Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problem

This study treats a multi-item single-machine dynamic lot size scheduling problem with sequence-independent setup cost and setup time. This problem has various heterogeneous decision features, such as lot sizing and lot sequencing. Traditionally, the problem has been treated by putting artificial constraints on the other feature in order to determine one of them. The proposed model is a Lagrange decomposition and coordination method that aims at simultaneous optimization of these decision features; however, smooth convergence to a feasible near-optimal solution has been a problem. So, in this paper, we propose a model that improves the constraint equation of the existing model and showed that it satisfies the Karush–Kuhn–Tucker (KKT) condition when we obtained a feasible solution. In addition, by applying the surrogate gradient method, which has never been applied to this problem before, it was shown that smoother convergence than before can be achieved through actual example of printed circuit board.

Polynomial-Time Solvability of Dynamic Lot Size Problems

There has been a lot of research on dynamic lot sizing problems with different nonlinear cost structures due to capacitated production, minimum order quantity requirements, availability of quantity discounts, etc. Developing optimal solutions efficiently for dynamic lot sizing models with nonlinear cost functions is a challenging topic. In this paper, we present a set of sufficient conditions such that if a single-item dynamic lot sizing problem satisfies these conditions, then the existence of a polynomial-time solution method for the problem is guaranteed. Several examples are presented to demonstrate the use of these sufficient conditions.