Machine learning and mathematical optimization

Machine learning and mathematical optimization

"I want to make a ** demand forecast ** for each convenience store x product." → Machine learning / statistical modeling-like story Prediction and elucidation of phenomena

"I want to maximize profits ** based on demand forecasts for each convenience store x product." → Mathematical optimization-like story Maximize profits (maximize / minimize KPIs after the phenomenon is elucidated)

Between machine learning and mathematical optimization: There is also the BanBit problem (reinforcement learning)

Decision-making steps and analytics reach

There are various levels of data science / AI / analytics

Decision-making steps ① Aggregation (what will happen) ② Explanation (why it happened) ③ Prediction (what will happen) ④ Decision making (what to do) ⑤ Action (actual action)

Achievement stage of analytics ① Descriptive analytics ② Diagnostic analytics ③ Predictive analytics ④ Prescription analytics (decision support by AI) ⑤ Prescription analytics (decision-making by AI)

Typically ① Aggregation (what happens) DWH / BI tool ① Descriptive analytics

Opportunity learning / statistical analysis performs (2) explanation (why it happened) and (3) prediction (what happens) ① Descriptive analytics ② Diagnostic analytics ③ Predictive analytics

④ Make decisions (what to do) and ⑤ Actions (actual actions) by mathematical optimization ① Descriptive analytics ② Diagnostic analytics ③ Predictive analytics ④ Prescription analytics (decision support by AI) ⑤ Prescription analytics (decision-making by AI)

Machine learning vs mathematical optimization

task Input to the system System mechanism System output Typical technology
Forecast / estimation ⭕️ Unknown → estimated ⭕️ Machine learning / statistics
optimisation The best one is unknown → Search ⭕️ I want to minimize / maximize 数理optimisation

How much can you do?

Description Forecast Decision support Decision making
Stock Trading (DayTrading) ○(HFT)
Supermarket purchasing plan ○ (Demand forecast) ○ (optimal purchasing)
Rental of construction equipment ○ (Demand forecast) ○ (Optimization of equipment deployment between branches) ○/?(Conflict of incentives between branches)
Commodity trade ○ (Price forecast) ○ (Suggestion of trading timing) ?? (Evaluation of political risk)
Agriculture ○ (Harvest forecast) ○(Fertilizer optimization)/?(sales plan)
M&A ?? (High individuality) ? ?

Prone to issue / operation dependence

Examples of problems that can be solved by mathematical optimization

・ Advertising allocation problem → Maximizing advertising effectiveness (CVR / CTR) ・ Vehicle delivery planning → (weight of one package, optimal route, etc.) ・ Factory production plan → Adjustment of raw materials and production volume ・ Cooperation with other factories, etc. ・ Administrative facility placement problem → (school, etc.) ・ War → (Efficient attack) ・ Portfolio → (Balance of risk / return ・ Risk can be reduced even with the same return) ・ Shift creation → (Adjustment of roles and burdens)

reference

DWH and BI tools   https://it-trend.jp/bi/article/bi_dwh

python3   numpy pulp

How to study About 50 optimization problems for application (book)

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