Optimization Solutions by Industry


Airlines and Trucking

  • Crew Scheduling:  Given a flight schedule, aircraft assignments, and restrictions on duty periods, allocate crews most effectively to flights
  • Fleet Routing and Assignment:  Determine which aircraft to fly on each route, and the sequence of segments flown by each aircraft
  • Revenue Management:  For different classes of tickets, determine how many seats to sell or hold back as flight date approaches


Oil and Gas

  • Gasoline Blending: From hydrocarbons with specific octane ratings, vapor pressure, volatility and cost, determine how much of each should be blended together to produce regular, midgrade, and premium gasoline
  • Gas Contract Purchase:  With forecasted but uncertain demand for gas, determine which contracts to buy, and how much gas to store at different times
  • Pipeline Capacity Auction:  Determine which bids, at different prices, should be awarded to maximize sales revenue while not exceeding daily pipeline capacity


Lumber, Paper and Steel

  • Cutting Stock Problems:  Given large wood / paper sheets or steel slabs / bars, and demand for units of smaller lengths/widths, determine the cutting pattern of large into small pieces that meets demand while minimizing waste



  • Crop Planning:  Given forecasted crop prices and growing conditions, determine how much of each crop to plant
  • Feed Blending:  Given the nutritional requirements for feed animals and the price of available feeds, find the blend of feed ingredients that will minimize total cost


Electric Power

  • Generator Commitment:  Given forecasted demand by period and operating cost for each generator, determine which generators should be run in each time interval
  • Electricity Trading:  Maximize the value of electricity sales in an ongoing auction environment


Financial Services

  • Efficient Portfolios:  Given forecasts of stock, bond or asset class returns, variances and covariances, allocate funds to investments to minimize portfolio risk for a given rate of return
  • Index Fund Management:  Solve a portfolio optimization problem that minimizes "tracking error" for a fund mirroring an index composed of thousands of securities
  • Asset/Liability Management:  Allocate funds to various investments to maximize portfolio return while ensuring that periodic liabilities are fully funded