user arrival and treatment rates (e.g. sudden bursts in arrivals combined with more complex and hence slower treatments) combined with limited cubicle and bed numbers results in queues. There are three reasons why prospective evaluation is appropriate for these systems. First, capacity planning for such complex systems based on average occupancy fails to take queuing into account and will substantially underestimate capacity requirements [ 28 ]. Second, the processing time, i.e. the time taken to transfer a patient to a ward and then to make a clinical decision, within a CDU is uncertain, although it is likely to be slower than the high pressure environment of the ED. Third, as the same ED and AMU clinicians must staff the CDU, the (negative or positive) impact on their respective processing times is uncertain.

The model developed was a discrete-event simulation [ 29 ] that mimics the variation in service user arrival and treatment rates in order to predict waiting times. The uncertainty in CDU processing time was treated as an unknown and varied in a sensitivity analysis . The limits of this analysis were chosen as 2 and 7 h on average, as these were observed in similar wards elsewhere.

The model predicted that the number of CDU beds would need to be between 30 and 70 in order to achieve the ED target (for reference, the ED had 10 cubicles for minor cases and 18 cubicles for major cases). This result illustrated that even if a decision was made in 2 h on average with no negative effect on ED or AMU processing time, the CDU would need to be at least the same size as the ED overall. It also highlighted that the CDU impact on ED performance was highly sensitive to processing time.

The benefit of evaluating the CDU implementation upfront was that it ruled the CDU out as a feasible intervention before any substantial resource had been mobilised to implement it. The hospital could not safely staff a 30-bedded CDU or indeed provide space for that size of ward. As such, the modelling helped the management team abandon their CDU plan and consider alternative solutions with minimal cost and no disruption to the service.

OR as a tool for strategic reconfiguration

The previous section described an implementation science approach to evaluate a small number of competing options at an operational level. In some instances, particularly in healthcare logistics and estate planning, a more strategic view of a system is needed to shortlist or choose options for reconfiguration. In such implementation problems, there may be a large number of options reaching into the hundreds, if not hundreds of thousands of competing alternatives. To analyse these problems, mathematical and computational optimization techniques are required. For example, if a provider of sexual health services wanted to consolidate community clinics from 50 to 20 and there are 100 candidate locations, then there are in the order of 10 20 configurations to consider. OR’s implementation science role is to provide tools that identify options that help meet a strategic objective. For example, this might be maintaining equitable patient access to services across different demographics groups or modes of transportation while increasing service quality and reducing cost.

A case example—where should TIA outpatient clinics be located?

As a simple exemplar, consider a rural region in the UK that provided a 7-day transient ischemic attack (TIA) service through outpatient clinics in the community. Clinics ran at five locations but with only one location open per day. Magnetic resonance imaging (MRI) was available at three locations. Service users attending clinics without imaging but who require access to an MRI make an additional journey to the closest location with imaging capacity.

Service users are booked into clinic appointments across the week as they are referred to the TIA service by their diagnosing clinician, typically the patients local GP or an attending emergency department physician. The diagnosing clinician risk stratifies service users as high or low risk of a major stroke. High-risk service users require to be seen within 24 h of symptom onset and low-risk patients within 7 days [ 30 ].

The healthcare providers had concerns that splitting the clinics across five sites increased the variation in care received by service users and wished to consolidate to one to three clinic locations. Hence, there were two complicating factors when assessing equitable access: how many locations and which ones. There were also concerns that one location—clinic X—on the coast of the region was extremely difficult for high-risk TIAs to reach on the same day as diagnosis. There would also be political implications for any closure at clinic X. In total, there were 25 combinations of clinics for the providers to consider for both the low- and high-risk TIA groups, i.e. 50 options to review.

A discrete-choice facility location model was developed to evaluate the consequences of different TIA clinic configurations and inform the decision-making process for the reconfiguration of the service. Location analysis is a specialised branch of combinatorial optimisation and involves solving for the optimal placement of a set of facilities in a region in order to minimise or maximise a measure of performance such transportation costs, travel time, or population coverage [ 31 ]. In this, case an analysis was conducted separately for high-risk and low-risk TIAs. The analysis of high-risk TIAs aimed to minimise the maximum travel time of a service user from their home location to the closest clinic (as these service users must be seen the same day). The low-risk analysis minimised the weighted average travel time to their closest clinic. The weighted average measure allows for locations with the highest level of demand to have the greatest impact on results, diminishing the impact of outlying points. In general, if there are n demand locations and on a given day the travel time x from locations i to the nearest clinic, then the weighted average travel \( \overline{x} \) time is given by the simple formula depicted in Eq. ( 1 ). Table  1 illustrates the use of the equation with two fictional locations. For each location, the number of patients who travel and the travel time for patients to a hospital is given. In the table, the weighted average is compared to the more familiar mean average.

The model demonstrated that clinics most central to the region were all good choices to provide equitable patient access. A three-clinic solution provided the most equitable solution for service users. The problematic clinic X on the coast of the region was not included in an optimal configuration; however, it could be included in a three-clinic solution without substantial effect on travel times if scheduled infrequently. This latter result allowed the decision makers to move on from the strategic debate about location and focus on the more detailed implementation issues of scheduling and capacity planning for clinics. This was again addressed upfront using a computer simulation study to evaluate a small number of competing options for scheduling the clinics.

Lessons for implementation science

Each of the three roles emphasises the use of OR to conduct implementation science upfront before any action to alter a care pathway or service has been taken. Many OR scholars argue that the benefit of constructing a model upfront is that it forces decision makers to move from a world of imprecise language to a world of a precise language (sometimes referred to as a common language [ 32 ]) and ultimately develop a shared understanding of the problem; although as I will argue later, there is very limited empirical evidence supporting this proposition. Such a shared understanding increases the likelihood if implementation will actually go ahead and importantly if it will be sustained or normalised.

It is important to emphasise that the three case studies illustrate the simpler end of what can be achieved in using OR for upfront implementation science. This is partly a stylistic choice in order to aid reader understanding, for example, many optimisation problems are hugely complex, but also because in my experience simpler models tend to be accepted and used more in healthcare. Simpler models also need less input data and hence can be built and run quickly.

Along with the three case studies, OR is in general grounded in the use of models to improve upfront decision-making in complex implementation problems. Although there is a significant overlap between OR and implementation research, there are differences. For example, OR would not provide the rich contextual information collected in a process evaluation.

Implementation science challenges for OR

Implementation science poses a number of challenges for OR. I propose that these lie at three levels: disciplinary, organisational, and interventional. Table  2 summarises these key challenges.

Challenges at a disciplinary level

This article describes three roles for OR within implementation science. An irony is that OR interventions themselves are poorly understood with barely any published evaluation of practice or impact [ 33 – 36 ]. Limited examples can be found in Monks et al. [ 37 ], Pagel et al. [ 38 ], and Brailsford et al. [ 39 ]. The explanation for this can be found at a disciplinary level. That is, academic OR is predominately driven and rewarded by the development of theory for modelling methodology as opposed to understanding interventions and the issues they raise for practice. As such, a discipline that promotes the use of evidence for decision-making in healthcare cannot confidently answer the question does OR in health work ? I am regularly challenged on this point by healthcare professionals.

A second disciplinary challenge is to systematically involve service users in the co-design of OR interventions. To date, evidence of service user involvement is limited (see Walsh and Holstick [ 40 ] for an example). There is also confusion between service users framed as research participants (typically treated as a data source to parameterise models with behavioural assumptions) and co-designers of research objectives and methods, although there has been an effort to clarify the important difference [ 41 ].

Challenges at the organisational level

The three roles of OR outlined above are widely applicable across healthcare implementation problems. However, before OR can be used within practice, users of the research, in this case, healthcare managers, clinicians and service users, must be aware of the approaches. This is currently a substantial barrier to a wide scale adoption in health services [ 42 – 44 ] and stands in stark contrast to domains such as manufacturing and defence where it is used frequently to generate evidence before action [ 45 ]. The implication of low awareness of OR in health is that it is often difficult to engage senior decision makers in the complex operational and logistical problems that matter the most for service users.

Challenges at an interventional level

Fifty years ago, Churchman and Schainblatt [ 46 ] wrote about a ‘dialectic of implementation’ in the journal management science. In this paper, the two authors advocated that a position of mutual understanding between a researcher and manager was necessary in order to implement results of a study. That is, the researcher must understand the manager’s position, values, and implementation problem in order to tackle the correct problem in the right way. The manager must understand the method that the researcher has applied, at least at the conceptual level, in order to scrutinise, challenge, and implement results. The concept of mutual understanding is an elegant one, but in practice, achieving it is a challenge for both sides. As a simple example from a researcher perspective, it is difficult to assess if the users of a model understand why a model is producing certain results [ 42 ]. That is, do users understand how the model works or are they simply accepting the results based on some heuristic, such as ‘these are the results I want’ or ‘I trust the person telling me the results’? Given the disciplinary challenge outlined above, to date, there is limited validated guidance about how to manage such complex interventions within OR.

The computer software used in the three case studies have been available for considerable time, but appropriate data to parameterise the quantitative models used to illustrate the second and third roles are potentially not collected routinely. All models require data from the system studied. The TIA clinic study had relatively low requirements: individual service user-level data detailing date of clinic attendance, clinic attended, the risk classification of patient, and a home location of the patient—much of which is collected routinely by a health system for financial reporting purposes. Simulation modelling studies such as that described in the emergency department case study have high data requirements, including fine-grained timings of processes such as triaging and doctor assessment. It is unlikely such data are collected routinely as they have no use in financial reporting.

An agenda for OR in implementation science

Given the organisational, interventional, and disciplinary issues outlined in the ‘ Implementation science challenges for OR ’ section, I propose the following agenda for OR within implementation science.

Priority 1: creating the evidence base

At the forefront of the research agenda is the need to evaluate the impact of OR on complex interventions. The focus here should be on the consumers of research as opposed to the modellers and the process they follow [ 47 , 48 ]. There is a need to understand how stakeholders make sense of an OR intervention and how the results of studies are used to assist decision-making. Recent research offers some promise in progressing this aim. PartiSim [ 49 ] is a participative modelling framework that aims to involve stakeholders in structured workshops throughout a simulation study. Structured frameworks like PartiSim provide an opportunity to study the user side of OR more efficiently, as the modelling steps are known upfront. Another area showing promise is the recent emergence of Behavioural OR [ 50 ]. One of the core aims of Behavioural OR is to analyse and understand the practice and impact of OR on context (e.g. [ 51 – 53 ]).

Priority 2: raising demand and the liberation of OR

Much of the challenge in the use of OR as an implementation science technique that I outline is rooted in the lack of organisational awareness and experience of the approach. But what if this challenge were to be resolved? To examine this further, consider a counterfactual world where all health service users, managers, and clinicians are well versed in the three implementation science roles of OR and all have free access to a substantial evidence base detailing the efficacy of the approach. In this world, where OR is an accepted implementation science approach, the constraint has now moved from demand to supply of modelling services. Current supply is predominately provided by the (relatively) small specialist consultancy and research communities. There is a great need to liberate OR from its roots as the tool of the ‘specialist’ and transfer knowledge to research users. Two initial efforts to achieve this priority include the Teaching Operational Research for Commissioning in Health (TORCH) in the UK [ 54 ] and the Research into Global Healthcare Tools (RIGHT) Project [ 55 ]. TORCH successfully developed a curriculum for teaching OR to commissioners, although it has yet to be implemented on a wide scale or evaluated. The RIGHT project developed a pilot web tool to enable healthcare providers select an appropriate OR approach to assist with an implementation problem. Both of these projects demonstrate preliminary efforts at liberating OR from the traditional paradigm of specialist delivery.

The liberation of OR has already taken place in some areas in the form of Community OR . The three case studies illustrated interventions where the collaboration puts the emphasis on a modeller to construct the model and provide results for the wider stakeholder group. Alternatively, service users could develop or make use of OR methods to analyse a problem themselves. Community OR changes the role of an operational researcher from a modeller to a facilitator in order to aid those from outside of OR to create appropriate systematic methodology to tackle important social and community-based issues. In a rare example of community OR in healthcare [ 40 ], two examples illustrate where service users take the lead. In the first example, users of mental health services used system methods to produce a problem structuring tool to evaluate the impact of service users on NHS decision-making. In the second example, service users developed and applied an idealised planning approach for the future structure of mental health services. These approaches are qualitative in nature but are systematic and in-line with an OR implementation science approach.

Priority 3: PPI education for OR modellers

The first two priorities listed might be considered long-term goals for the OR implementation science community. An immediate priority that is arguably achievable over the short term is Patient and Public Involvement (PPI) education for OR modellers. The co-design of healthcare models with decision makers is often held up as a critical success factor for modelling interventions [ 42 ]. For ethical and practical reasons, co-design of OR modelling interventions should also include service users [ 41 ]. Education need not be complicated and could at first be done through widely read OR magazines and a grass roots movement delivered through master degree courses.

Conclusions

Operational research offers improvement scientists and individuals who work in complex health systems the opportunity to do more upfront system thinking about interventions and change. OR's upfront role within implementation science aims to answer questions such as where best to target interventions, will such an intervention work even under optimistic assumptions, which options out of many should we implement, and should we consider de-implementing part of a service in favour of investing elsewhere. As OR becomes more widely adopted as an implementation science technique, evaluation of the method through the lens of implementation science itself becomes more necessary in order to generate an evidence base about how to effectively conduct OR interventions. It is also necessary to liberate OR from its traditional roots as a specialist tool.

Operational research (OR) is a mature discipline that has developed a significant volume of methodology to improve health services. OR offers implementation scientists the opportunity to do more upfront system thinking before committing resources and taking risks. OR has three roles within implementation science: structuring an implementation problem, upfront evaluation of implementation problems, and a tool for strategic reconfiguration of health services. Challenges facing OR as implementation science include limited evidence or evaluation of impact, limited service user involvement, a lack of managerial awareness, effective communication between research users and OR modellers, and availability of healthcare data. To progress the science, a focus is needed in three key areas: evaluation of OR interventions, transferring the knowledge of OR to health services, and educating OR modellers about the aims and benefits of service user involvement.

Abbreviations

AMU, Acute Medical Unit; CDU, clinical decision-making unit; ED, emergency department; GP, general practitioner; MRI, magnetic resonance imaging; NHS, National Health Service; OR, operational research (UK)/operations research (US); PPI, Patient and Public Involvement; PPT, psychology and psychiatric talking therapies; RIGHT, Research into Global Healthcare Tools; RIL, recovering independent life; SD, system dynamics; TIA, transient ischemic attack; TORCH, Teaching Operational Research for Commissioning in Health

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Acknowledgements

This article presents independent research funded by the National Institute for Health Research (NIHR) Collaboration for Leadership in Applied Health Research and Care (CLAHRC) Wessex. The views expressed in this publication are those of the author(s) and not necessarily those of the National Health Service, the NIHR, or the Department of Health.

Case studies 1 and 3 were funded by NIHR CLAHRC South West Peninsula. Case study 3 used Selective Analytics MapPlace software.

Author’s contribution

TM developed the models described in the case studies, conceived the idea for debate, and wrote the paper.

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TM leads the NIHR Collaboration in Leadership in Health Research and CLAHRC Wessex’s methodological hub where he conducts applied health service research in collaboration with the NHS. He is an operational researcher with experience in industry, the public sector, and academic research.

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Monks, T. Operational research as implementation science: definitions, challenges and research priorities. Implementation Sci 11 , 81 (2015). https://doi.org/10.1186/s13012-016-0444-0

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Advantages & Limitations of Operations Research

Operations research is a robust tool and offers directions in making the best decisions possible given the data available.

Advantages of Operations Research

Better Systems: Often, an O.R. approach is initiated to analyze a particular problem of decision making such as best location for factories, whether to open a new warehouse, etc. It also helps in selecting economical means of transportation , jobs sequencing, production scheduling, replacement of old machinery, etc.

Better Control: The management of large organizations recognize that it is a difficult and costly affair to provide continuous executive supervision to every routine work. An O.R. approach may provide the executive with an analytical and quantitative basis to identify the problem area. The most frequently adopted applications in this category deal with production scheduling and inventory replenishment.

Better Decisions: O.R. models help in improved decision making and reduce the risk of making erroneous decisions. O.R. approach gives the executive an improved insight into how he makes his decisions.

"If you don't actively attack the risks, they will actively attack you." - Tom Gilb

Better Co-ordination: An operations-research-oriented planning model helps in co-ordinating different divisions of a company.

Limitations of Operations Research

Dependence on an Electronic Computer: O.R. techniques try to find out an optimal solution taking into account all the factors. In the modern society, these factors are enormous and expressing them in quantity and establishing relationships among these require voluminous calculations that can only be handled by computers.

Non-Quantifiable Factors: O.R. techniques provide a solution only when all the elements related to a problem can be quantified. All relevant variables do not lend themselves to quantification. Factors that cannot be quantified find no place in O.R. models.

Distance between Manager and Operations Researcher: O.R. being specialist's job requires a mathematician or a statistician, who might not be aware of the business problems. Similarly, a manager fails to understand the complex working of O.R. Thus, there is a gap between the two.

Money and Time Costs: When the basic data are subjected to frequent changes, incorporating them into the O.R. models is a costly affair. Moreover, a fairly good solution at present may be more desirable than a perfect O.R. solution available after sometime.

Implementation: Implementation of decisions is a delicate task. It must take into account the complexities of human relations and behaviour.

Operations Research Uses (Role)

Operations research plays an important role in almost all areas of business decisions. Some problems where operational research (OR) approach can be used:

1. Finance, Budgeting and Investments

• Credit policy analysis.
• Cash flow analysis.
• Dividend policies.
• Investment portfolios.

2. Marketing

• Product selection, timing, etc.
• Advertising media, budget allocation.
• Number of salesman required.
• Selection of product mix.

3. Purchasing, Procurement and Exploration

• Optimal buying and reordering.
• Replacement policies

4. Production Management

• Location and size of warehouses, factories, retail outlets, etc.
• Distribution policy.
• Loading and unloading facilities for trucks, etc.
• Production scheduling.
• Optimum product mix.
• Project scheduling and allocation of resources.

5. Personnel Management

• Selection of suitable personnel.
• Recruitment of employees.
• Assignment of jobs.
• Skills balancing.

6. Research and Development

• Project selection.
• Control of R&D projects.
• Reliability and alternative design.

O.R. is a relatively new academic discipline. It has its origin in World War II and soon became very popular throughout the world. Developing appropriate mathematical models for situations, processes, systems is the basic essence of O.R. study. Linear programming , dynamic programming , game theory , simulation , etc. are some of the models & techniques that are used in O.R. There is role for O.R. in almost all areas of business decisions.

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Operations Research – Types, Advantages, Disadvantages

June 12, 2023 | By Hitesh Bhasin | Filed Under: Marketing

Operations research, popularly known as OR, is a scientific research method or a mathematical technique to determine the right decision for a problem. Operations research is used to provide aid to people in decision-making who manage large organizations or organized system.

The primary purpose of operations research is to improve the performance of the existing system rather than developing a new system. In operations research, a team of experts from the different fields first define the problem then represent that problem in the form of a set of mathematical equations. After that, the computer analysis of these mathematical equations is done to find a solution for the problems, and then these solutions are applied to solve managerial and administrative problems.

Operations research is concerned with the systems in which human behavior plays an important role. The operations research focuses on the whole system rather than focusing on individual parts of the system. Different types of approaches are applied by Operations research to deal with different kinds of problems. For example, Linear programming and dynamic programming is used to manage complex information.

The operations research concerns what information and data are required to make decisions, how to create and implement managerial decisions, etc. In this article, you will learn about the types of operations research, advantages, disadvantages, and different phases of operations research.

Table of Contents

Types of Operations Research

1. Simulation

Simulation can be defined as creating a fake model of a real system. Different experiments are conducted on this artificial model to determine various outcomes by varying random variables.

New strategies and concepts are designed and implemented in simulation to test them before applying them to a real system. The purpose of using different approaches on a fake system is to check the effectiveness of different strategies without disturbing the real system.

2. Linear programming

Linear programming is one of the most important operations research tools. This approach is used to determine solutions by considering both constraints and objectives. For example, the aim of your organization is to maximize productivity by considering the limiting factors.

Linear programming tools determine all possible combinations of goals and limiting factors to determine what can be done to achieve the desired outcome and also unexpected factors can affect the desired ideal outcome.

3. Non-linear programming

Non-linear programming tool is more suitable for real problems of the system because not all factors are linear all the time.

Advantages of Operations research

1. Enhanced productivity

Operations research helps in improving the productivity of the organizations. Operations controls provide significant information to the managers before making an important decision. It helps in making small decisions for important decisions for an organization. Many organizations make the use of simulation operations research methods to enhance their productivity by applying different combinations.

It also helps in performing day-to-day tasks like inventory control, workforce planning , expansion of the business , installation, and up-gradation of technology. Effective and accurate decision making helps in improving the productivity of the organization.

Management is responsible for making important decisions about the organization. Operations research provides many alternatives for one problem, which helps the management to choose the best decision and implement it to get a positive outcome.

Managers can evaluate the risks associated with each solution and can decide whether they want to go with the solution or not.

3. Improved coordination

Operations research improves the coordination between different departments and employees of an organisation . Because operations research focuses on the whole organisation and does not focus on one department.

As a result of that, managers of each department know what they should do to achieve a common objective of the organisation. Therefore, managers of different departments can coordinate with one another better when solutions are applied to all the departments altogether.

4. Lower risks of failure

Operations research lowers the chances of failure as with the help of operations, and research managers get to know about all the alternative solutions for a single problem.

All risks associated with a solution are analysed before implementing it. As a result of which the risk of failure reduces unless something unexpected event takes place.

5. Control on the system

Operations research helps in redefining the control of a system. Operations research provides in-depth knowledge about a particular action, which allows managers to take better control of the work. They can control their subordinates in a better way and can make the most relevant job done on priority.

In addition to this, operations research also provides information about the expected outcome. Hence, managers know what standards of performance he should expect from his subordinates.

Using this information, he can measure the performance of employees and can compare it with the standard performance.

Disadvantages of Operations research

The first and foremost disadvantage of operations research is its high cost. The operations research works on mathematical equations that require expensive technology to create them. In addition to this, experts are needed to perform simulations.

All of this might provide effective solutions but at a very high cost. Organizations with a small budget can be adopted operations research because of its high cost of implementation.

2. Technology dependent

Another limitation of operations research is its technology dependence. The mathematical equations can only be analyzed on computers. Its reliance on technology makes it a non-popular choice of managers.

3. Dependence on experts

A team of experts is required to perform operations research. There are various factors associated with this, which makes operations research an unpopular choice for management.

For example, the solutions will not be effective and can’t be implemented if there is a communication gap between managers and OR experts. Besides this, all solutions will become useless and might cause loss rather than benefit if the 3wrong information is shared with the experts.

4. Unquantifiable factors

The effectiveness of solutions developed using operations research largely depends on the various factors. It is easy to measure quantifiable factors and use them for the operations research, but the problem arises when important factors are in unquantifiable form.

Unquantifiable factors result in inaccurate solutions.

5. Difficult to implement

The solutions obtained from operations research are difficult to implement, as most of them are usually unrealistic. Some modifications are required to make to implement the solutions which hamper the effectiveness of the solution.

Different phases of Operations Research Model

1. orientation.

In the first steps, understanding and familiarity with the system are made through orientation.

2. Defining problems

In the next steps, problems associated with the system are identified and defined.

3. Data collection

Data required for operations research is collected.

4. Identifying limitations and objectives of operations research

In the next step, identify all the constraints and objectives of the organization.

5. Creating a solution

In the next step, develop all possible solutions for the problem.

6. Analysis of alternatives

In the next step, the analysis of all solutions will be done, and the best solution will be picked among all solutions.

7. Implementation

In the next step, the solution will be implemented and monitored for its performance.

Liked this post? Check out the complete series on Market research

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About Hitesh Bhasin

Hitesh Bhasin is the CEO of Marketing91 and has over a decade of experience in the marketing field. He is an accomplished author of thousands of insightful articles, including in-depth analyses of brands and companies. Holding an MBA in Marketing, Hitesh manages several offline ventures, where he applies all the concepts of Marketing that he writes about.

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