Note on cyclic sequences in the product rate variation problem

Sequencing units on a production or assembly line in order to attenuate the variations in the rates of resource consumption is a problem that has received growing attention in recent years. In the present study, a particular case, the product rate variation (PRV) problem with convex discrepancy function, is analysed. Its equivalence to the determination of a minimal path on a graph is shown. In addition, a useful property when the number of units for each kind of product to be sequenced is divisible by k (with k as a positive integer) is established. In this case an optimum sequence is obtained by repeating k times an optimum sequence in the reduced problem, once the units of each product have been divided by k.