The present work addresses the issue of Order Acceptance Scheduling (OAS) problem on a single machine, incorporating periodic energy constraints and time-of-use (TOU) electricity pricing. The objective is to maximize net revenue by strategically selecting and scheduling orders while ensuring compliance with energy constraints and TOU pricing structures. This optimization process involves making informed decisions about order acceptance based on profitability, processing time, and energy requirements, while considering the cost fluctuations imposed by TOU pricing. To effectively address this problem, a time-indexed formulation is proposed that provides a structured approach to optimizing scheduling decisions under these constraints. In order to further enhance the performance of the proposed MILP model, two families of valid constraints have been developed. These developments have led to significant improvements in computational efficiency and solution quality.

The addressed problem considers a market model where a firm produces and sells a single product over a finite horizon divided into different periods. The firm aims to set the price of each period such that the total profit is maximized, while also satisfying constraints on available production capacity and price bounds. The market demand for each period is represented by the multinomial logit (MNL) model. This problem has been previously tackled in the literature, where it was formulated as a non-convex nonlinear programming (NLP) model. The solution approach involved the integration of neural networks and evolutionary algorithms. In this paper, the initial non-convex (NLP) model is transformed into a convex one based on properties of the MNL model. This new formulation enables the resolution of the addressed problem in an optimal way. A large experimental study is carried out to evaluate the solution quality and computational times of the two models. The obtained results show the effectiveness of the convex formulation compared to the non-convex one.

This paper addresses the problem of scheduling different non-preemptive jobs on a single machine under time of use electricity tariffs consideration. The considered machine has three main states (OFF, ON, Idle) and two transition states (Turn-on and Turn-off), Each of these machine's states as well as the processing jobs, consume a specific amount of energy. Moreover, a speed-scalable case of the problem is considered, in which jobs can be processed at an arbitrary speed with a trade-off between speed and energy consumption. First, an integer linear programming model with the objective of minimizing total energy consumption costs formulates this scheduling problem. Then, since this problem is strongly NP-hard, different approximate optimization methods are investigated to provide near-optimal solutions. Finally, an extensive computational study is carried out to establish the efficiency of the proposed algorithms. The obtained results show, how a well-tuned genetic algorithm combined with an adequate local search procedure constitutes an efficient method for solving this energy-aware scheduling problem.

Reliability & redundancy allocation is one of the most frequently encountered problems in system design. This problem is subject to constraints related to the design, such as required structural, physical, and technical characteristics; and the components available in the market. This last constraint implies that system components, and their reliability, must belong to a finite set. For a parallel-series system, we show that the problem can be modeled as an integer linear program, and solved by a decomposition approach. The problem is decomposed into as many sub-problems as subsystems, one sub-problem for each subsystem. The sub-problem for a given subsystem consists of determining the number of components of each type in order to reach a given reliability target with a minimum cost. The global problem consists of determining the reliability target of subsystems. We show that the sub-problems are equivalent to one-dimensional knapsack problems which can be solved in pseudopolynomial time with a dynamic programming approach. We show that the global problem can also be solved by a dynamic programming technique. We also show that the obtained method YCC converges toward an optimal solution.