Discrete-time Mixed Integer Linear Programming Research Articles

Efficient formulation for transportation scheduling of single refinery multiproduct pipelines

Multiproduct pipeline transportation scheduling is a complex operations research problem that is characterized by the movement of the cargo rather than the carrier. Hence, it cannot be solved using vehicle routing methods. While most formulations for short-term scheduling adopt a continuous-time representation, they often lead to suboptimal solutions because of the dependence on the number of time slots in the grid, which is difficult to predict. Furthermore, some of these formulations have poor linear relaxations due to the presence of inefficient big-M constraints. In this paper, we develop a discrete-time mixed integer linear programming (MILP) model for the detailed scheduling of a straight pipeline with a single refinery and multiple depots. The proposed formulation rigorously detects interface material generated between adjacent products and considers planned shutdowns in pipeline segments due to maintenance operations, as well as local market demands occurring at multiple intermediate due dates. The main novelty is that continuous tasks can span multiple time slots to enforce minimum batch sizes on injection and delivery nodes, which allows for the model to generate better schedules than those obtained with previously proposed formulations. To ensure an efficient model by design, we rely on generalized disjunctive programming (GDP) and on the convex hull reformulation of disjunctions, which results in stronger and often more computationally efficient formulations. We present numerical results for a set of benchmark instances and show that the proposed model applies to large-scale industrial cases.

Optimal Maintenance for Degrading Assets in the Context of Asset Fleets-A Case Study

Decision-making for maintenance of engineering assets is a common challenge in the process industry due to ongoing degradation. With an increasing company-size, this problem becomes more complex from an operational and computational point of view. This paper introduces a case study to the academic community that represents the problem of optimal decision-making in the context of large asset fleets. The case study poses a large fleet of offshore compressors for gas production with a specific network structure. Two exemplary discrete-time mixed integer linear programming models following the Resource Task Network framework are presented. They address asset deterioration due to effects such as fouling by suggesting specific maintenance actions as a set of different countermeasures. Novel enumerator formulations are a computationally efficient and extendable way to model the various degradation types. Results show the benefit of optimal maintenance in the application to asset fleets. The decision-support that is delivered by the scheduling and planning approach helps to determine which maintenance type should be conducted and at what time. The paper demonstrates the benefits of optimal (long-term) schedules for maintenance, but indicate at the same time the need for efficient algorithms in the context of large asset fleets, in contrast to common industrial case studies that are rather small-scale.

A solution framework for the long-term scheduling and inventory management of straight pipeline systems with multiple-sources

This paper addresses the long-term scheduling of pumping and delivery operations on straight multiproduct pipeline systems connecting multiple-sources to multiple-destinations. A generic solution framework is proposed, combining heuristic procedures and mixed integer linear programming (MILP) models. The pipeline scheduling problem is decomposed into two sub-problems: the allocation and sequencing of pumping operations of the initial source, and the scheduling of delivery operations and also pumping operations of the intermediate sources. An innovative execution procedure using a rolling horizon strategy is developed to solve both problems. We focus on a new discrete-time MILP model formulation, covering several operational aspects of real-world pipeline systems, such as rigorous treatment of forbidden sequences and preventive tank maintenance and pipeline maintenance periods, while considering rigorous inventory management during the scheduling horizon. The approach is validated by solving an illustrative example and two real-world based pipeline problems. Results show that the proposed framework is able to obtain solutions in reasonable run time with detailed inventory management and respecting several operational constraints of the system.

Scheduling of a single-source multiproduct pipeline system by a matheuristic approach: Combining simulated annealing and MILP

Pipeline systems are used for distribution of oil derivatives, where the optimization of transport activities impact considerably in the oil company’s economy. We focused on the scheduling of pumping and delivery operations on straight multiproduct pipeline systems connecting a single-source to multiple-destinations. This paper develops new preprocessing heuristics and a discrete-time mixed integer linear programming (MILP) formulation for the allocation and sequencing activity (ASM model). The new MILP model includes constraints concerning the scheduling of pumping interruptions considering stoppages in order to avoid inventory problems. A preprocessing block is also proposed to better estimate the delivery operations for the initialization batches using a simulated annealing metaheuristic to provide a more robust input data for the ASM model. The results for two case studies of a real-world pipeline system were studied. Better inventory management is observed when facing low demand instances due to its capacity to effectively propose pipeline interruptions.

Discrete-Time MILP Formulation for the Optimal Scheduling of Maintenance Tasks on Oil and Gas Production Assets

In this work, we address the scheduling of general maintenance tasks on oil and gas wells and surface facilities, using a mixed integer linear programming (MILP) formulation. The problem involves multitask workorders with precedence relations, comprising both preemptive and nonpreemptive operations, using parallel heterogeneous resources. Crews with different capabilities and work shifts are accounted for. The model introduces novel ideas for expanding the scope of discrete-time formulations. We solve a scheduling problem that includes crew traveling decisions to minimize operational costs and production losses. Different instances of real-world examples are efficiently solved in reasonable times for the industry. Results demonstrate the benefits from optimizing the maintenance schedule of oil and gas production assets and the effectiveness of the solution approach.

Novel Formulation for Optimal Schedule with Demand Side Management in Multiproduct Air Separation Processes

In this article, we address the optimal scheduling of continuous air separation processes with electricity purchased from the day-ahead market, for which we propose a generalized framework to represent different operating states. Specifically, a discrete-time mixed-integer linear programming (MILP) model is developed based on this representation for operating states, which has proven to provide a tight LP relaxation for handling industrial-scale instances. The computational efficiency of the model is demonstrated with data from real industrial production. The response of the scheduling and production level is also tested with various interval lengths for the electricity pricing and length of the time horizon.

Emergency Operations Scheduling for a Blood Supply Network in Disaster Reliefs

Abstract Emergency blood supply plays an important role in disaster relief. However, large fluctuations in blood demand make precise blood forecasting a challenge. The demand for blood and information about transportation disruption are dynamically revealed over time. A discrete-time Mixed Integer Linear Programming (MILP) mathematical formulation will be developed to cope with the underlying uncertainty through a rolling horizon approach with the purpose to optimally manage the blood supply chain system in disaster relief (i.e., determining the amount of blood collection, location of the blood collection stations, transport and storage needed to meet the demand in the worst-case scenario and minimize the total response time and total operational costs). The model also takes blood characteristics and blood emergency supply constraints into consideration. The performance of the proposed model and solution method is then investigated in a real case study from the 2008 Wenchuan earthquake and the results are discussed in detail.

Fast genetic algorithm approaches to solving discrete-time mixed integer linear programming problems of capacity planning and scheduling of biopharmaceutical manufacture

The previous research work in the literature for capacity planning and scheduling of biopharmaceutical manufacture focused mostly on the use of mixed integer linear programming (MILP). This paper presents fast genetic algorithm (GA) approaches for solving discrete-time MILP problems of capacity planning and scheduling in the biopharmaceutical industry. The proposed approach is validated on two case studies from the literature and compared with MILP models. In case study 1, a medium-term capacity planning problem of a single-site, multi-suite, multi-product biopharmaceutical manufacture is presented. The GA is shown to achieve the global optimum on average 3.6 times faster than a MILP model. In case study 2, a larger long-term planning problem of multi-site, multi-product bio-manufacture is solved. Using the rolling horizon strategy, the GA is demonstrated to achieve near-optimal solutions (1% away from the global optimum) as fast as a MILP model.

An MILP approach for detailed scheduling of multi-product pipeline in pressure control mode

Scheduling with hydraulic constraints is one of the crucial aspects to guarantee multi-product pipeline safety. This paper develops a discrete-time mixed-integer linear programming (MILP) model for a single-source multi-product pipeline in pressure control mode, minimizing the pump cost as well as the labor cost of pump stoppage/restart. Instead of limiting pressure through flowrate constraints, this paper adopts piecewise linear approximation to deal with pump characteristic curves and frictional loss associated to flowrate and establish corresponding pressure constraints. The pressure at all key points along the pipeline should be within the allowable range to ensure transport safety. In this way, the proposed model can attain the integrated optimization of the pipeline scheduling and pump scheduling, thereby avoiding the possible mismatch between pressure and flowrate obtained by two-step solving strategy. Finally, the proposed method is compared with another discrete-time MILP model (Chen et al., 2017) which sets the minimum pump rate variation as objective function for the operating economy. Two cases tested on a Chinese real-world pipeline are given to demonstrate that the optimal detailed schedules obtained by the proposed model perform better in both economy and the convenience of pump operations.

Scheduling in aerospace composite manufacturing systems: a two-stage hybrid flow shop problem

This research investigates a real-world complex two-stage hybrid flow shop scheduling problem which is faced during the manufacturing of composite aerospace components. There are a number of new constraints to be taken into account in this special hybrid flow shop, in particular limited physical capacity of the intermediate buffer, limited waiting time between processing stages, and limited tools/molds used in both stages in each production cycle. We propose a discrete-time mixed integer linear programming model with an underlying branch and bound algorithm, to solve small- and medium-size problems (up to 100 jobs). To solve the large instances of the problem (up to 300 jobs), a genetic algorithm with a novel crossover operator is developed. A new heuristic method is introduced to generate the initial population of the genetic algorithm. The results show the high level of computational efficiency and accuracy of the proposed genetic algorithm when compared to the optimal solutions obtained from the mathematical model. The results also show that the proposed genetic algorithm outperforms the conventional dispatching rules (i.e., shortest processing time, earliest dues date and longest processing time) when applied to large-size problems. A real case study undertaken at one of the leading aerospace companies in Canada is used to formulate the model, collect data for the parameters of the model, and analyze the results.

Optimizing detailed schedules of a multiproduct pipeline by a monolithic MILP formulation

A multiproduct pipeline is an economical way for transporting several products from a single source to multiple delivery stations over a long distance. This paper addresses how to optimize detailed schedules of a multiproduct pipeline. A discrete-time mixed integer linear programming model is developed, which adopts a novel objective function to seek the minimum summation of pumping rate variations in every pipeline segment along a pipeline during a scheduling horizon. The feasibility of the new objective function is demonstrated in theory. A conclusion is drawn that the more stable pumping rate of a pipeline segment is, the lower frictional loss for pumping products is. Besides operational constraints, two sets of special constraints are introduced into the model for improving the operability and practicability of detailed schedules. One is the stopping and running duration limitations of injection operations and another one is the flow rate stability requirements of injection and delivery operations. The proposed MILP model is successfully tested on two real world multiproduct pipelines using CPLEX as solver.

Capacity planning for batch and perfusion bioprocesses across multiple biopharmaceutical facilities

Production planning for biopharmaceutical portfolios becomes more complex when products switch between fed-batch and continuous perfusion culture processes. This article describes the development of a discrete-time mixed integer linear programming (MILP) model to optimize capacity plans for multiple biopharmaceutical products, with either batch or perfusion bioprocesses, across multiple facilities to meet quarterly demands. The model comprised specific features to account for products with fed-batch or perfusion culture processes such as sequence-dependent changeover times, continuous culture constraints, and decoupled upstream and downstream operations that permit independent scheduling of each. Strategic inventory levels were accounted for by applying cost penalties when they were not met. A rolling time horizon methodology was utilized in conjunction with the MILP model and was shown to obtain solutions with greater optimality in less computational time than the full-scale model. The model was applied to an industrial case study to illustrate how the framework aids decisions regarding outsourcing capacity to third party manufacturers or building new facilities. The impact of variations on key parameters such as demand or titres on the optimal production plans and costs was captured. The analysis identified the critical ratio of in-house to contract manufacturing organization (CMO) manufacturing costs that led the optimization results to favor building a future facility over using a CMO. The tool predicted that if titres were higher than expected then the optimal solution would allocate more production to in-house facilities, where manufacturing costs were lower. Utilization graphs indicated when capacity expansion should be considered. © 2013 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 30:594–606, 2014

Integrated production and utility system approach for optimizing industrial unit operations

To meet utility demands some industrial units use onsite utility system. Traditionally, the management of such type of industrial units is carried out in three sequential steps: scheduling of the manufacturing unit by minimizing inventory, estimating the utility needs of manufacturing unit and finally operation planning of the utility system. This article demonstrates the value of an integrated approach which couples the scheduling of manufacturing unit with operational planning of the utility system. A discrete-time mixed integer linear programming (MILP) model is developed to compare traditional and integrated approaches. Results indicate that the integrated approach leads to significant reduction in energy costs and at the same time decreases the emissions of harmful gases.