Historically we have all taken care of ‘our own’ without looking beyond and analyzing the impact of our decisions on the processes occurring upstream or downstream. In this post we want to comment on some considerations about the problems of Task Sequencing (Scheduling) and Vehicle Routing (Routing), especially in scenarios of continuous production of goods that must be subsequently delivered to customers, surely with very strict time windows.

For sure, those responsible for the production and sequencing of tasks have never stopped to think whether finishing one task before another could have a positive impact on the subsequent routing for the delivery of goods to customers. Likewise, traffic managers have planned the routes for the completed tasks in production that were coming to them. But aren’t these routes and their quality-efficiencies conditioned by the sequence of the production chain? Indeed, let’s look at a couple of ‘toy’ examples:

Let’s imagine that 7 products must be produced that require two different machines or processes, M1 and M2, with run times equal to the width of their ‘boxes’ (see image below). As they are finished they must be shipped to different locations. In the following image we have determined an order of production for the 7 products in the M1 machine and when they are finished in M1 they will be moved to M2. It is also decided that once the first two products (light blue and green) are finished, they will be sent on the light green route. Meanwhile, 3 more products have been produced, which are delivered on the red route. Although the last two products are ready, they have to wait until the red route is finished to be delivered on the dark green route. If we note on the timeline in the figure the times, Dj, at which they have been delivered, it is easy to see the time elapsed between the first delivery (light blue) and the last (orange).