Blending modelling in a process manufacturing system

integer programming;manufacturing;blending;production

Algorithmic And Mathematical Programming Approaches To Scheduling Problems With Energy-Based Objectives

This dissertation studies scheduling as a means to address the increasing concerns related to energy consumption and electricity cost in manufacturing enterprises. Two classes of problems are considered in this dissertation: (i) minimizing the makespan in a permutation flow shop with peak power consumption constraints (the PFSPP problem for short) and (ii) minimizing the total electricity cost on a single machine under time-of-use tariffs (the SMSEC problem for short). We incorporate the technology of dynamic speed scaling and the variable pricing of electricity into these scheduling problems to improve energy efficiency in manufacturing.The challenge in the PFSPP problem is to keep track of which jobs are running concurrently at any time so that the peak power consumption can be properly taken into account. The challenge in the SMSEC problem is to keep track of the electricity prices at which the jobs are processed so that the total electricity cost can be properly computed. For the PFSPP problem, we consider both mathematical programming and combinatorial approaches. For the case of discrete speeds and unlimited intermediate storage, we propose two mixed integer programs and test their computational performance on instances arising from the manufacturing of cast iron plates. We also examine the PFSPP problem with two machines and zero intermediate storage, and investigate the structural properties of optimal schedules in this setting. For the SMSEC problem, we consider both uniform-speed and speed-scalable machine environments. For the uniform-speed case, we prove that this problem is strongly NP-hard, and in fact inapproximable within a constant factor, unless P = NP. In addition, we propose an exact polynomial-time algorithm for this problem when all the jobs have the same work volume and the electricity prices follow a so-called pyramidal structure. For the speed-scalable case, in which jobs can be processed at an arbitrary speed with a trade-off between speed and energy consumption, we show that this problem is strongly NP-hard and that there is no polynomial time approximation scheme for this problem. We also present different approximation algorithms for this case and test the computational performance of these approximation algorithms on randomly generated instances

Models and Algorithms for Production Planning and Scheduling in Foundries – Current State and Development Perspectives

Mathematical programming, constraint programming and computational intelligence techniques, presented in the literature in the field of operations research and production management, are generally inadequate for planning real-life production process. These methods are in fact dedicated to solving the standard problems such as shop floor scheduling or lot-sizing, or their simple combinations such as scheduling with batching. Whereas many real-world production planning problems require the simultaneous solution of several problems (in addition to task scheduling and lot-sizing, the problems such as cutting, workforce scheduling, packing and transport issues), including the problems that are difficult to structure. The article presents examples and classification of production planning and scheduling systems in the foundry industry described in the literature, and also outlines the possible development directions of models and algorithms used in such systems

Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion

Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class of optimization problems and using MISOCP solvers. It is shown how various performance metrics of M/G/1 queues can be molded by different MISOCPs. To motivate our method practically, it is first applied to a challenging stochastic location problem with congestion, which is broadly used to design socially optimal service networks. Four different MISOCPs are developed and compared on sets of benchmark test problems. The new formulations efficiently solve large-size test problems, which cannot be solved by the best existing method. Then, the general applicability of our method is shown for similar optimization problems that use queue-theoretic performance measures to address customer satisfaction and service quality

New formulations for the conflict resolution problem in the scheduling of television commercials

We consider the conflict-resolution problem arising in the allocation of commercial advertisements to television program breaks. Due to the competition-avoidance requirements issued by advertisers, broadcasters aim to allocate any pairs of commercials promoting highly conflicting products to different breaks. Hence, the problem consists of assigning commercials to breaks, subject to time capacity constraints, with the aim of maximizing a total measure of the conflicts among commercials assigned to different breaks. Since the existing formulation can hardly be solved via exact methods, we introduce three new and efficient (mixed-) integer programming formulations of the problem. Our computational study is based on two sets of test problems, one from the literature and another more challenging data set that we generate. Numerical results show the excellent performance of the proposed formulations in terms of solution quality and computation times, when compared against an existing formulation and an effective heuristic approach. In particular, for the existing data set, all three formulations significantly outperform the existing formulation and heuristic, and moreover, for the new data set, our best formulation outperforms the heuristic on 76% of the test examples in terms of solution quality. We also provide theoretical evidence to demonstrate why some of our new formulations should outperform the existing formulation