Cyclic Just-In-Time Sequences Are Optimal

Abstract

Consider the Product Rate Variation problem. Given n products 1,…,i,…,n, and n positive integer demands d1,…, di,…,dn. Find a sequence α=α1,…,αT, T=\sumi=1ndi, of the products, where product i occurs exactly di times that always keeps the actual production level, equal the number of product i occurrences in the prefix α1,…, αt, t=1,…,T, and the desired production level, equal rit, where ri=di/T, of each product i as close to each other as possible. The problem is one of the most fundamental problems in sequencing flexible just-in-time production systems. We show that if β is an optimal sequence for d1,…,di,…,dn, then concatenation βm of m copies of β is an optimal sequence for md1,…, mdi,…,mdn.