Розробка моделі дуополії логістичних ланцюгів поставок з врахуванням маркетингової та інноваційної активності виробничих підприємств

This paper reports the construction and analysis of the economic and mathematical model of the duopoly of supply chains, based on the model of optimization of plans for the release and delivery of multi-range articles, taking into consideration the marketing and innovative activities of industrial enterprises. Demand for goods is supposed to be an increasing function of advertising costs. In this case, marketing investments affect only the base selling prices of articles and do not affect competitive discounts. The explicit form of this dependence can be established as a result of marketing research. It is also assumed that investments in innovative technological projects could reduce industrial costs; production costs are decreasing functions of the size of the investment. It is believed that the demand function is linearly dependent on the total volume of output produced. The criterion of optimality for supply chains is the maximum of the total profit received from the sale and delivery of finished products to points of consumption, taking into consideration the costs of production and advertising. As a result of this study, equilibrium solutions of the duopoly according to Cournot and Stackelberg were found. That has made it possible to determine the optimal values of product volumes for output, the size of investment investments, as well as product advertising costs. The model helped study the impact of investment deductions and advertising costs on the acquisition of competitive advantages by manufacturing enterprises. A numerical illustration of the results obtained is given. The proposed approach could be used to build and analyze dynamic optimization models taking into consideration the innovation and marketing activities of enterprises, as well as to study other market structuresНа основі моделі оптимізації планів випуску та доставки багатономенклатурної продукції побудовано та проаналізовано економіко-математичну модель дуополії ланцюгів поставок з урахуванням маркетингової та інноваційної активностей виробничих підприємств. Вважається, що попит на продукцію є зростаючою функцією від розмірів витрат за рекламу. При цьому маркетингові вкладення впливають лише на базові продажні ціни продукції та не впливають на конкурентні знижки. Явний вид цієї залежності може бути встановлений у результаті маркетингових досліджень. Також передбачається, що інвестиції в інноваційні технологічні проекти дозволяють зменшити витрати на виробництво, і витрати на випуск продукції є спадними функціями від обсягу інвестицій. Вважається, що функція попиту лінійно залежить від сумарних обсягів виробленої продукції. Критерієм оптимальності для ланцюгів поставок є максимум сумарного прибутку від продажу та доставки готової продукції до пунктів споживання з урахуванням додаткових витрат. В результаті дослідження знайдено рівноважні рішення дуополії за Курно та Стекельбергом. Це дало можливість визначити оптимальні значення обсягів продукції для випуску, розміри інвестиційних вкладень та витрат на рекламу продукції. Модель дозволила дослідити вплив інвестиційних відрахувань і витрат на рекламу на придбання виробничими підприємствами конкурентних переваг. Наведено чисельну ілюстрацію отриманих результатів. Запропонований підхід може бути використаний для побудови та аналізу динамічних моделей оптимізації з урахуванням інноваційної та маркетингової активностей підприємств, а також для дослідження інших ринкових структу

Analysis of the supply chain design and planning issues: Models and algorithms

Ph.DDOCTOR OF PHILOSOPH

Co-evolutionary Hybrid Bi-level Optimization

Multi-level optimization stems from the need to tackle complex problems involving multiple decision makers. Two-level optimization, referred as ``Bi-level optimization'', occurs when two decision makers only control part of the decision variables but impact each other (e.g., objective value, feasibility). Bi-level problems are sequential by nature and can be represented as nested optimization problems in which one problem (the ``upper-level'') is constrained by another one (the ``lower-level''). The nested structure is a real obstacle that can be highly time consuming when the lower-level is $\mathcal{NP}-hard$. Consequently, classical nested optimization should be avoided. Some surrogate-based approaches have been proposed to approximate the lower-level objective value function (or variables) to reduce the number of times the lower-level is globally optimized. Unfortunately, such a methodology is not applicable for large-scale and combinatorial bi-level problems. After a deep study of theoretical properties and a survey of the existing applications being bi-level by nature, problems which can benefit from a bi-level reformulation are investigated. A first contribution of this work has been to propose a novel bi-level clustering approach. Extending the well-know ``uncapacitated k-median problem'', it has been shown that clustering can be easily modeled as a two-level optimization problem using decomposition techniques. The resulting two-level problem is then turned into a bi-level problem offering the possibility to combine distance metrics in a hierarchical manner. The novel bi-level clustering problem has a very interesting property that enable us to tackle it with classical nested approaches. Indeed, its lower-level problem can be solved in polynomial time. In cooperation with the Luxembourg Centre for Systems Biomedicine (LCSB), this new clustering model has been applied on real datasets such as disease maps (e.g. Parkinson, Alzheimer). Using a novel hybrid and parallel genetic algorithm as optimization approach, the results obtained after a campaign of experiments have the ability to produce new knowledge compared to classical clustering techniques combining distance metrics in a classical manner. The previous bi-level clustering model has the advantage that the lower-level can be solved in polynomial time although the global problem is by definition $\mathcal{NP}$-hard. Therefore, next investigations have been undertaken to tackle more general bi-level problems in which the lower-level problem does not present any specific advantageous properties. Since the lower-level problem can be very expensive to solve, the focus has been turned to surrogate-based approaches and hyper-parameter optimization techniques with the aim of approximating the lower-level problem and reduce the number of global lower-level optimizations. Adapting the well-know bayesian optimization algorithm to solve general bi-level problems, the expensive lower-level optimizations have been dramatically reduced while obtaining very accurate solutions. The resulting solutions and the number of spared lower-level optimizations have been compared to the bi-level evolutionary algorithm based on quadratic approximations (BLEAQ) results after a campaign of experiments on official bi-level benchmarks. Although both approaches are very accurate, the bi-level bayesian version required less lower-level objective function calls. Surrogate-based approaches are restricted to small-scale and continuous bi-level problems although many real applications are combinatorial by nature. As for continuous problems, a study has been performed to apply some machine learning strategies. Instead of approximating the lower-level solution value, new approximation algorithms for the discrete/combinatorial case have been designed. Using the principle employed in GP hyper-heuristics, heuristics are trained in order to tackle efficiently the $\mathcal{NP}-hard$ lower-level of bi-level problems. This automatic generation of heuristics permits to break the nested structure into two separated phases: \emph{training lower-level heuristics} and \emph{solving the upper-level problem with the new heuristics}. At this occasion, a second modeling contribution has been introduced through a novel large-scale and mixed-integer bi-level problem dealing with pricing in the cloud, i.e., the Bi-level Cloud Pricing Optimization Problem (BCPOP). After a series of experiments that consisted in training heuristics on various lower-level instances of the BCPOP and using them to tackle the bi-level problem itself, the obtained results are compared to the ``cooperative coevolutionary algorithm for bi-level optimization'' (COBRA). Although training heuristics enables to \emph{break the nested structure}, a two phase optimization is still required. Therefore, the emphasis has been put on training heuristics while optimizing the upper-level problem using competitive co-evolution. Instead of adopting the classical decomposition scheme as done by COBRA which suffers from the strong epistatic links between lower-level and upper-level variables, co-evolving the solution and the mean to get to it can cope with these epistatic link issues. The ``CARBON'' algorithm developed in this thesis is a competitive and hybrid co-evolutionary algorithm designed for this purpose. In order to validate the potential of CARBON, numerical experiments have been designed and results have been compared to state-of-the-art algorithms. These results demonstrate that ``CARBON'' makes possible to address nested optimization efficiently

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios

\u3ci\u3eThe Conference Proceedings of the 1998 Air Transport Research Group (ATRG) of the WCTR Society, Volume 1 \u3c/i\u3e

UNOAI Report 98-6https://digitalcommons.unomaha.edu/facultybooks/1154/thumbnail.jp

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy