Assembly-Production Lines and
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).
What would have happened to these times if production had been planned differently, i.e. in another order? Let’s look at another example.
If instead of the above order it had been planned as in the following figure, the routes would have been much more efficient (delivery points closer together), the waiting times or “dead” times of the machines lower and, above all, the difference between the first and the last delivery much smaller.
Do you have planning problems of this type in your company, and can you improve a downstream process that clearly impacts upstream?
Note that this problem does not always make sense to address. Let’s think about a couple of very simple cases. If the travel-shipping times are clearly shorter than the production times, it is sufficient to deliver as they are completed (think of home delivery of food).
Likewise, if production times are clearly shorter than shipping times, it is worthwhile to wait until all tasks are completed and plan routes with 100% of the products.
Acerca del autor
Professor at the Pablo de Olavide University (UPO) and PhD in Mathematics from the University of Seville. Senior Optimization Consultant at oga.
Passionate about Mathematics, as a fundamental science, but especially about Applied Mathematics. What motivates him most is solving real problems and that is why, after more than 20 years of experience, he has worked in Pure Mathematics, Operations Research, Multiobjective Optimization, Evolutionary Computation and finally in Machine Learning and Business Analytics.