LP is everywhere: allocating limited resources, scheduling production, choosing investment portfolios, routing flows in networks
You run a 12-person product team. The CFO just approved your $400K quarterly Budget - but your three project leads each submitted plans totaling $550K. You can't fund everything. The spreadsheet is open, and your VP wants a plan by Friday. Where does each dollar go?
Allocation is the discipline of distributing finite resources across competing uses so that the marginal value of the last unit spent in every category is equal. It turns the abstract idea of opportunity cost into a repeatable decision process.
Allocation is choosing how to divide finite resources - Budget, Labor, time, capacity - across competing uses to maximize some objective.
You already know opportunity cost: every dollar sent one direction can't go another. Allocation is what you do about that. It's the repeatable system for deciding where each unit of resource goes.
Four properties make it an allocation problem:
This structure shows up in quarterly Budgeting, Capital Allocation decisions, distributing engineering capacity across features and maintenance, and dividing Marketing Spend across channels with different ROI curves. The math is the same in every case: optimize an objective subject to constraints.
If resources are truly unlimited (rare) or there's only one possible use, you don't have an allocation problem. If the decision is purely all-or-nothing with no partial options, you have a selection problem - though the same marginal thinking still helps you rank.
Every line on a P&L is the result of an allocation decision someone made. When you set a Budget, you're allocating. When you staff a team, you're allocating Labor. When you decide which customer segments to pursue, you're allocating Marketing Spend and sales capacity.
Bad allocation is the most common way competent teams destroy value. You can have the right strategy, the right people, and the right product - and still lose because resources pooled in the wrong places.
Consider two Operators running identical $1M Budgets:
The gap between these two isn't intelligence or work ethic. It's allocation discipline. And the cost compounds - but not in the way most people assume. An Operator who consistently puts 15% of Budget into suboptimal positions doesn't lose that 15% entirely. Misallocated dollars still produce some value, just less than they would in the optimal position. The waste is the delta between actual returns and optimal returns. If the misallocated portion earns half the marginal value it would in the right place, that's roughly 7% of total Budget value destroyed per quarter. Over a full year, that gap accumulates to nearly 30% of a quarter's output - real money, and entirely preventable.
The core principle is called the equimarginal principle: equalize marginal value across all uses. If the last dollar you put into engineering generates $3 of value but the last dollar in marketing generates $7, you're misallocated. Move dollars from engineering to marketing until the marginal values converge.
A practical note: your marginal value estimates will be rough. You're working with forecasts, historical averages, and judgment calls - not exact measurements. The framework still outperforms intuition even with significant estimation error, because it forces you to compare uses on the same scale rather than funding things based on who made the most persuasive pitch.
Here's the process:
Every project, team, channel, or initiative that wants resources.
Not average value - marginal. The 10th engineer doesn't add the same value as the 1st. Most resource categories hit diminishing returns as you scale them up.
Put the next dollar (or hour, or hire) where marginal value is highest.
As you add resources to the top-ranked use, its marginal value drops (diminishing returns). Eventually another use becomes highest-value. Keep shifting until marginal values equalize or you run out of resources.
Sometimes the real constraint isn't Budget - it's capacity, time, or a dependency. Allocating more money to a team that's blocked on an upstream Bottleneck adds zero marginal value no matter how productive that area looks in isolation. Identify the Bottleneck first.
The Shadow Price of a constraint tells you how much your objective would improve if that constraint relaxed by one unit. A Budget with a high Shadow Price is one you should fight to expand. A Budget with a near-zero Shadow Price means the real constraint is somewhere else - spending more there buys you nothing.
You manage Marketing Spend for a SaaS product with $200K per quarter to allocate across three channels. Historical data gives you marginal Revenue per $1K spent at each funding level:
Rank first-dollar marginal values: Events ($6K/$1K) > Paid search ($4K/$1K) > Content ($2.5K/$1K). Events wins the first allocation.
Fund events to $30K: captures $180K in Revenue. After $30K, events drops to $1K/$1K - now paid search ($4K/$1K) is highest.
Fund paid search to $60K: captures $240K in Revenue. Budget remaining: $110K. Paid search drops to $1.5K/$1K. Next highest is content at $2.5K/$1K.
Fund content to $80K: captures $200K in Revenue. Budget remaining: $30K. Content drops to $800/$1K. Remaining marginal values: paid search $1.5K, events $1K, content $800. Paid search wins the last $30K.
Final allocation: Paid search $90K, Content $80K, Events $30K. Expected Revenue: $180K + $240K + $200K + $45K = $665K on $200K spend, a blended 3.3x ROI.
Insight: The optimal split doesn't match average ROI rankings. Events had the best first-dollar return but hit diminishing returns fastest. The final allocation is driven by where marginal values equalize - not by which channel has the best average.
Your team has 6 approved new roles for Q3. Engineers cost $160K/year in total compensation and each adds roughly $600K/year in product capacity. Sales reps cost $120K/year (base salary plus expected Commissions) and each new rep has a $400K annual Revenue target. Based on historical data, first-year reps typically achieve about 60% of target, yielding roughly $240K in first-year Revenue per rep. You currently have 15 engineers and 3 sales reps. Product capacity is $9M/year. Current ARR is $1.8M.
Identify the Bottleneck: Product capacity ($9M/year) far exceeds current Revenue ($1.8M ARR). That's $7.2M in unused capacity. The constraint is on the Demand side, not Supply-Side.
Marginal value of an additional engineer: Adds $600K in capacity to a system with $7.2M of unused capacity. Unless this engineer builds something that directly unlocks new Demand, the marginal Revenue impact is near zero.
Marginal value of an additional sales rep: Expected $240K in new first-year Revenue on $120K in cost. Clear positive ROI. With only 3 existing reps covering a product with $9M in capacity, the addressable market has ample room before Demand-side diminishing returns set in.
Allocate heavily toward sales. The first 4-5 new reps should each achieve close to $240K given the size of the opportunity relative to current coverage. But notice: as you grow the sales team from 3 to 8, you'll eventually need product improvements to support what the expanded team is selling. Reserve at least 1 engineering role for the feature that sales data shows would improve Close Rate on a key customer segment.
Final allocation: 5 sales reps, 1 engineer. Expected first-year Revenue impact from sales: 5 reps at $240K = ~$1.2M in new ARR. The engineer's direct Revenue impact is harder to measure but supports Close Rate for the expanded team.
Compare to an even split of 3 engineers and 3 reps: 3 reps generate ~$720K in new ARR, while 3 engineers add capacity the business can't use - their marginal Revenue contribution is approximately zero. Total for the even split: ~$720K. The Demand-focused allocation produces roughly $480K more in first-year Revenue - about 67% more output from the same 6 hires.
Insight: The even split feels fair but ignores the Bottleneck. When capacity far exceeds Demand, more capacity is nearly worthless. Allocation follows the constraint - and because the constraint shifts as you add resources, you must re-evaluate marginal value at each step, not just at the start.
Optimal allocation equalizes marginal value across all competing uses - if one area returns more per dollar than another, you're misallocated and should shift resources
Most resources hit diminishing returns, which means the right allocation almost never matches the 'split it evenly' instinct that feels safe and fair
Always identify the Bottleneck before allocating - adding resources to a constraint that isn't the Bottleneck generates near-zero marginal value no matter how productive that area looks in isolation
Allocating proportionally to past spend or team size instead of marginal value - this locks in yesterday's priorities and ignores that constraints shift quarter to quarter as the business changes
Treating allocation as a one-time annual exercise rather than a continuous process - your Bottleneck in Q1 may not be your Bottleneck in Q3, and the optimal allocation shifts with it. Operators who re-evaluate monthly outperform those who set-and-forget
You have $120K and three projects. Project A returns $50K on the first $40K spent and $10K on the next $40K. Project B returns $30K on the first $40K and $25K on the next $40K. Project C returns $35K on the first $40K and $20K on the next $40K. What's the optimal allocation, and what's the total return?
Hint: Treat each $40K tranche as an independent investment with its own return. Rank all six tranches by return and fund from the top until you run out of Budget.
Rank all tranches: A-first ($50K), C-first ($35K), B-first ($30K), B-second ($25K), C-second ($20K), A-second ($10K). You have $120K, enough for 3 tranches. Fund A-first, C-first, B-first: $40K each. Total return: $50K + $35K + $30K = $115K. Compare to the naive strategy of fully funding Project A ($80K for $60K return) plus one other project ($40K for $35K) = $95K. The optimal allocation beats the 'pick the best project' approach by $20K because it exploits the fact that first-dollar returns are higher across the board than second-dollar returns.
Your engineering team has 200 hours per week of capacity. Three workstreams compete for it:
Allocate the 200 hours and calculate total quarterly value created.
Hint: Convert everything to the same unit (value per 10-hour block per quarter), rank the blocks, and allocate from the top. Remember that you have 20 blocks to allocate across the three categories.
Value per 10-hour block: Features-first (8 blocks at $8K = $64K), Defect-fixes-first (6 blocks at $5K = $30K), Cost Reduction (up to 10 blocks at $3K each), Features-remaining ($2K/block), Defect-fixes-remaining ($1K/block).
Rank and allocate 20 blocks: Features-first 8 blocks (80 hrs, $64K) + Defect-fixes-first 6 blocks (60 hrs, $30K) + Cost Reduction 6 blocks (60 hrs, $18K) = 20 blocks, 200 hours. Total quarterly value: $112K.
Compare to giving all 200 hours to features (the highest single-category average): 8 blocks at $8K + 12 blocks at $2K = $64K + $24K = $88K. The diversified allocation wins by $24K per quarter because it captures high-marginal-value blocks across all three categories instead of riding one category deep into diminishing returns.
You manage a team where the CFO just cut your annual Budget from $500K to $350K. Current spend: $200K on a growth initiative (Expected Value: $600K Revenue), $150K on maintenance operations (prevents an estimated $400K in losses), and $150K on a new-market experiment (Expected Value: $200K Revenue). How do you absorb the $150K cut?
Hint: Calculate the value-to-cost ratio for each area, but also consider how each expenditure degrades when you cut it. Cutting a maintenance Budget by even a small amount might cause disproportionate damage compared to trimming a growth initiative by the same amount. Some expenditures degrade smoothly when reduced; others collapse once you cut past a threshold.
Value-to-cost ratios: Growth initiative $600K/$200K = 3.0x. Maintenance $400K/$150K = 2.67x. Experiment $200K/$150K = 1.33x.
But ratios alone aren't enough - you need to consider how value degrades as you cut each area.
Maintenance value drops disproportionately when underfunded. Failures cascade: one missed inspection leads to a breakdown that causes three more. Cutting $50K from a $150K maintenance Budget likely costs far more than one-third of its protective value. Don't touch it.
Growth initiatives often have a minimum viable investment below which the spend produces little. Cutting from $200K to $50K doesn't give you 25% of the result - it may give you nearly nothing.
The experiment, at 1.33x, delivers the lowest value per dollar and can be paused cleanly. It hasn't created dependencies or ongoing obligations.
Best cut: Eliminate the experiment (-$150K). New allocation: Growth $200K, Maintenance $150K, Experiment $0. Value preserved: ~$1,000K ($600K + $400K). Value lost: $200K from the experiment.
The experiment can restart next quarter when Budget frees up. A maintenance failure or a gutted growth initiative can't be easily unwound. When absorbing cuts, protect expenditures that degrade non-linearly before protecting those with smooth, reversible degradation.
Allocation is the operational consequence of opportunity cost. Where opportunity cost tells you that tradeoffs exist, allocation tells you what to do about them. Every dollar you allocate carries the opportunity cost of its next-best use, and the discipline of equalizing marginal value is how you minimize total opportunity cost systematically. Downstream, this connects to Shadow Price (the value of relaxing a constraint by one unit - which tells you which Budgets are worth fighting to expand), Capital Allocation (the same marginal-value logic applied to Capital Investment and Capital Budgeting decisions), and marginal dollar allocation (asking 'where does the next dollar go?' at every increment rather than planning in bulk).
Disclaimer: This content is for educational and informational purposes only and does not constitute financial, investment, tax, or legal advice. It is not a recommendation to buy, sell, or hold any security or financial product. You should consult a qualified financial advisor, tax professional, or attorney before making financial decisions. Past performance is not indicative of future results. The author is not a registered investment advisor, broker-dealer, or financial planner.