A survey of optimization models on cancer chemotherapy treatment planning

While chemotherapy is an effective method for treating cancers such as colorectal cancer, its effectiveness may be dampened by the drug resistance and it may have significant side effects due to the destruction of normal cells during the treatment. As a result, there is a need for research on choosing an optimal chemotherapy treatment plan that minimizes the number of cancerous cells while ensuring that the total toxicity is below an allowable limit. In this paper, we summarize the mathematical models applied to the optimal design of the cancer chemotherapy. We first elaborate on a typical optimization model and classify relevant literature with respect to modeling methods: Optimal control model (OCM) and others. We further classify the OCM models with respect to the solution method used. We discuss the limitations of the existing research and provide several directions for further research in optimizing chemotherapy treatment planning.     

Crew rostering problem in a public transport company

In this paper, we present an applied study commissioned by Metro Bilbao on how to establish a more egalitarian annual allocation of work to drivers. Task allocation is mixed, with some tasks allocated on a rotating basis and others not. The model proposed is solved as a sequence of four types of integer programming problem. The solution obtained is quasi-optimal: all drivers carry out practically the same tasks over the full year. The main contribution of this paper is its method for combining semi-rotating allocation with a planning time frame divided into five periods of three different types with a workload distributed in a non uniform fashion over the days of the week, and with constraints agreed with employees to obtain an egalitarian solution. This method is being implemented at Metro Bilbao, and Eusko Tren has commissioned a study into a similar method by the authors.     

Towards a reference model for timetabling and rostering

Timetabling and rostering research often starts from particular real world problems. The last two decennia have seen a large number of papers discussing cases, models and approaches. This large body of publications does not presently constitute a structured domain that provides guidelines for addressing particular problem instances, nor does it allow identifying gaps where new research is needed.     

Selecting and weighting features using a genetic algorithm in a case-based reasoning approach to personnel rostering

Personnel rostering problems are highly constrained resource allocation problems. Human rostering experts have many years of experience in making rostering decisions which reflect their individual goals and objectives. We present a novel method for capturing nurse rostering decisions and adapting them to solve new problems using the Case-Based Reasoning (CBR) paradigm. This method stores examples of previously encountered constraint violations and the operations that were used to repair them. The violations are represented as vectors of feature values. We investigate the problem of selecting and weighting features so as to improve the performance of the case-based reasoning approach. A genetic algorithm is developed for off-line feature selection and weighting using the complex data types needed to represent real-world nurse rostering problems. This approach significantly improves the accuracy of the CBR method and reduces the number of features that need to be stored for each problem. The relative importance of different features is also determined, providing an insight into the nature of expert decision making in personnel rostering.     

Using Bayesian network analysis to support centre of gravity analysis in military planning

Centre of gravity (COG) analysis is an integral and cognitively demanding aspect of military operational planning. It involves identifying the enemy and friendly COG and subsequently determining the critical vulnerabilities that have to be degraded or negated to influence the COG of each side. This paper describes a modelling framework based on the causal relationships among the critical capabilities and requirements for an operation. The framework is subsequently used as a basis for the construction, population and analysis of Bayesian networks to support a rigorous and systematic approach to COG analysis. The importance of this work is that it uses existing planning process concepts to facilitate the construction of comprehensive models in which uncertainties and subjective judgements are clearly represented, thus enabling future re-use and traceability. The visual representation of the COG causal structure helps to clarify thinking and provides a way to record and impart this thinking. Moreover, it gives planners the capability to perform impact analysis, that is, to determine which actions are most likely to achieve a desirable end-state. The paper discusses the methodology, development and implementation of the COG Network Effects Tool (COGNET) suite for model population and model checking as well as impact analysis.     

Joint employee weekly timetabling and daily rostering: A decision-support tool for a logistics platform

To deal with their highly variable workload, logistics companies make their task force flexible using multi-skilled employees, flexible working hours or short-term contracts. Together with the legal constraints and the handling equipments’ capacities, these possibilities make personnel scheduling a complex task. This paper describes a model to support their chain of decisions from the weekly timetabling to the daily rostering (detailed task allocation).     

An optimal control problem in cancer chemotherapy

We consider a mathematical model for the control of the growth of tumor cells which is formulated as a problem of optimal control theory. It is concerned with chemotherapeutic treatment of cancer and aims at the minimization of the size of the tumor at the end of a certain time interval of treatment with a limited amount of drugs. The treatment is controlled by the dosis of drugs that is administered per time unit for which also a limit is prescribed. It is shown that optimal controls are of bang-bang type and can be chosen at the upper limit, if the total amount of drugs is large enough.     

Improving product location and order picking activities in a distribution centre

This article examines the effect of different product location strategies on the distance that order pickers must cover to do their job. This distance is an important cost component in warehousing activities. Our empirical study is based on a real industrial setting, in which the products are located on both sides of a conveyor belt. We show that choosing the right product location strategy allows the current picking distance to be reduced more than 10%. We also propose a post-optimization procedure that can further reduce picking distances—up to 20% of the current distances. Through a study of the routing strategy used to dispatch pickers, we demonstrate that solving a simple travelling salesman problem can further reduce distances up to 13%, compared with the distances incurred using a predetermined route. We show that reductions of up to 27% compared to current picking distances are possible if our product location and routing methods are combined.     

Master disassembly scheduling in a remanufacturing system with stochastic routings

Remanufacturing is an important source of sustainable development. Remanufactured products have proven to be high quality and low cost. Due to their unique characteristics, remanufacturing processes have many differences compared to manufacturing processes. These characteristics, which make remanufacturing complex, require good performance from Production Planning and Control (PPC) activities. The goal of the paper is to propose a mathematical model for disassembly master production scheduling considering stochastic routings in the remanufacturing environment. The proposed model is based on stochastic dynamic programming and it is applied to a real case of automotive clutch remanufacturing. The results contribute to the development of theory and practice by filling a gap in knowledge of the use of PPC systems, developing a mathematical method that can be easily implemented in a spreadsheet. The findings also show some decisions that are counterintuitive. For example, in some situations disassemble more products than necessary to meet the demand can result in a lower expected total cost.     

Process planning in a fuzzy environment

Mixed-integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted. As precise forecasts are difficult to obtain, process planning usually involves uncertainty and ambiguity in the data. This paper presents an application of fuzzy programming to process planning. The forecast parameters are assumed to be fuzzy with a linear or triangular membership function. The process planning problem is then formulated in terms of decision making in a fuzzy environment with fuzzy constraints and fuzzy net present value goals. The model is transformed to a deterministic mixed-integer linear program or mixed-integer nonlinear program depending on the type of uncertainty involved in the problem. For the nonlinear case, a global optimization algorithm is developed for its solution. This algorithm is applicable to general possibilistic programs and can be used as an alternative to the commonly used bisection method. Illustrative examples and computational results for a petrochemical complex with 38 processes and 24 products illustrate the applicability of the developed models and algorithms.     

Distribution planning in a turbulent environment

This paper looks at planning within the present distribution environment, paying particular attention to recent trends and developments. The idea of a depot as the traditional building block of a distribution network is questioned and the various functions of a regional depot are explored.The concept of a transit point as a simple alternative to a depot is developed and examples are given of its use in practice. Several refinements are available, particularly in the area of trailer technology, and these are discussed. The necessary support system for transit point operation is identified and finally the implications for distribution planning are considered.     

Soft with a hard centre: discrete-event simulation in facilitation

Discrete event simulation is normally described as a ‘hard’ OR technique. This may not, however, always be the case. An example of a simulation of a user support helpline is described which, it is argued, has many of the traits of a ‘soft’ OR intervention. In particular, the study involved a facilitated discussion around a simulation model about possible improvements to a problem situation. The nature of the intervention is considered from both a methodological and paradigmatic perspective, and conclusions are drawn about where the intervention lies on a ‘hard’ to ‘soft’ continuum. It is argued that ‘soft’ issues need to be subsumed into the prescribed methodology for discrete-event simulation.     

Problem structuring in a hospital

A management methodology for a hospital is discussed in this paper. We go further than the usual diagrammatical presentations of subsystems and individuals of a system in order to determine their positionings and role. The concept of the different levels of structures for the system, the identification and hierarchy in the systems are examined extensively and a new notation is introduced. Formulated expressions on the communications are presented, and matrices and graphs are used. Finally, a case study of this methodology is given.     

Locating a metro line in a historical city centre: application to Sevilla

When constructing a metro alignment under a historical city centre, it is important to generate a cost-effective path while maintaining a minimum distance between the alignment and historical buildings. This paper describes a simple methodology for generating a set of good alternative solutions. It is based on the use of Voronoi diagrams. The method was applied to data from the city of Sevilla.     

Slow rotation of a sphere with source at its centre in a viscous fluid

In this note, the problem of a sphere carrying a fluid source at its centre and rotating with slow uniform angular velocity about a diameter is studied. The analysis reveals that only the azimuthal component of velocity exists and is seen that the effect of the source is to decrease it. Also, the couple on the sphere is found to decrease on account of the source.     

Residential location and school planning in a tightening urban economy

Facing worse fiscal plight, many municipalities in Sweden must today carefully reexamine their activities. In urban planning, this has resulted in a growing interest in how the urban development could be designed to support and facilitate the efficient use of existing public investments. This paper focuses on the school sector as being one of the most costly. A location-allocation model of the capacitated facility location type is formulated. A set of potential schools consisting of existing and new ones are considered. The school-age children are assigned to a subset of these schools so as to minimize the sum of the capital costs of this subset and the transportation costs of the children. The model is applied to the municipality of Uppsala in Sweden. Different future settlement structures proposed by the planners as well as different housing allocations generated by a separate optimization model are evaluated.     

A mixed radiotherapy and chemotherapy model for treatment of cancer with metastasis

In this paper, a mathematical model of cancer treatment, in the form of a system of ordinary differential equations, by chemotherapy and radiotherapy where there is metastasis from a primary to a secondary site has been proposed and analyzed. The interaction between immune cells and cancer cells has been examined, and the chemotherapy agent has been considered as a predator on both normal and cancer cells. The metastasis may be time delayed. For better investigation of the treatment process and based on physical investigation, the immanent effects of inputs on cancer dynamic have been investigated. It is supposed that the interaction between NK cells and tumor cells changes during the chemotherapy. This novel approach is useful not only to gain a broad understanding of the specific system dynamics but also to guide the development of combination therapies. The analysis is carried out both analytically (where possible) and numerically. By considering such immanent effects, the tumor‐free equilibrium point will be stable at the end of treatment, and the tumor can not recur again, and the patient will totally recover. So, the present analysis suggests that a proper treatment method should change the dynamics of the cancer instead of only reducing the population of cancer cells. Copyright © 2016 John Wiley & Sons, Ltd.     

Multiscale cancer modeling: In the line of fast simulation and chemotherapy

Although Multiscale Cancer Modeling has a realistic view in the process of tumor growth, its numerical algorithm is time consuming. Therefore, it is problematic to run and to find the best treatment plan for chemotherapy, even in case of a small size of tissue. Using an artificial neural network, this paper simulates the multiscale cancer model faster than its numerical algorithm. In order to find the best treatment plan, it suggests applying a simpler avascular model called Gompertz. By using these proposed methods, multiscale cancer modeling may be extendable to chemotherapy for a realistic size of tissue.In order to simulate multiscale model, a hierarchical neural network called Nested Hierarchical Self Organizing Map (NHSOM) is used. The basis of the NHSOM is an enhanced version of SOM, with an adaptive vigilance parameter. Corresponding parameter and the overall bottom-up design guarantee the quality of clustering, and the embedded top-down architecture reduces computational complexity.Although by applying NHSOM, the process of simulation runs faster compared with that of the numerical algorithm, it is not possible to check a simple search space. As a result, a set containing the best treatment plans of a simpler model (Gompertz) is used. Additionally, it is assumed in this paper, that the distribution of drug in vessels has a linear relation with the blood flow rate. The technical advantage of this assumption is that by using a simple linear relation, a given diffusion of a drug dosage may be scaled to the desired one.By extracting a proper feature vector from the multiscale model and using NHSOM, applying the scaled-best treatment plans of Gompertz model is done for a small size of tissue. In addition, simulating the effect of stress reduction on normal tissue after chemotherapy is another advantage of using NHSOM, which is a kind of “emergent”.