Capacity acquisition for the single-item lot sizing problem under energy constraints

摘要: We study a single-item lot sizing problem integrated with some energy constraints, called energy-LSP in the rest of paper. consider production system composed identical and capacitated machines parallel. One has to decide how many start much produce serve demand and/or replenish inventory. In addition capacity limit each period, induced by on, we have on that can be consumed start-ups units. first provide mixed integer programming formulation for general case. then develop efficient polynomial time algorithms running O(Tlog T), T length planning horizon, several subproblems: (i) where all parameters are set 0, (ii) only machine consume energy, (iii) units consumes energy. show that, these special cases, seen as an extension acquisition problem. This allows us, by-product our approach, significantly improve existing result proposed without constraint nor subcontracting.