Time representations and mathematical models for process scheduling problems

Abstract

During the last 15 years, many mathematical models have been developed in order to solve process operation scheduling problems, using discrete or continuous time representations. In this paper, we present a unified representation and modeling approach for process scheduling problems. Four different time representations are presented, compared, and applied to single-stage and multi-stage batch scheduling problems, as well as crude-oil operations scheduling problems. We introduce three solution methods that can be used to achieve global optimality or obtain near-optimal solutions depending on the stop criterion used. Computational results show that the Multi-Operation Sequencing time representation is superior to the others as it allows efficient symmetry-breaking and requires fewer priority-slots, thus leading to smaller model sizes.

A Mixed-Integer Linear Programming Model for Optimizing the Scheduling and Assignment of Tank Farm Operations

“…One of the examples in this paper shows the impact of including optimal scheduling in the TFOP, as opposed to assuming a fixed schedule. Even though the scheduling part of the problem corresponds to an efficient model for continuous-time scheduling based on the idea of Multi-operation Sequencing (Mouret et al, 2011), the scheduling horizon that can be contemplated within reasonable computational time is limited to a few weeks. For this reason a representative set of production orders and release dates has to be chosen in order to obtain an efficient product-assignment for medium to long-term operation.…”

“…Multi-operation sequencing (MOS) receives its name from the fact that several operations can be assigned to the same slot unless they are considered as non-overlapping. To illustrate this concept, consider the six operations and three resources shown in Table 1 (Mouret et al, 2011).…”

“…Yet another type of continuous time models relevant to the TFOP comes from the study of tank transfer and crude oil scheduling problems in the refining industry (Furman et al, 2007;Mouret et al, 2009;Mouret et al, 2011 ). Among these alternative models, we use the Multi-operation Sequencing (MOS) model described by Mouret et.…”

“…The objective of the problem is to minimize blocking of the finished lines by obtaining an optimal schedule and an optimal allocation of storage resources. The scheduling part of the model is based on the Multi-operation Sequencing (MOS) model by Mouret et al, (2011). The formulation is tested in three examples of different size and complexity.…”

The block planning approach for continuous time-based dynamic lot sizing and scheduling

“…In this regard, it also combines issues of lot sizing and scheduling in a realistic way. Motivated by the early development of continuous time-based model formulations for scheduling chemical batch operations (see Mouret et al 2011 for a comprehensive overview), Grunow et al (2003) developed a continuous time-based approach for scheduling production campaigns in a supply network of the chemical-pharmaceutical industry. From their model formulation, the basic block planning approach (Günther et al 2006), was derived as a single-stage model formulation primarily for application in high-variant production systems with volatile demand.…”