Department of Applied Informatics

The purpose of the paper is to present an overview of stochastic programs focusing on scenario-based stochastic linear programs. The ways of involving dynamic pricing idea into the selected models is discussed in short together with the decision dependent randomness case. At the end, the particular case of scenario-based model of transportation network involving a random demand and dynamic pricing is introduced.

"The main purpose of the paper is to present a specific case of dynamic pricing for the newsvendor
problem. Firstly, a short overview of the newsvendor problem is given together with references to selected
literature and remarks to its applicability. Then, dynamic pricing principles are discussed together with references
to a decision dependent randomness case in stochastic programming. The dynamic pricing problem deals with
determination of selling prices over time for a product whose demand is random and whose supply is fixed. We
approach this problem by formulating the newsvendor problem, which is introduced as a single period problem
in our case. We focus on specific features of the demand function assuming a decision dependent uniform
distribution. We assume that its support size linearly decreases with the increase of the price. Under such
assumptions, the model has suitable computational features related to the expectation of the objective function.
In addition, a possibility to increase the profit by change of the price may appear. The model formulation allows
us to use the MAPLE software for symbolic computations and visualization of results. The test results for
the selected data set are visualized at the end of the paper."

The purpose of the paper is to present a step-by-step development of the transportation optimization
model with random parameters, network design variables and with pricing. The well-known deterministic linear
transportation model with network design 0-1 variables is shortly discussed and it is extended in two separate
ways. Firstly, randomness is modeled by so-called here-and-now approach and secondly the deterministic model
is enriched with dynamic pricing elements. Then, the combined case is built and the original model is detailed.
All cases are illustrated by computations and figures.

"The purpose of the paper is to present a hybrid
algorithm to solve a transportation optimization model with
random demand parameters and network design variables. At
first, the classical deterministic linear transportation model
with network design 0-1 variables is introduced. Then, randomness
is considered for demand parameters and modeled
by here-and-now approach. The obtained scenario-based model
leads to a mixed integer linear program (MILP) that can be
solved by common integer programming techniques, see e.g.
the branch-and-bound algorithm implemented in the CPLEX
solver. Such a program may reach solvability limitations of MIP
algorithms for large scale real world data, so a suitable heuristic
development is welcome. Therefore, the idea of combination
of traditional optimization algorithm and genetic algorithm is
discussed and developed. At the end, the results are illustrated
and also verified for a small test instance by figures."

The aim of the paper is to introduce a modified hybrid algorithm to solve a wait-and-see reformulation of transportation optimization model with random demand parameters and 0-1 network design variables. Firstly, the deterministic linear transportation model with network design variables is reviewed. Then, uncertain demand parameters are introduced and modeled by random variables. The following deterministic reformulation is based on the wait-and-see (WS) approach. Finite discrete probability distributions are assumed for all random variables, and hence, the obtained separable scenario-based model can be repeatedly solved as a finite set of mixed integer linear programs (MILPs) by means of integer programming techniques or some heuristics. However, the authors combine a traditional optimization algorithm and a suitable genetic algorithm to obtain a hybrid algorithm that is modified for the WS case. Its implementation and test results illustrated by figures are also discussed in the paper.

The purpose of the paper is to present existing and discuss modified optimization models and solution techniques which are suitable for engineering decision-making problems containing random elements with emphasis on two decision stages. The developed approach is called two-stage stochastic programming and the paper links motivation, applicability, theoretical remarks, transformations, input data generation
techniques, and selected decomposition algorithms for generalized class of engineering problems. The considered techniques have been found applicable by the experience of the authors in various areas of engineering problems. They have been applied to engineering design problems involving constraints based on differential equations to achieve reliable solutions. They have served for technological process control e.g. in melting, casting, and sustainable energy production. They have been used for industrial production technologies involving related logistics, as e.g. fixed interval scheduling under uncertainty. The paper originally introduces several recent improvements in the linked parts and it focuses on the unified two-stage stochastic programming approach to engineering problems in general. It utilizes authentic experience and
ideas obtained in certain application areas and advises their fruitful utilization for other cases. The paper follows the paper published in 2010 which deals with the applicability of static stochastic programs to engineering design problems. Therefore, it refers to the basic concepts and notation introduced there and reviews only the principal ideas in the beginning. Then, it focuses on motivation of recourse concepts
and two decision stages from engineering point of view. The principal models are introduced and selected theoretical features are reviewed. They are also accompanied by the discussion about difficulties caused by real-world cases. Scenario-based approach is detailed as the important one for the solution of engineering problems, discussion in data input generation is added together with model transformation remarks.
Robust algorithms suitable for engineering problems involving nonlinearities and integer variables are selected and scenario-based decomposition is preferred. An original experience with using heuristics is shared. Several postprocessing remarks are added at the end of the paper, which is followed by an extensive literature review.

This paper presents the use of a hybrid algorithm for solving a wait-and-see reformulation of a specic transportation network design problem, which includes linear pricing with random demand parameters and 0-1 network design variables. Stochastic demand is modeled as linearly price-dependent. The formulated model is scenario-based and is solved with a combination of a mixed integer optimization algorithm and a suitable genetic algorithm. This hybrid algorithm, when compared to the previous research of the authors, contains specic adjustments in the heuristic part, and modications mostly related to the wait-and-see structure. Computational
results are illustrated by network and function graphs and discussed in the conclusion of the paper, especially in relation with the linear pricing.

The transportation network design problem is a well-known optimization problem with many practical applications. This paper deals with demand-based applications, where the operational as well as many other decisions are often made under uncertainty. Capturing the uncertain demand by using scenario-based approach, we formulate the two-stage stochastic mixed-integer linear problem, where the decision, which is made under uncertainty, of the first-stage program, is followed by the second-stage decision that reacts to the observed demand. Such a program may reach solvability limitations of algorithms for large scale real world data, so we refer to the so-called hybrid algorithm that combines a traditional optimization algorithm and a suitable genetic algorithm. The obtained results are presented in an explanatory form with the use of a sequence of figures.

The aim of this paper is to develop a model for the waste processing facility location problem in selected regions of the Czech Republic and to test a heuristic algorithm that would provide an effective solution to similar larger problems. Within this context, it is understood that the facility location decisions are made on the basis of the minimization of the total costs. The total costs include waste collection costs, facility location investments (or waste treatment costs) and penalty costs for underutilized capacity. Two modelled problems are illustrated on the basis of two examples of limited size. In order to determine whether similar, larger problems can be solved e.g. covering the whole of the Czech Republic, a heuristic algorithm is put forward and test computations performed. The algorithm used in this paper is a novel variant of Success-History Based Parameter Adaptation for Differential Evolution which implements Multi-Chaotic parent selection (MC-SHADE).

The effect of advertising on sales has been the subject of recent studies as an important aspect in many demand-based problems. Herein, we deal with the newsvendor problem, due to its simple structure, as a suitable tool for illustrating how facets of marketing may affect decision-making concerning operational problems. In the setting presented, the newsvendor is faced with advertising-sensitive stochastic demand, where a demand-related random element comprises an advertising decision of the multiplicative or additive form. We assume that a suitable advertising strategy results in increased sales. Two advertising response functions are considered, these being concave downward and S-shaped. We review and extend the existing results relating to the newsvendor problem with marketing effects, which mostly pertain to the concave function. These are generalized by defining the S-shaped function, and some original insights into the effect of advertising are given. We establish that the optimal advertising expenditure for the multiplicative case is always less than or equal to the optimal amount in the equivalent deterministic model while it is always equal in the additive case. We finally illustrate the results that are obtained by providing numerical examples involving various advertising response functions, as well as management-related interpretations.

The paper deals with the so-called waste processing facility location problem (FLP), which asks for establishing a set of operational waste processing units, optimal against the total expected cost. We minimize the waste management (WM) expenditure of the waste producers, which is derived from the related waste processing, transportation, and investment costs. We use a stochastic programming approach in recognition of the inherent uncertainties in this area. Two relevant models are presented and discussed in the paper. Initially, we extend the common transportation network flow model with on-and-off waste-processing capacities in selected nodes, representing the facility location. Subsequently, we model the randomly-varying production of waste by a scenario-based two-stage stochastic integer linear program. Finally, we employ selected pricing ideas from revenue management to model the behavior of the waste producers, who we assume to be environmentally friendly. The modeling ideas are illustrated on an example of limited size solved in GAMS. Computations on larger instances were realized with traditional and heuristic algorithms, implemented within MATLAB.