Quantitative Methods

Stochastic Programming and Decisions You Make in Two Stages

Set the commitment you have to make now by modelling the moves you will make later — and get two numbers that tell you whether to buy a better model or buy better information.

  • Expert
  • 15 min total
  • 14 chapters

What decision this helps you make: How much to commit before the uncertainty resolves, given what you will be able to do about it afterwards — and whether the money is better spent on planning or on learning demand earlier.

What this topic is

A two-stage stochastic program splits a decision in half. First-stage decisions are made now, before you know anything: the production run, the capacity, the contracted volume. Second-stage decisions are recourse — what you do after the uncertainty resolves, such as expediting, discounting, or subcontracting. You choose the first stage to maximise its own value plus the expected value of the best recourse in each scenario. The first-stage answer is frequently nowhere near what planning on the average would give you.

Why it matters

Almost every operating commitment has this shape and almost nobody models it. Planning on the forecast and then handling the variance by exception is a two-stage decision made badly: the first stage is set as though there were no second stage, and the second stage absorbs whatever the first one got wrong, at whatever it costs. When the recourse is asymmetric — cheap to discount, brutally expensive to be short — the correct first-stage commitment can be nearly double the mean forecast, and no amount of forecasting accuracy would have revealed that.

Who should learn it

Anyone making a commitment ahead of demand: production runs, capacity bookings, seasonal buys, hiring plans, energy contracts, media commitments.

What you will understand

  • Why the plan built on average demand is not the average of the plans, and how far apart they can be
  • How the shape of the recourse cost — not the forecast — sets the right first-stage commitment
  • The two diagnostic numbers: what a stochastic model is worth, and what better information would be worth
  • When the answer is not a better model at all, but a mechanism that reveals demand earlier

Prerequisites

Common misconception

"Plan on the expected demand and adjust as you go." That is a two-stage decision solved by ignoring the second stage. Whether it works depends entirely on whether being over and being under cost roughly the same, and they almost never do. In the worked example in this lesson, expediting is capped at 15,000 units and anything beyond that loses both the margin and a contractual service penalty. Under that structure the optimal first-stage production run is 80,000 units against an expected demand of 48,750 — the mean-based plan is wrong by 64%, and it is wrong in a direction no forecasting improvement would have corrected.