Cyclic Just-In-Time Sequences Are Optimal

  • Authors:

  • Wieslaw Kubiak

  • Affiliations:

  • Faculty of Business Administration, Memorial University of Newfoundland, St. John's, NF, Canada, A1B 3X5 (E-mail: wkubiak@mun.ca)

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2003

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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.