OpenSpecEngineering

Finds how many forklifts, tuggers or automated guided vehicles (AGVs) you need to make a given number of moves per hour. It gives the vehicle-minutes of work each hour, the exact and whole number of vehicles, and how busy that fleet will be. Warehouse and plant planners use it to size a fleet, and to check whether the one they have can take on more work [1], [2].

Equations

W = r · t_c     N = ⌈W / a⌉     U = W / (N · a)

r is the number of trips needed per hour. t_c is the cycle time of one trip in minutes: pick up the load, travel loaded, drop it, travel back empty, plus any wait in a queue or at a dock. W is the vehicle-minutes of work in an hour. a is the minutes each vehicle is really free to work in an hour, after breaks, battery changes or charging, traffic and other delays; it must be 60 or less. W/a is the exact number of vehicles, N that number rounded up, and U the share of the fleet’s available time spent on trips [1].

Limits and common mistakes

• Use the peak hour, not the daily average. A fleet sized for the average falls behind at shift start and before shipping cutoffs.
• Count the empty trip back in t_c. Leaving it out is the most common reason fleets come out too small.
• Don’t count the same lost time twice. If t_c already includes waiting and congestion, a should cover only breaks and charging.
• A utilization near 100 % leaves no room for a breakdown or a late truck. Many planners add a vehicle, or a spare, when U is above about 85 %.
• The result assumes any vehicle can do any trip. Vehicles that are assigned to one area, or that can’t reach some racks, have to be sized area by area.

Worked example

A distribution center must move 45 pallets an hour from receiving to storage at its peak. A round trip, with the wait at the dock, takes 7.5 min. Each forklift works about 50 min in an hour after breaks and battery changes. How many forklifts does it need?

1. Enter Required Trips per Hour 45.
2. Enter Cycle Time per Trip 7.5 and Available Minutes per Vehicle-Hour 50.
3. Press Solve. The Solution shows: Vehicle-minutes of work required per hour: 337.5 min
   Vehicles required (exact): 6.75
   Vehicles required (rounded up): 7
   Fleet utilization at N vehicles: 96.4286 %

Check by hand. 45 × 7.5 = 337.5 min of work an hour, and 337.5 / 50 = 6.75, so 7 forklifts. Seven trucks have 350 min to give, and the work takes 337.5 of them, or 96 %. That leaves almost no margin, so an eighth truck (84 %) is the safer plan.