Time Horizon Of Interest Research Articles

Forecasting Changes in the Hurricane Wind Vulnerability of a Regional Inventory of Wood-Frame Houses

Current regional hurricane loss estimation models use the present-day vulnerability of the building inventory in predicting future losses and assume that it remains static throughout the time horizon of interest. In reality, the hurricane vulnerability of a region changes with time due to changes in the types and conditions of buildings. Loss estimation models, therefore, may misestimate risk and the effectiveness of mitigation plans based on these loss estimates may be compromised. In this paper, the writers develop a regional vulnerability change model to estimate changes over time in the hurricane wind vulnerability of a regional inventory of wood-frame houses. The model integrates the effects of five types of changes—changing building codes, changing technologies, building demolition and construction, structural aging, and upgrading efforts—in a simulation framework to forecast changes in the vulnerability of a region. Projectile impacts, falling trees, and flooding are not considered currently. A cas...

Heat integration of multipurpose batch plants using a continuous-time framework

Presented in this paper is a continuous-time mathematical formulation for optimization of heat integrated batch chemical plants. This formulation is applicable to both multipurpose and multiproduct facilities in which opportunities for direct heat integration exist. It is assumed that thermal driving forces and heat duties between operations identified as potential heat integration candidates are sufficient. These operations can either belong to the same batch plant or distinct batch facilities within the same site. Two scenarios are explored in this paper. The first scenario entails a situation where energy requirement is dependent on batch size, which is allowed to vary with distinct task occurrences within the time horizon of interest. The second scenario is based on fixed batch sizes in which the duty requirement is specified as a parameter. In the first scenario, the resulting formulation is initially cast as a nonconvex mixed integer nonlinear program (MINLP), which is linearized exactly to yield a convex MILP problem. This linearization is not necessary in the second scenario, as the resulting model is readily an MILP problem. A literature example and a case study are used to demonstrate the effectiveness of the formulation.

Efficient scheduling of consumer goods manufacturing processes in the continuous time domain

A new model for scheduling fast consumer goods manufacturing processes is developed using mixed-integer linear programming (MILP) techniques combined with a continuous representation of time. Key features of the model include sequence-dependent changeovers and flexible intermediate storage requirements typically arising in industrial manufacturing problems. Due to the utilization of a continuous time representation, the formulation is shown to result in reduced model sizes in terms of both variables and constraints. Near-optimal solutions are reported for the case study under investigation. Scope and purpose Off-line scheduling of batch/continuous chemical processes has traditionally been tackled within the general framework of mixed-integer linear or non-linear mathematical programming (MILP/MINLP). A number of relevant models are available in the literature, their applicability usually demonstrated via small-size academic examples. A common feature of these models is the discretization of the time horizon into equal-length intervals, the base-time of which is chosen based on the smallest processing time of the particular problem instance at hand. Depending upon the time horizon of interest and the resolution of the time grid employed, this approach can become computationally prohibitive for most realistic manufacturing processes. Continuous time formulations can in principle be used to alleviate some of the computational problems incurred by discrete time-indexed formulations, and relevant models are also available in the process systems engineering literature. However, their computational performance is usually affected by large integrality gaps, commonly defined as the relative difference of the best possible integer solution to the best integer solution found. This work documents a simple new scheduling model for continuous processes stimulated by a particular case study in fast consumer goods manufacturing. Despite its specific origin, the underlying mathematical formulation is applicable to a wide class of manufacturing processes in the chemical, petrochemical, and food industries. Application of the method to the particular case study is shown to yield near-optimal schedules in reasonable computational times.

Interactions of Maintenance and Production Planning for Multipurpose Process PlantsA System Effectiveness Approach

Process design and operations are typically concerned with the optimal selection, design, and efficient utilization of assets and resources over a time horizon of interest. The degree of utilization of process plant components critically depends on the availability level of equipment components. These availability levels are mainly associated with equipment reliability, failure characteristics, and maintenance policies. This paper presents a system effectiveness optimization framework for multipurpose plants that involves a novel preventive maintenance model coupled with a multiperiod planning model. This provides the basis for simultaneously identifying production and maintenance policies by exploiting (i) opportunities to perform preventive maintenance during equipment idle time and (ii) flexibility in selecting different production routes to potentially mitigate the adverse effects of equipment failure on the production plan. Extensions to include design decisions are also discussed. All problems are formulated as mixed integer linear programming (MILP) models, and their applicability is demonstrated by a number of illustrative examples.

Maintenance scheduling and process optimization under uncertainty

In this paper, we describe an optimization framework for (i) deriving optimal maintenance policies in continuous process operations in the presence of parametric uncertainty and (ii) analyzing and quantifying the impact of uncertainty on optimal maintenance schedules. A systems effectiveness measure is introduced which depends on expected process profitability and process and reliability/maintenance characteristics. A mixed integer nonlinear optimization model is proposed which aims at identifying the number of maintenance (preventive or corrective) actions required over a given time horizon of interest, the time instants and sequence of these maintenance actions on the various components of the process system, so that the system effectiveness is maximized. By introducing the concept of availability threshold values, it is shown that an efficient solution strategy can be established which requires the solution of much smaller nonlinear optimization problems. The application of the proposed framework to an example problem highlights the important interactions between process operation and maintenance scheduling in the presence of uncertainty.

Process design for maintainability: an optimization approach

Process design and operation is typically concerned with the optimal selection and efficient utilization of assets and resources during a time horizon of interest. The degree of utilization of these assets (e.g. equipment units) and resources, however, is critically associated with the availability level of equipment components, which is determined by the initial reliability characteristics and the implemented maintenance policy. This work introduces a system effectiveness optimization framework to properly account for maintainability characteristics at the process design level. This requires: (i) the quantification of the impact of process design on the selection of optimal maintenance policies, and (ii) the consideration of the interactions between production and maintenance planning in the operation phase of the process. The overall problem is formulated as a mixed integer linear programming (MILP) model and the applicability of the latter model is demonstrated by a numerical example.

An age reduction approach for finite horizon optimization of preventive maintenance for single units subject to random failures

We consider a single unit working in a continuous mode of operation characterized by an increasing failure rate. We determine the optimal number of preventive maintenance activities to be scheduled within a time horizon of interest, the required extent of the preventive maintenance by means of an age reduction of the unit and the corresponding optimal value of the expected profit. We assume that any breakdown occuring is minimally repaired, the repair is performed instantaneously, and the repair cost is the same for any repair. On the other hand, the cost associated with a preventive maintenance activity may vary as well as its duration.

Modelling and optimisation of general hybrid systems in the continuous time domain

This paper presents a mathematical formulation for the dynamic optimisation of hybrid processes described by general state-transition networks. In each state, the system behaviour is described by a set of differential and algebraic equations (DAEs). Transitions occur from one state to another whenever certain logical conditions are satisfied. The time horizon of interest is divided into a number of periods of variable duration, with the system potentially being in a different state in each period. Neither the initial nor the final state of the system, nor indeed any of its intermediate states, need to be known a priori. The resulting dynamic optimisation problem involves both continuous and discrete variables and is solved using a complete discretisation approach. Two examples of the application of the proposed methodology are presented.

Short-term scheduling of pipeless batch plants

Pipeless batch plants comprise a number of processing stations of varying functionality (e.g., filling, mixing, reacting and emptying stations). A number of mobile vessels are used to hold material while it is being processed at stations, or being transferred from one station to another. The vessels may have their own built-in motion mechanism, or may be transported by a shared fleet of automated guided vehicles (AGVs). Examples of processes operated in this fashion include lubricants, adhesives, pharmaceuticals and paints manufacturing. In many applications pipeless plants have advantages over more conventional ones because of their increased flexibility with respect to material transfers, and the reduced downtime of processing units caused by product changeovers. However, the full realization of these potential benefits during operation necessitates solving a complex scheduling problem. The solution details the utilization of the processing stations, the transferable vessels, and, where appropriate, the AGVs over the time horizon of interest. This paper presents a systematic and rigorous approach to the optimal detailed short-term scheduling of pipeless plants. The mathematical formulation of the problem as a mixed-integer linear programme allows recipes of arbitrary complexity to be accommodated while exploiting fully the flexibility of the available plant equipment.

Increasing long-term response to selection

Selection on estimated breeding value (EBV) alone maximises response to selection observed in the next generation, but repeated use of this selection criterion does not necessarily result in a maximum response over a longer time horizon. Selection decisions made in the current generation have at least 2 consequences. Firstly, they influence the immediate genetic response to selection and, secondly, they influence the inbreeding of the next and subsequent generations. Accumulation of inbreeding has a negative impact on future genetic response through reduction in future genetic variance and a negative impact on future performance if inbreeding depression affects the selected trait. Optimum selection decisions depend on the time horizon of interest. If this is known, then a breeding objective can be defined. A selection criterion is proposed in which the positive contributions of a selected group of parents to immediate genetic response (determined by their average EBV) is balanced against their negative contribution to future genetic response (determined by their contribution to inbreeding). The value assigned to the contribution to inbreeding is derived from the breeding objective. Selection of related individuals will be restricted if the detrimental value associated with inbreeding is high; restrictions on the selection of sibs, however, is flexible from family to family depending on their genetic merit. A selection algorithm is proposed which uses the selection criterion to select sires on 3 selection strategies, to select on i) a fixed number of sires; ii) a variable number of sires each allocated an equal number of matings; or iii) a variable number of sires allocated an optimal proportion of matings. Using stochastic simulation, these selection strategies for sires are compared with selection on EBV alone. When compared at the time horizon specified by the selection goal, the proposed selection criterion is successful in ensuring a higher response to selection at a lower level of inbreeding despite the selection of fewer sires. The selection strategy iii) exploits random year-to-year variations in the availability of individuals for selection and is successful in maximising response to the selection goal. The derivation of the value assigned to inbreeding is not exact and cannot guarantee that the overall maximum response is found. However, simulation results suggest that the response is robust to the detrimental value assigned to inbreeding.

Optimization of discrete charge batch reactors

A special class of multistage optimal control problems arises in the case of batch reactors fed by discrete instantaneous additions of raw material. The underlying differential-algebraic equations (DAEs) remain unchanged throughout the time horizon of interest, but the instantaneous additions of material are impulsive inputs that result in discontinuities in the state variables. Optimization parameters can include, among others, the amount of each charge and the reaction stage duration following each addition. In this paper, the problem of optimizing the operation of discrete charge batch reactors is addressed within a general framework that is independent of kinetic mechanisms and nonidealities. No approximation need be involved as the solution procedure is based on a general purpose robust algorithm for dynamic optimization problems.

An approach to optimal planning for SO/sub 2/ emission compliance

The Clean Air Act of 1990 mandated limits on the sulphur dioxide emission of coal-burning units by 1995 (Phase I) and 2000 (Phase II). The evaluation of options for economically complying with these limits is complicated by uncertainties in a number of key variables such us the price of emission allowances, the price premiums to be paid for low sulphur coal and other costs associated with viable, unit-specific compliance options: installing scrubbers, switching to lower sulphur coal and taking no compliance action. The problem is further complicated by the fact that minimum cost compliance options for individual units can only be determined as the units are committed and dispatched over time taking into account planned and expected forced outages. A method is proposed for solving this combined planning-operation optimization problem over a time horizon of interest using a fast unit commitment and dispatch heuristic. The method is applied to a large utility with 26 coal burning units subject to the provisions of the 1990 Clean Air Act. Representative runs indicate that the method generally converges to optimal solutions in 30 minutes or less on a personal computer. Thus, the planner can quickly explore the impacts of various assumptions regarding the prices of emission allowances, fuel premiums etc. upon optimal compliance options for individual units. >

A general algorithm for short-term scheduling of batch operations—I. MILP formulation

A general framework for handling a wide range of scheduling problems arising in multiproduct/multipurpose batch chemical plants is presented. Batch processes involving a variety of complexities are represented using a state-task network. The novel feature of this representation is that both the individual batch operations (“tasks”) and the feedstocks, intermediate and final products (“states”) are included explicitly as network nodes. Processes involving sharing of raw materials and intermediates, batch splitting and mixing and recycles of material, can be represented unambiguously as such networks. The short-term scheduling problem is formulated as a mixed integer linear program (MILP) based on a discrete time representation. Flexible equipment allocation, variable batchsizes and mixed intermediate storage policies involving both dedicated and multipurpose storage vessels are taken into account. Limited availability of raw materials, both at the start and during the time horizon of interest, is accommodated. Product deliveries may take place at any time during the horizon, and the amounts involved may be either fixed or variable. The use of utilities by the various tasks may vary over the task processing time, and may be constant or proportional to the batchsize. The availability and/or cost of utilities may vary over the time horizon of interest. The objective function is the maximization of a profit function involving the value of the products, and the cost of raw materials, utilities and material storage. The formulation may result in MILPs involving large numbers of binary variables. Issues pertaining to the efficient solution of these problems are discussed in Part II of this paper.

Decision Aids for the Management of Large Non-Job Shop Type Manufacturing Systems

In this paper we examine the problems of management and control of large scale multi-product multi-line batch manufacturing outside the mechanical engineering industries. The main examples of such non-job shop type manufacturing arises in the making of frequently purchased products e.g. small consumer goods, processed foods, cigarettes, candy, etc. The decision making problems which arise in such systems are extremely complex and the decision support tools for helping management at various levels could be of significant advantage in improving the productivity of such businesses. This paper describes a number of decision support tools which could be used at the different levels of the production hierarchy.The production hierarchy in virtually all manufacturing can be conveniently divided into 4 levels each of which is characterised by a significantly different time scale from that of the other levels. At the highest level, the time horizon of interest is 1 to 5 years and the decision making is of a strategic nature. At the next level down where the time horizon of interest is from 1-2 months to 1 year, the decision making is operational/tactical. The third level down concentrates on issues of production planning and scheduling and its horizon of interest varies from 1 hour to about 20 weeks. The lowest level deals with disturbances occurring over a very short horizon (a few seconds to about 1 hour) and at this level, most of the decision making is automatic (PID controllers, optimal control, self tuning regulators, etc.). Each higher level provides performance targets for the next level down.In this paper we examine the main issues which arise at the top three levels in the hierarchy and describe some decision support tools which have been developed by the author and others. At the top two levels the tools are designed to cope with the issues of competition whilst at the lower level (production planning and scheduling) the problems of allocating tasks to limited resources in the most cost effective way are addressed. Overall, we show how improved efficiency at each level can lead to significant improvements in productivity.