Complexity of a Dynamic Lot-production Planning Problem Formulated by a Oil Pure Integer Programming

Abstract

A dynamic lot-production planning problem can be formulated by a 0-1 pure integer programming instead of the traditional 0-1 mixed integer programming. This paper analyzes the 0-1 pure integer programming model which may be suitable for planning a short-range lot production, and three results are obtained. The first rusult is to propose an efficient algorithm for a single-item problem. The second result is to establish a polynomial-time algorithm for a two-item problem, even though the two-item problem in the 0-1 mixed integer programming model has a property of NP-completeness. The last result is to prove that the problem with three or more items is NP-complete.