Scheduling under a non-reversible energy source: An application of piecewise linear bounding of non-linear demand/cost functions

Piecewise linear bounding of univariate nonlinear functions and resulting mixed integer linear programming-based solution methods

“…If it is not the case, then a specific solution method may need to be designed for them. An example of such case is presented in Ngueveu et al (2016), which focused on the solution of the resulting MILP without specifying how to obtain the piecewise linear functions.…”

“…29) Definition 6.1 generalizes the one ofNgueveu et al (2016) by taking into account D ⊂ R instead of D ⊂ R + .The resulting PLB+MLP method shares the advantages of the δPLB+MILP method but, in addition, thanks to the use of relative tolerance, guarantees can be obtained on the quality of resulting bounds under conditions expressed in Proposition 6.2. Models and algorithms from Sections 3 and 4 can be adapted to ensure satisfaction of the relative tolerance constraints(27)-(29) instead of the absolute δ tolerance constraints expressed in Definitions 4.1 and 4.2.…”

Energy-aware lot sizing problem: Complexity analysis and exact algorithms

“…We propose in this paper an approach considering a given limit on the energy available in each period, which hence also limits the quantity that can be produced. Notice that a limit on the amount of available energy is also considered by Artigues et al [1], Nattaf et al [15], [16], Ngueveu et al [17] and Modos et al [14] for scheduling problems, by Schultz et al [22] for a short term production control problem and by Masmoudi et al [12] for a single-item capacitated LSP. In [12], the authors consider a flow-shop system with a maximum allowable energy level, as well as an electricity price in their objective function.…”

Cumulative scheduling with variable task profiles and concave piecewise linear processing rate functions

“…As a typical example, the non-linear function given in Fig. 3 gives the shape of the processing rate function of a fuel cell [7]. An extension of the work of [2] to linear processing rate functions as well as several solution methods was proposed in [12,13].…”