Finance & Banking
4 optimization problems
Fixed Budget, Many Candidate Projects — Which Subset Should I Pick So That Total Return Is Maximised?
A mid-size holding or SMB investment committee faces 50-200 candidate projects every year (factory capacity, new line, warehouse, IT modernisation, digital transformation) against a fixed annual budget (50-500M TRY): which subset gets picked so the budget is respected and total return (NPV) is maximised? The intuitive 'sort by NPV / investment ratio, take from the top' rule misses small but high-return projects that fit the last 5-10% of the budget — empirically it deviates from the optimum by 5-15%, and with multi-dimensional constraints (budget + labour + machine-hours) the gap widens to 10-25%. The same structure recurs in monthly marketing campaign selection, capacity-bounded cargo loading, and supplier subset selection. The widespread committee belief 'no mathematical optimum exists, we just pick by judgement' is wrong — an optimal solution for 200-1000 candidates is delivered in minutes.
How Much Cash in Which ATM, How Often to Refill — Balancing Empty-ATM Complaints Against High Immobilisation Cost
If you are a mid-size commercial or participation bank running 50-500 ATMs, every morning you must answer three questions: how much cash should each ATM hold, how often should each one be replenished, and which route should the armoured vehicle take. The wrong extremes are expensive: too much cash sitting inside an ATM inflates the annual 5-15% interest-opportunity cost plus the insurance premium; too little cash empties the machine, customers cannot withdraw, complaints and brand damage follow. Because a shopping centre, a bus stop, a campus and an office district all have very different withdrawal patterns, an intuitive 'same amount everywhere' rule hurts both ends at once. This page is for bank operations teams who want to take all three decisions together, driven by data.
Multiple Inputs + Multiple Outputs — How Do I Measure the Relative Efficiency of My Branches or Units?
This page is for you if you run a bank with 100-500 branches, a multi-site hospital chain with 200-1,500 beds, an education directorate with hundreds of schools, or a public body comparing performance province by province. The core question: which of your branches/hospitals/schools is efficient and which is not — and for those that are not, which 'peer' unit should they learn from and by how much? Each unit consumes several inputs at once (headcount, floor space, budget) and produces several outputs at once (revenue, customers/patients/students, quality); a single-ratio metric like 'revenue per employee' does not capture that and can flag an efficient unit as weak, or vice versa. Done properly — because the peer benchmark gives a concrete improvement reference — acceptance of improvement plans for weak units rises by 40-70%, which is worth roughly 10-50 million TRY a year in operating margin on a mid-size branch network.
What Share of My Money Should Go Into Which Investment?
One of the basic questions for an SMB or individual investor: there is a sum of capital, multiple investment options (stocks, bonds, FX, commodities, deposits, real estate, reinvestment in the business), each with different expected return and risk, and correlations among them (when one falls, another rises, and so on). What percent of the capital goes where? The mathematical name is the Portfolio Optimization Problem. In 1952 Harry Markowitz introduced the mean-variance framework — the Nobel-winning foundation of modern portfolio theory. Maximize expected return while minimizing variance (risk) is a quadratic-programming problem.