This study presents a comprehensive analysis on the Economic Lot Scheduling Problem (ELSP) without capacity constraints. We explore the optimality structure of the ELSP without capacity constraints and discover that the curve for the optimal objective values is piecewise convex with repsect to B, i.e., the values of basic period. The theoretical properties of the junction points on the piecewise convex curve not only provides us the information on "which product i" to modify, but also on "where on the B-axis" to change the set of optimal multpliers in the search process. By making use of the junction points, we propose an effective search algorithm to secure a global optimal solution for the ELSP without capacity constraints. Also, we use random experiments to verify that the proposed algorithm is efficient. The results in this paper lay important foundation for deriving an efficient heuristic to solve the conventional ELSP with capacity constraints.
- Lot sizing
- Search algorithm