How to Design Decision Making? : For Social Innovation with Numerical Optimization (Part 1)
In this column, Mr. Hirai from Hitachi Consulting, who supports the dissemination of Annealing Cloud Web, will introduce the methodology for implementing numerical optimization technology in society.
This column is filled with hints for advancing issue clarification and requirement definition, so if you're unsure where to start or how to articulate your thoughts as you progress in your study of numerical optimization, please take a moment to read it.
Nobuyuki Hirai
Joined Hitachi Consulting in 2017. Engaged in data analytics projects such as proof of concept and requirement definition for social application of machine learning and numerical optimization. Utilizing his knowledge and experience, he is also involved in activities such as internal education on the application and utilization of numerical optimization technology, as well as creating educational content for the Hitachi Group.
He also applies his experience in studying design during his university days to UI/UX design of optimization systems and design study sessions within the company.
Introduction
In this column, I would like to introduce the know-how for applying numerical optimization technology, including CMOS annealing, to issues that require human decision-making.
This column is divided into two parts. In the first part, I will introduce the method of issue identification using the decision architecture design framework (Indicate the following as 'FW') that we use, through familiar decision-making scenarios as examples.
In the second part, I would like to introduce some tips for using the FW, the commonalities between familiar issues and business issues, and hints for discovering business use cases for optimization technology.
Summary
Making Spaghetti Aglio e Olio
Now let's make Spaghetti Aglio e Olio as an example of a familiar decision-making problem.
Since I don't have the ingredients at hand, let's go to the nearest supermarket to get the ingredients (spaghetti, olive oil, garlic, chili pepper, Italian parsley, salt). Once you have obtained the ingredients, you can start cooking. There are two stoves in the kitchen, and there is one cutting board and one knife.
Now, in order to finish shopping and cooking quickly, what order should you get the ingredients and how should you proceed with the cooking? There are two optimization problems here: ingredient procurement and cooking. If you represent these as problems, they would look like Figure 1-1.
Click to enlarge the image.
From now on, I will use the decision architecture design FW to delve deeper into these issues.
Decision Architecture Design Framework
Now, let's get to the heart of this column. Figure 1-2 shows the decision architecture design FW.
Click to enlarge the image.
In design of decision, information related to decision-making is classified into four elements: actions, value, rules, and reference.
If we plot the information related to ingredient procurement and cooking on the FW, it would look like Figure 1-3. I would like to explain the details of these four elements based on these figures.
Click to enlarge the image.
Action: Defined using the 5W2H method
Actions refers to what you want to decide upon. For example, in the case of ingredient procurement, it would be the order of visiting the sections in the supermarket, and in the case of cooking, it would be the order of tasks. These are expressed using the 5W2H method. Specifically:
Ingredient Procurement:
to visit
(Where) from
(Where) to
(When) order
Cooking:
to start
(What) tasks
(Where) facilities
(when) time
In numerical optimization, actions are referred to as decision variables, and the optimal solution is sought by rearranging these decision variables.
Values: Defined what needs to be maximized/minimized and their priorities
Values refers to the gains you want to achieve through actions. In business, it refers to quantifiable indicators defined as KPIs or KGIs.
In these examples, we aim to minimize the distance or time from obtaining the ingredients to leaving the store, and minimize the cooking time from the start of cooking to serving the spaghetti on a plate.
Among KPIs and KGIs, there are indicators that we want to increase, such as sales or profit margins, and indicators that we want to decrease, such as manufacturing lead time or inventory fluctuations. In numerical optimization, the value is called the objective function, and as the problem size increases, it becomes necessary to optimize multiple indicators simultaneously. Therefore, for each issue, it is crucial to carefully select the values you want to maximize or minimize, ensuring there are no leftovers, and visualize their dependencies and priorities.
Actions and values are the foundation of decision-making, so they can be seen as the "skeleton of the issue."
Rules are defined as what should be prohibited.
Rules are considerations when taking action. Actions that deviate from the rules cannot be taken.
Rules should include not only explicit ones but also implicit ones.
For example, in ingredient procurement, if you do not define the rule that each section can only be visited once, proposals may be made to go around the same place repeatedly. Also, if you do not define that we should visit all places, including the cash register, proposals may suggest routes that involve forgetting to buy ingredients or shoplifting.
In the cooking example, definitions of the places where each task can be performed and the order of tasks are required. Chopping ingredients can only be done on a cutting board, and using fire can only be done on the stove. Also, boiling water needs to be done before cooking the noodles. Although humans can understand these to some extent through experience, it is necessary to make them explicit.
In numerical optimization, these rules are called constraints, and the model searches for combinations that maximize or minimize values while adhering to the constraints.
References: defined as information or data that can be known in advance.
References are the information needed to determine whether the rules are being followed and to quantify the values. Therefore, they need to be known before making decisions.
In the case of ingredient procurement, it would be the distance or time between any two of the eight points, which are the supermarket entrance, the cash register, and each ingredient section. In the case of cooking, it would be the time required for each task and the location where the task can be performed.
These pieces of data are defined as values that can be called using the 5W2H defined when defining actions. For example, in ingredient procurement, the distance between the oil and fat section (where) and the aromatic vegetable section (where) is 15m. In cooking, the time required for the task of boiling water (what) when performed on stove 1 (where) is 10 minutes.
In numerical optimization, references are called input variables, and by combining input variables and decision variables, constraints and objective functions are defined using numerical expressions, and modeling of numerical optimization is performed.
Rules and references can be called the "outline of the issue" in relation to the "skeleton of the issue."
Afterword
In this column, I introduced the method of issue identification using the decision architecture design FW, using familiar decision-making scenarios as examples.
In the second part, I will go into more detail and explain tips for using the decision architecture design FW, the commonalities between familiar issues and business issues, and hints for discovering business use cases for optimization technology.
Thank you for reading this far, and let's meet again.
