Multi-criteria decision making (MCDM) for Project selection - Revision history

Tkokotas at 12:45, 18 December 2018

2018-12-18T12:45:24Z

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			''Developed by Christian Lolk Thomsen''


	Multi-criteria decision making (MCDM) also called Multi-criteria decision analysis (MCDA), can be used as a decision support tool when making decisions with multiple criterions to evaluate simultaneously. In Portfolio management, ensuring that the resources are allocated optimally, is a complex task. No company have one single objective to maximize, but several conflicting objectives to manage simultaneously. MCDM can be used as a decision support tool and provide assistants in the process of making such decisions. MCDM is a good method for selecting which projects a company should initiate. This decision is based on a list of potential projects. All potential projects have assigned values or scores to all criterions. The objective function in the model could be to maximize the sum of scores in the selected projects subject to a number of constraints, such as available capacity (man hours, budget) and project diversity (at least one project in every category). The decision variables will be which projects to initiate and which not to. This list provides the decision makers with a starting point, and argumentation for making the decision.		Multi-criteria decision making (MCDM) also called Multi-criteria decision analysis (MCDA), can be used as a decision support tool when making decisions with multiple criterions to evaluate simultaneously. In Portfolio management, ensuring that the resources are allocated optimally, is a complex task. No company have one single objective to maximize, but several conflicting objectives to manage simultaneously. MCDM can be used as a decision support tool and provide assistants in the process of making such decisions. MCDM is a good method for selecting which projects a company should initiate. This decision is based on a list of potential projects. All potential projects have assigned values or scores to all criterions. The objective function in the model could be to maximize the sum of scores in the selected projects subject to a number of constraints, such as available capacity (man hours, budget) and project diversity (at least one project in every category). The decision variables will be which projects to initiate and which not to. This list provides the decision makers with a starting point, and argumentation for making the decision.

S162918 at 21:41, 26 September 2016

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	# Decision making		# Decision making

	==Identify criterions==		===Identify criterions===
	It is important that the objectives are known. This step has a link to the strategy, and should be aligned with the overall goals. For example, if a research and development department has a goal of bringing new innovative products to the market place quickly, development time and degree of innovation could be very relevant criterions to include.		It is important that the objectives are known. This step has a link to the strategy, and should be aligned with the overall goals. For example, if a research and development department has a goal of bringing new innovative products to the market place quickly, development time and degree of innovation could be very relevant criterions to include.

	==Weighting of criterions==		===Weighting of criterions===
	When all criterions are identified, the weighting of them needs to be undertaken. The weighting is very essential for the results, and need to be done in a systematic and transparent way.		When all criterions are identified, the weighting of them needs to be undertaken. The weighting is very essential for the results, and need to be done in a systematic and transparent way.
	One method is to just assign weights to the criterions. A major benefit from this technique is that it is simple and fast. The risks are though, that this method will not obtain the “correct” weights.		One method is to just assign weights to the criterions. A major benefit from this technique is that it is simple and fast. The risks are though, that this method will not obtain the “correct” weights.
	Another possible method is Analytical Hierarchy process (AHP). AHP uses parallel comparison to compute the weights. This gives more reliable and robust weights. A disadvantage with AHP is that it can be time consuming. <ref> Aragonés-Beltrán, P., Chaparro-González, F., Pastor-Ferrando, J. P., & Pla-Rubio, A. (2014). An AHP (Analytic Hierarchy Process)/ANP (Analytic Network Process)-based multi-criteria decision approach for the selection of solar-thermal power plant investment projects. Energy, 66, 222-238.</ref>		Another possible method is Analytical Hierarchy process (AHP). AHP uses parallel comparison to compute the weights. This gives more reliable and robust weights. A disadvantage with AHP is that it can be time consuming. <ref> Aragonés-Beltrán, P., Chaparro-González, F., Pastor-Ferrando, J. P., & Pla-Rubio, A. (2014). An AHP (Analytic Hierarchy Process)/ANP (Analytic Network Process)-based multi-criteria decision approach for the selection of solar-thermal power plant investment projects. Energy, 66, 222-238.</ref>

	==Identify constraints==		===Identify constraints===
	If there are no constraints, the solution will in many cases be to initiate all projects, because no scarce resources are limiting the number of projects that can be initiated. Constraints can be divided into two main categories: Resource- and Political constraints.		If there are no constraints, the solution will in many cases be to initiate all projects, because no scarce resources are limiting the number of projects that can be initiated. Constraints can be divided into two main categories: Resource- and Political constraints.

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	Political constraints are rules that needs to be complied. A portfolio manager for dairy products in a supermarket chain could have a political constraint saying that at least 30% of all dairy products needs to be organic.		Political constraints are rules that needs to be complied. A portfolio manager for dairy products in a supermarket chain could have a political constraint saying that at least 30% of all dairy products needs to be organic.

	==Collect data==		===Collect data===
	To facilitate MCDM data is needed. If each potential projects should be evaluated by a number of criterions and constraints this information needs to be present. Values for all criterions and resource consumption are normally the information needed.		To facilitate MCDM data is needed. If each potential projects should be evaluated by a number of criterions and constraints this information needs to be present. Values for all criterions and resource consumption are normally the information needed.

	==Formulate a mathematical model==		===Formulate a mathematical model===
	Based on the weights and criterions the objective function will be formulated. The objective function is what we want to maximize or minimize eg. profit or cost. In a MCDM model we will have more than one criteria in the objective functions, and in some mathematical models we will have several objective functions.		Based on the weights and criterions the objective function will be formulated. The objective function is what we want to maximize or minimize eg. profit or cost. In a MCDM model we will have more than one criteria in the objective functions, and in some mathematical models we will have several objective functions.
	All identified constraints are formulated. Constraints can both be equalities, inequalities and functions.		All identified constraints are formulated. Constraints can both be equalities, inequalities and functions.

	==Solve model==		===Solve model===
	Based on the type of mathematical model a suitable technique for solving the problem is chosen. An example could be, if the objective function and all constraints are linear the problem can be solved by using the simplex method.		Based on the type of mathematical model a suitable technique for solving the problem is chosen. An example could be, if the objective function and all constraints are linear the problem can be solved by using the simplex method.
	The result will be the values of the decision variables. These variables could be as simple as 1 and 0 that show if a project should be initiated or not (1=yes, 0=no).		The result will be the values of the decision variables. These variables could be as simple as 1 and 0 that show if a project should be initiated or not (1=yes, 0=no).

	==Evaluate results==		===Evaluate results===
	In this step the decision makers will evaluate the computed results. A model cannot include all aspects of the real world and the results needs be understood hereafter. The result can also be used as argumentation.		In this step the decision makers will evaluate the computed results. A model cannot include all aspects of the real world and the results needs be understood hereafter. The result can also be used as argumentation.

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Limitations

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	In LP it is assumed, that all variables are known. In this case it means, that the scores and requested resources for each project are assumed to be that precise value. In reality all these variables are associated with uncertainty. If a value of a constraint changes, it can result in the computed decisions not being optimal anymore and/or one or more constraint violated. The impact of changing variables can be investigated by conduction a sensitivity analysis.		In LP it is assumed, that all variables are known. In this case it means, that the scores and requested resources for each project are assumed to be that precise value. In reality all these variables are associated with uncertainty. If a value of a constraint changes, it can result in the computed decisions not being optimal anymore and/or one or more constraint violated. The impact of changing variables can be investigated by conduction a sensitivity analysis.

	""Limitations of the model:""		==Limitations of the model:==
			The model is static and only consists of a single time period. This limitation can be released by extending the model. The decision variables are not just if a project should be initiated, but also in what time period. Extending the model have the benefits of a more precis decision where time and planning of when to initiate witch projects are included, but it also adds complexity because the number of decision variables and constraints will increase. Instead of including the time horizon in the selection model, this planning step can also be modelled by itself.

	The model is static and only consists of a single time period. This limitation can be released by extending the model. The decision variables are not just if a project should be initiated, but also in what time period. Extending the model have the benefits of a more precis decision where time and planning of when to initiate witch projects are included, but it also adds complexity because the number of decision variables and constraints will increase. Instead of including the time horizon in the selection model, this planning step can also be modelled by itself.


	=Annotated bibliography=		=Annotated bibliography=

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	Political constraint:		'''Political constraint:'''


	Specific projects must be initiated. This is formulated by making a constraint that a specific x must be equal to 1. In this example must Project 1 be initiated. This is formulated as following:		Specific projects must be initiated. This is formulated by making a constraint that a specific x must be equal to 1. In this example must Project 1 be initiated. This is formulated as following:
	<math>x_1=1</math>		<math>x_1=1</math>
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	===Solve model===		===Solve model===
	There are many different programs that can solve a BIP problem. In this example will OpenSolver be used. OpenSolver is a spreadsheet based solver. This means that the problem can be formulated in excel and solved by the add-on program OpenSolver<ref> opensolver.org </ref>.		There are many different programs that can solve a BIP problem. In this example will OpenSolver be used. OpenSolver is a spreadsheet based solver. This means that the problem can be formulated in excel and solved by the add-on program OpenSolver<ref> opensolver.org </ref>.


	The spreadsheet used to solve the model can be seen in the figure below.		The spreadsheet used to solve the model can be seen in the figure below.
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	The excel spreadsheet can be downloaded from: https://www.dropbox.com/s/kz9vir71knlyfr7/MCDM%20model.xlsx?dl=0		The excel spreadsheet can be downloaded from: https://www.dropbox.com/s/kz9vir71knlyfr7/MCDM%20model.xlsx?dl=0

	===Comparing BIP with sorting method===		==Comparing BIP with sorting method==
	A different approach to select which projects to initiate, could be by sorting the score from high to low, and then initiate projects until one or more resource groups are used up. The results of this method can be seen in the figure below.		A different approach to select which projects to initiate, could be by sorting the score from high to low, and then initiate projects until one or more resource groups are used up. The results of this method can be seen in the figure below.

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	In LP it is assumed, that all variables are known. In this case it means, that the scores and requested resources for each project are assumed to be that precise value. In reality all these variables are associated with uncertainty. If a value of a constraint changes, it can result in the computed decisions not being optimal anymore and/or one or more constraint violated. The impact of changing variables can be investigated by conduction a sensitivity analysis.		In LP it is assumed, that all variables are known. In this case it means, that the scores and requested resources for each project are assumed to be that precise value. In reality all these variables are associated with uncertainty. If a value of a constraint changes, it can result in the computed decisions not being optimal anymore and/or one or more constraint violated. The impact of changing variables can be investigated by conduction a sensitivity analysis.

	Limitations of the model:		""Limitations of the model:""


	The model is static and only consists of a single time period. This limitation can be released by extending the model. The decision variables are not just if a project should be initiated, but also in what time period. Extending the model have the benefits of a more precis decision where time and planning of when to initiate witch projects are included, but it also adds complexity because the number of decision variables and constraints will increase. Instead of including the time horizon in the selection model, this planning step can also be modelled by itself.		The model is static and only consists of a single time period. This limitation can be released by extending the model. The decision variables are not just if a project should be initiated, but also in what time period. Extending the model have the benefits of a more precis decision where time and planning of when to initiate witch projects are included, but it also adds complexity because the number of decision variables and constraints will increase. Instead of including the time horizon in the selection model, this planning step can also be modelled by itself.

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	===Formulate mathematical model===		===Formulate mathematical model===
	To include criterions with different scales the number needs to be normalized. This is done by dividing each score by the sum of all scores for that criteria, see equation below.		To include criterions with different scales the number needs to be normalized. This is done by dividing each score by the sum of all scores for that criteria, see equation below.
	[[File:Screen Shot 2016-09-26 at 22.04.52.png\|center\|~~400px~~]]		[[File:Screen Shot 2016-09-26 at 22.04.52.png\|center\|100px]]


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	Resources must not exceed the available resources:		Resources must not exceed the available resources:

	[[File:Screen Shot 2016-09-15 at 21.52.11.png\|center\|~~200px~~]]		[[File:Screen Shot 2016-09-15 at 21.52.11.png\|center\|300px]]

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Show changes

S162918 at 18:55, 26 September 2016

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	===Project selection process===		===Project selection process===
	The process of selecting witch projects to initiate evolves several steps. Archer and Ghasemzadeh (1999) present a framework for portfolio selection in new product development (NPD). This framework is specially developed for NPD portfolio, but project portfolio selection could follow similar steps. In figure 1 is an illustration of the framework.		The process of selecting witch projects to initiate evolves several steps. Archer and Ghasemzadeh (1999) present a framework for portfolio selection in new product development (NPD). This framework is specially developed for NPD portfolio, but project portfolio selection could follow similar steps. In figure 1 is an illustration of the framework.
	[[File:FrameworkPS.png\|center\|600px]]		[[File:FrameworkPS.png\|frame\|center\|600px\|Framework for Project Portfolio Selection<ref>Archer, N. P., & Ghasemzadeh, F. (1999). An integrated framework for project portfolio selection. International Journal of Project Management, 17(4), 207-216..</ref>]]

	Multi-criteria decision making (MCDM) theory		Multi-criteria decision making (MCDM) theory
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	==Annotated bibliography==		==Annotated bibliography==

			==References==
			<references />

S162918 at 06:15, 16 September 2016

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	The criterions are then weighted. NPV is the most important and is weighted 0.5. Innovation is the second most important and is weighted 0.3. Risk the least important of the three criterions and is rated 0.2.		The criterions are then weighted. NPV is the most important and is weighted 0.5. Innovation is the second most important and is weighted 0.3. Risk the least important of the three criterions and is rated 0.2.

	===Constraints===		====Constraints====
	In this example is there two types of constraints. The most important constraint is resource constraint. All personal is divided into four different categories: Project manager, Non-technical Project employee, Technical Project employee and Expert. There are limitations on the number of resources that can be used for each of these four personal groups. Five project managers are available. 50 non-technical Project employees are available. Only five Technical Project employees available and 10 experts.		In this example is there two types of constraints. The most important constraint is resource constraint. All personal is divided into four different categories: Project manager, Non-technical Project employee, Technical Project employee and Expert. There are limitations on the number of resources that can be used for each of these four personal groups. Five project managers are available. 50 non-technical Project employees are available. Only five Technical Project employees available and 10 experts.
	There is also one political constraint that stats that Project 1 must be initiated.		There is also one political constraint that stats that Project 1 must be initiated.
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	Only 5 Project managers and 5 Technical Project employees are available. 50 Non-technical Project employees are available and 10 experts.		Only 5 Project managers and 5 Technical Project employees are available. 50 Non-technical Project employees are available and 10 experts.

	==Formulate mathematical model==		===Formulate mathematical model===
	To include criterions with different scales the number needs to be normalized. This is done by dividing each score by the sum of all scores for that criteria. All normalized criterion scores can be seen in the figure below. C1 is NPV, C2 is Risk and C3 is Innovation.		To include criterions with different scales the number needs to be normalized. This is done by dividing each score by the sum of all scores for that criteria. All normalized criterion scores can be seen in the figure below. C1 is NPV, C2 is Risk and C3 is Innovation.
	[[File:Screen Shot 2016-09-15 at 21.49.56.png\|center\|400px]]		[[File:Screen Shot 2016-09-15 at 21.49.56.png\|center\|400px]]
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	==Solve model==		===Solve model===
	There are many different programs that can solve a BIP problem. In this example will OpenSolver be used. OpenSolver is a spreadsheet based solver. This mean that the problem can be formulated in excel and solved by the add-on program OpenSolver.		There are many different programs that can solve a BIP problem. In this example will OpenSolver be used. OpenSolver is a spreadsheet based solver. This mean that the problem can be formulated in excel and solved by the add-on program OpenSolver.

S162918 at 20:09, 15 September 2016

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	~~==Abstract==~~
	Multi-criteria decision making (MCDM) also called Multi-criteria decision analysis (MCDA) can be used as a decision support tool when making decisions with multiple criteria to evaluate simultaneously. In Portfolio management ensuring that the resources are allocated optimally is a complex task. No company have one single objective to maximize, but several and conflicting objectives to manage simultaneously. MCDM can be used as a decision support tool and provide assistants in the process of making such decisions. MCDM is a good method for selecting which projects a company should initiate. This decision is based on a list of potential projects. All potential projects have assigned values or scores to all criteria’s. The objective function in the model could be to maximize the sum of scores in the selected projects subject to a number of constraints such as available capacity (man hours, budget) and project diversity (at least one project in every category). The decision variables will be which projects to initiate and which not to. This list provides the decision makers with a starting point and augmentation for the decisions made.		Multi-criteria decision making (MCDM) also called Multi-criteria decision analysis (MCDA) can be used as a decision support tool when making decisions with multiple criteria to evaluate simultaneously. In Portfolio management ensuring that the resources are allocated optimally is a complex task. No company have one single objective to maximize, but several and conflicting objectives to manage simultaneously. MCDM can be used as a decision support tool and provide assistants in the process of making such decisions. MCDM is a good method for selecting which projects a company should initiate. This decision is based on a list of potential projects. All potential projects have assigned values or scores to all criteria’s. The objective function in the model could be to maximize the sum of scores in the selected projects subject to a number of constraints such as available capacity (man hours, budget) and project diversity (at least one project in every category). The decision variables will be which projects to initiate and which not to. This list provides the decision makers with a starting point and augmentation for the decisions made.
	MCDM relies on assigning all potential projects with values for all criteria. This process can be time consuming so a pre-screening process will in many cases come before the MCDM process.		MCDM relies on assigning all potential projects with values for all criteria. This process can be time consuming so a pre-screening process will in many cases come before the MCDM process.

S162918 at 20:06, 15 September 2016

2016-09-15T20:06:09Z

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	The spreadsheet used to solve the model can be seen in figure 2.		The spreadsheet used to solve the model can be seen in figure 2.
	[[File:Screen Shot 2016-09-15 at 22.02.51.png\|center\|~~800px~~]]		[[File:Screen Shot 2016-09-15 at 22.02.51.png\|center\|700px]]

			When the problem is solved a solution is displayed. 11 out of the 20 potential projects should be initiated. Not all resources are utilized fully. There is one Project Manager and 6 Non-technical employees not allocated. The objective function gives 0,678. If all projects were initiated the value would be 1. The total sum of NPV is 764.000$ and the average Risk and Innovation is 5,4 and 6,6 respectively.
			The solution should now be evaluated by management before making the final decision.

			==Comparing BIP with sorting method==
			A different approach to select the which projects to initiate could be by sorting the score from high to low and then initiate projects until one or more resource groups are used up. The results of this method can be seen in the figure below.
			[[File:123.png\|center\|700px]]

			Only 8 projects can be initiated before the expert resource are used up. The value of the objective function is 0,58 witch is lower than 0,68 from the BIP solved model.

			More complex sorting systems can be used, but the results can never exceed the optimized method.

			==Project selection including time planning==

			==Supplier portfolio management==
			Using MCDM and LP to select suppliers in the supplier portfolio (REF A decision support system for supplier selection using AHP and linear programming

			==Limitations==

			==Annotated bibliography==