1. Single-item lot-sizing with quantity discount and bounded inventory
- Author
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Douglas G. Down, George Karakostas, Stavros G. Kolliopoulos, and Somayye Rostami
- Subjects
Mathematical optimization ,021103 operations research ,Computer science ,Applied Mathematics ,0211 other engineering and technologies ,Holding cost ,02 engineering and technology ,Management Science and Operations Research ,Single item ,01 natural sciences ,Industrial and Manufacturing Engineering ,Sizing ,Piecewise linear function ,010104 statistics & probability ,Bounded function ,Key (cryptography) ,Production (economics) ,0101 mathematics ,Special case ,Software - Abstract
In this paper, an efficient O ( n 2 ) algorithm is proposed to solve a special case of single-item lot-sizing problems (SILSP) in which both the production and holding costs are piecewise linear, there is an all-unit discount with one breakpoint for the production cost, and the inventory is bounded. The algorithm is based on a key structural property that may be of more general interest, that of a just-in-time ordering policy. Finally, we show that when the problem is extended to two items, it is NP-complete.
- Published
- 2021