This paper is a polyhedral study of a generalization of the mixing set where two different, divisible coefficients are allowed for the integral variables. Our results generalize earlier work on mixed integer rounding, mixing, and extensions. They also directly apply to applications such as production planning problems involving lower bounds or start-ups on production, when these are modeled as ...

Vertical flight planning concerns assigning optimal cruise altitude and speed to each trajectory-composing segment, such that the fuel consumption is minimized, and the arrival time constraints are satisfied. The previous work that assigns continuous speed to each segment leads to prohibitively long computation time. In this work, we propose a mixed integer linear programming model that assigns...

In this paper, we investigate the problem of optimal planning and deployment of multiple relays to support energyefficient uplink transmissions of Internet of Things (IoT) devices. A novel approach is proposed to optimize the relay locations with the objective of minimizing the total energy consumption of the network. In addition, the uplink transmit power of IoT devices and the device-relay-ch...

Due to the stochastic uncertainties in ramp area aircraft trajectories, the optimization of push back time windows has to account for randomness associated with the trajectories. This paper formulates a mixed integer linear program for computing the optimal chanceconstrained aircraft push back time windows. The solutions are chance-constrained because they allow for a non-zero but bounded proba...

This work addresses the topic of constrained dynamic programming for problems involving multi-stage mixed-integer linear formulations with a linear objective function. It is shown that such problems may be decomposed into a series of multi-parametric mixed-integer linear problems, of lower dimensionality, that are sequentially solved to obtain the globally optimal solution of the original probl...

The solution of single-objective unit commitment problems for generation companies participating in deregulated markets may not directly be implementable mainly because of neglecting some conflicting secondary objectives arising from policy-making at internal/external environment. Benefiting an efficient multi-objective approach to improve the applicability of price-based unit commitment soluti...

over the two last decades, distribution companies have been aware of the importance of paying attention to the all aspects of a distribution system simultaneously to be successful in the global market. these aspects are the economic, the environmental, the social and the safety aspects. in the vehicle routing problem (vrp) literature, the economic issue has often been used, while the environmen...

in some industries as foundries, it is not technically feasible to interrupt a processor between jobs. this restriction gives rise to a scheduling problem called no-idle scheduling. this paper deals with scheduling of no-idle open shops to minimize maximum completion time of jobs, called makespan. the problem is first mathematically formulated by three different mixed integer linear programming...