정수성과 부등식의 도입으로 "IP문제"가 어려워지는건맞는데, NP hardness는 IP문제뿐만 아니라 일반적인 의사결정문제를 분류하는 논의라서요 저는 정수성과 부등식 하나씩만 도입할땐 npc가 아닌데 두개가 다 도입될땐 npc가 되는게 예전부터 참 신기하더라구요. 그 두 조건 사이에 폭발적인 복잡도 증가가 있나하구요 구체적으로는 솔루션공간이 전체 정수점이아니라 양의정수로 줄어서 그런일이 생기는데, 간단하게는 꼭지점이 정수점이 아닌게 생기게 돼서 그런거라고 이해하면돼요; 최적조건, LP duality 같은게 성립하지않아서 enumeration을 일단 할수밖에 없는거구요; 만약 IP에서 enumeration을 안하고도 최적성을 보장하는방법이 발견된다면 많이 달라지겠죠?; 아니요 그냥 solution들을 하나하나 다 체크하는거죠 branch and bound 중 cut 부등식을 더한 각 subproblem을, ip relaxation 해서 feasible한 해들의 정수성 "체크" 라 이해하면 될까요? 그냥 냅색같은거도 브랜치바운드를 해도 본질은 아이템들의 부분집합을 다 확인하는거잖아요? | generator: $p(theta, y)lt;br>inference: $p_A(\theta\|y)$ | simple phenomena (dgp) | high dim/complex phenomena | | ------------------------------------------------------- | ------------------------------------------------- | -------------------------- | | inference algorithm | fresh ingredient e.g. vegetable, texture molecule | | | | | | | chef and researcher | chef | researcher | | --------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | input1 raw material | fresh ingredient e.g. vegetable, texture molecule | timely phenomena e.g. research questions from cancer, brain, ai, entrepreneurship | | input2 process | past recipes | past theories | | input3 measurement tool | measurement tool e.g. thermometer, scale | survey, interview, experiment, simulation | | output | cuisine | paper | | input123 $\rightarrow$ output | cooking which **assembles ingredients under certain recipe with the help of measurement** | research which **combines phenomena under theory with the help of measurement** | | desirability of user | - eater who's goal is nourishment need higher importance weight on ingredients <br>- gourmet would care more about recipe and measurement | - general public or lay audience may prioritize accessibility and applicability of findings<br>- academic or specialized audience may focus on methodological rigor, theoretical contribution, and relevance to existing literature | | desirability of producer | easier, cost efficient, user-satisfying, getting good review, selected as michelin star | easier, effort efficient, meaningful research, paper being cited, published in top journal | | | | | | efforts to maintain process consistency | - buy ingredient by bulk and freeze (cabbage for kimchi)<br>- test different combination of ingredient and recipe on target customer | - conduct systematic reviews and meta-analyses<br>- perform pilot studies and pre-register designs<br>- follow established protocols and engage in open science practices<br>- tailor research outputs to audience needs | | process step1: understand desire from sampled user | understand the taste of different target customers $\theta_t$ | - learn important phenomena in the field by going to seminars and talk<br>- attending interdisciplinary conferences to gather diverse research questions and trends | | process step2: develop feasible and viable process for desired product | develop recipe $\phi_t$ for each target customers $\theta_t$ | Develop a research methodology $\psi_t$ tailored to each specific research question $\theta_t$, involving a combination of qualitative and quantitative methods<br>e.g. designing a mixed-methods study that combines surveys and interviews to explore new aspects of consumer behavior in digital marketplaces | | process step3: make process scalable to maintain quality of design and compliance | Standardize cooking processes and ingredient sourcing to ensure consistency | - reproducible and replicable research<br>- ensure the scalability of research practices by adopting standardized data collection and analysis protocols that can be applied across various studies for consistency e.g. developing a template for data management and analysis that ensures consistency in research practices | | | | | | how to adopt when $\theta_t$ evolves faster than $\phi_t$? | 1. modularity (modular recipes with interchangeable components that can be easily modified to create new dishes)<br><br>2. innovative culture (experiment with new techniques and ingredients)<br><br>3. flexible supply chain management (quickly adapt to new menu needs) | 1. Modularity <br>1.1 Develop Modular Research Frameworks: research designs with interchangeable or adaptable components, such as modular questionnaires or flexible experimental setups, that can be easily adjusted to study new phenomena or incorporate emerging theories. This approach reduces the time needed to design new studies from scratch<br><br>1.2 Utilize Existing Data Sets: use existing data sets for preliminary analysis or to test new hypotheses. Need final clean test on newly collected data set though...<br><br>2. Innovation<br>2.1 Promote Interdisciplinary Collaboration: bring in fresh perspectives and methodologies that can be adapted to your research area<br><br>2.2 Rapid Research Prototyping: preliminary studies or exploratory analyses that can be quickly executed to test new ideas or methods. This approach supports the iterative refinement of research methodologies in response to new developments.<br><br>3. Flexible Supply Chain<br>3.1 Build Collaborator Network: Establish relationships with a broad network of collaborators, including other research institutions, industry partners, and cross-disciplinary teams. This network can provide rapid access to new theories, data sources, and analytical tools.<br><br>3.2 Adopt Open Science Practices: Engage in open science practices by sharing data, research instruments, and methodologies. This can facilitate the rapid dissemination and adoption of innovative research methods and encourage collaborative improvements.<br><br>3.3 Utilize Agile Research Methods: Implement agile methodologies, traditionally used in software development, to manage research projects. This involves breaking down large research questions into smaller, manageable tasks with short cycles of planning, execution, and evaluation. This allows for quick adjustments in response to new findings or changing phenomena. | | steps | behavior identification | intervention/algorithm prescription | | -------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------ | | null hypothesis | behavior doesn't exist | algorithm is not effective | | e.g. | - competition influence the inventory holdings of General Motors’ dealerships operating in isolated U.S. markets (Olivares09)<br>- increase in global sourcing results in an increase in inventory investment (Jain14) | Fast Learning and Pricing for Varying Assortments algorithm (Ferreira23) | | increase of speed (sensor) | | | <span style="color:purple">customer_action(researcher)</span> | | | integer programming | entrepreneurial decision | | ------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | 1. complexity | | | | | | polynomial-time | linear algebra with linear equations | additive opportunity independent utility functions | | | polynomial-time | integer linear algebra with linear diophantine equations | additive opportunity dependent utility functions | | | polynomial-time | linear programming with linear inequalities | non additive opportunity independent utility functions | | | NP complete | integer linear programming with linear diophantine inequalities | non additive opportunity dependent utility functions | | 2. approximation algorithm<br><br>s: subproblem's dimension, 2^s: number of extreme point, m: number of variables, n: number of constraints | | | | | | goal | iterative cut generation to converge to ideal formulation | iterative hypothesis testing to converge to product market fit | | | method1: bender’s decomposition | number of variable and constraints from m, n to m+2^s, n-1 | | | | bender’s decomposition's example | Stochastic service system design (facility location)'s First-stage decisions: where and how to operate; Uncertainty regarding customer demand; Second-stage decisions: which customers served by which servers<br><br>Stochastic network design in telecommunications, logistics, electricity's First-stage decisions: which arcs to activate; Uncertainty regarding customer demand; Second-stage decisions: how to serve customer demand on network<br><br>Stochastic vehicle routing (a priori routing); First-stage decisions: planned vehicle routes; Uncertainty regarding customer demand and travel times; Second-stage decisions: adjustments to vehicle routes or to vehicle loads when capacities are violated<br><br>Stochastic unit commitment's First-stage decisions: which power plants to turn on/off, and when; Uncertainty regarding customer demand and wind/solar production; Second-stage decisions: production amounts, line switching | | | | method2: dantzig wolfe | number of variable and constraints from m, n to m-1+2^s, n | | | | method3: lagrangian relaxation | number of variable and constraints from m, n to m-1, n+1 | | | 3. additive vs subtractive approximation algorithm | | | | | | additive | outward approximation | more hardware | | | subtractive | inward approximation | more software | | | example of additive | | pwdfi (fintech), b2c, b2b, b2g, not on the market, platform, need smaller funding (1m) | | | example of subtractive | | via, b2b, founded based on long experience; not on the market, 100 (solar developer (pj sponser)(lookinto equipment, more power), installers), need larger funding (3.2m) | ![[Pasted image 20240302084627.png]]