Lower and upper bounds for scheduling energy-consuming tasks with storage resources and piecewise linear costs

This paper considers the problem of scheduling a set time- and energy-constrained preemptive tasks on discrete time horizon. At each period, total energy required by that are in process can be provided two sources: reversible one non-reversible one. The source provide an unlimited amount for given period but at expense time-dependent piecewise linear cost. is storage resource. goal to schedule task preemptively inside its window dispatch sources while satisfying capacity constraints minimizing We propose mixed integer program pseudo-polynomial size solve this NP-hard problem. Acknowledging limits model instances modest size, we iterative decomposition matheuristic compute upper bound. method relies efficient branch-and-price or local search procedure without storage. allocation fixed turn solved efficiently dynamic programming as particular lot-sizing also lower bound obtained solving relaxation new extended formulation column generation. Experimental results show quality bounds compared ones using program.