Ready-mix concrete dispatching: which mixer brings which load, and when
Which truck mixer loads at which plant when and delivers to which site, so that every pour runs without interruption and the concrete is placed within 90 minutes of mixing?
Drag to rotate, right-drag or shift-drag to move the map, scroll or pinch to zoom. Each site shows how much of its concrete is placed. It turns red while the pump waits for concrete. Hover a site, a mixer or a bar for details. Plan computed with a Timefold model.
The planning question
Two fictional concrete plants supply 12 construction sites for one day. The orders range from a 20 m³ foundation slab of a family house to the 152 m³ floor slab of a logistics hall, 786 m³ in all. Each order has a start time between 07:00 and 14:00 and a placing rate: how many cubic metres per hour the pump or the crane at the site can place, including the change of trucks. Ten sites pour with a truck-mounted pump (20 to 38 m³/h), two with a crane and bucket (12 and 16 m³/h).
A pour is the continuous placing of one part of a structure. If the pump stands still for too long, the concrete already placed begins to set and the next layer no longer bonds with it. This weak seam is called a cold joint. Concrete must also be placed within 90 minutes of mixing.
Each plant has one loading bay, where one truck mixer at a time is loaded in 8 minutes. 16 truck mixers of 8 m³, 8 at each plant, bring the concrete in 101 equal loads. The roads are real roads from OpenStreetMap. Assumptions for this example: travel times from the road speeds plus 2 minutes to leave the yard and to reach the site, 5 minutes to rinse the chute at the site. Plants, sites, orders and mixers are fictional.
How we plan it
The Timefold model plans each truck mixer as a list of loads. For every change it simulates the whole day. A mixer is loaded so that it reaches its site when the pour there is due for the next load. It takes the plant from which the concrete is placed within 90 minutes and arrives on time, and of those the one with fewer kilometres. At each plant the bay loads one mixer after the other. At the site the pump waits when the next mixer is late, and a mixer waits when the load before it is not yet placed. The weights are assumed costs: 5 euros for every minute a pump and its crew wait, 1.30 euros for a waiting mixer, 1.50 euros per kilometre.
The comparison is a rule that many dispatchers know, computed with the same code. The orders are taken in the order of their start times. Each site gets a fixed group of mixers for its whole pour, as many as the round trip from the nearest plant needs, and these are the first mixers to become free. The Timefold plan starts from this plan and improves it for 3 minutes.
What the plan shows
| KPI | Optimized plan | Comparison: order of call, first free mixers, fixed mixers per site |
|---|---|---|
| pump waiting for concrete | 58 min −139 | 197 min |
| mixers waiting at the sites | 124 min −175 | 299 min |
| mixer kilometres | 2,854 km −345 | 3,199 km |
Decisions
- truck mixer for every load
- order of the loads on each mixer, and with it when it loads and at which plant
Constraints
- continuous pour at every site: the pump should never wait for concrete, a gap over 30 minutes risks a cold joint
- concrete placed within 90 minutes of mixing (loading at the plant)
- one truck mixer at a time in each loading bay (8 minutes per load), 16 truck mixers of 8 m³
Objective
first, the pumps hardly ever wait for concrete; second, the mixers stand at the sites only briefly; third, few kilometres are driven
Questions
Why do the pumps wait in the comparison?
Each site keeps its fixed group of mixers until its pour ends. The group is sized by the rule of thumb and has no reserve: when one of its mixers comes late from its previous site or waits at the loading bay, the pump stands still. At the base slab of a water tank the pump waits 31 minutes, which risks a cold joint. Six gaps are longer than 10 minutes, and one pour starts 16 minutes late. In the plan the mixers move between sites as they become free. No gap is longer than 10 minutes, and the pumps wait 58 minutes in all instead of 197.
Why does the plan drive fewer kilometres?
A mixer that has just unloaded takes its next load for a site near its position. In the comparison it drives to the same site until that pour ends, even when another site is closer. The plan drives 2,854 km instead of 3,199.
Does the 90-minute rule matter here?
It limits which plant may load for a site. For the walls of the underground car park, poured with a crane and bucket, a load from the far plant takes 8 minutes to load, 41 minutes to drive and 34 minutes to place: 83 minutes in all. The plan uses this once, while the bay of the near plant is busy. If that mixer also had to wait at the site, the load would break the rule. On average, the concrete is placed 44 minutes after mixing.
Can the plan follow changes during the day?
Yes. When a site calls off a pour, a pump breaks down or a mixer is stuck in traffic, the model is run again from the current time. Loads already on the road stay fixed, the rest is planned again.
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