The treatment of optimizing container transportation dynamic programming and planning

Dynamic Programming (DP) is a useful approach to multi-stage decision problems. On the basis of Bellman’s optimality principle such a problem can be decomposed into subproblems through recursive formulae. Bellman (1957), 1957a and Dantzig (1957) introduced a DP method for integer-variable linear programs. This method yields pseudo-polynomial algorithms when the number of constraints is fixed (Papadimitriou (1981)). In the class of linear programs, problems with a staircase structure can be efficiently treated by DP methods which can be interpreted as iterative predictor-corrector processes using a pricing mechanism for subproblems at individual stages (e.g., Dantzig (1963), Ho and Manne (1974), Ho (1978), Ho and Loute (1980), Abrahamson (1981) . Various applications of DP have also been developed in production planning (Manne (1958) , Wagner and Whitin (1959), Clark and Scarf (1960), Veinott (1965), 1969), Bessler and Veinott (1966), Zangwill (1965), 1966) (1969), Konno (1973), (1988), Bitran and Yanasse (1982), Bitran et al. (1984),... In particular, polynomial algorithms have been obtained for concave cost lotsizing problems and their extensions (e.g., Wagner and Whitin (1959), Zangwill (1965), (1966), (1959), Dreyfus and Law (1977).

Optimal load clipping with time of use rates

An Islamic Boarding School is one of Islamic religious education institutions that have an important role in supporting Islamic religious education in Indonesia. Islamic Boarding School has physical facilities to support the learning activities and all supporting activities. This study aims to determine the influence model between the performance factors of physical facilities based on Islamic Boarding School needs and user satisfaction. The research location is Islamic boarding school Al-Fatah Malang Regency East Java. Performance factors are structured with reference to green and smart building principles. The methods used are Multiple Linear Regression, Dynamic Programming, and Quantitative Method (QM). The research results generated ten performance factors including Security, Safety and Healthy, Facilities Function, Architectural Aesthetics, Easiness and Affordability, Structural Reliability, Building Durability, Comfortable and Regularity, Availability and Capacity of Facilities, and Implementation of Environmentally Friendly Concept. The ten performance factors have a significant influence on green and smart building performance. The steps of optimization results include Security on Luggage-Free from accidents caused by building design-Natural lighting function-Aesthetic in landscapes, sculpture, and vegetation-Easy in location accessibility from the surrounding areas-Comfort in roof structure performance-Condition in dormitory building-Comfort in dormitory rooms-Availability and capacity of bathrooms-Alternative energy from solar source.

In the dynamic programming paradigm the value of an optimal solution is recursively defined in terms of optimal solutions to subproblems. Such dynamic programming definitions can be very tricky and error-prone to specify. This paper presents a novel, elegant method based on tabled logic programming that simplifies the specification of such dynamic programming solutions. Our method introduces a new mode declaration for tabled predicates. The arguments of each tabled predicate are divided into indexed and non-indexed ones so that tabled predicates can be regarded as functions: indexed arguments represent input values and non-indexed arguments represent output values. The non-indexed arguments in a tabled predicate can be further declared to be aggregate, e.g., the minimum, so that while generating answers, the global table will dynamically maintain the smallest value for that argument. This mode declaration scheme, coupled with recursion, provides a considerably easy-to-use method for dynamic programming: there is no need to define the value of an optimal solution recursively, instead, defining a general solution suffices. The optimal value as well as its corresponding concrete solution can be derived implicitly and automatically using tabled logic programming systems. Experimental results are shown to indicate that the mode declaration improves both time and space performances in solving dynamic programming problems on tabled LP systems. Additionally, our mode declaration scheme provides an alternative implementation vehicle for preference logic programming.

In the dynamic programming paradigm the value of an optimal solution is recursively defined in terms of optimal solutions to subproblems. Such dynamic programming definitions can be tricky and error‐prone to specify. This paper presents an elegant method based on tabled logic programming (TLP) that simplifies the specification of such dynamic programming solutions. Our method introduces a new mode declaration for tabled predicates. The arguments of each tabled predicate are divided into indexed and non‐indexed arguments so that tabled predicates can be regarded as functions: indexed arguments represent input values and non‐indexed arguments represent output values. The non‐indexed arguments in a tabled predicate can be further declared to be aggregated, for example, the minimum, so that while generating answers, the global table will dynamically maintain the smallest value for that argument. This mode‐declaration scheme, coupled with recursion, provides an easy‐to‐use method for dynamic programming: there is no need to define the value of an optimal solution recursively, as the definition of a general solution suffices. The optimal value as well as its corresponding concrete solution can be derived implicitly and automatically using tabled logic programming systems. Our experimental results show that mode declarations improve performance in solving dynamic programming problems on TLP systems. Copyright © 2007 John Wiley & Sons, Ltd.

Dynamic time warping (DTW) has successfully been used in feature extraction and analysis of brain data [1,2]. However, DTW and other dynamic programming (DP) methods are not nearly as widespread in neuroscientific contexts, as they are in bioinformatics, where they are central [3]. DP algorithms are extremely powerful and efficient [4], so we explored further uses of DTW in the analysis of brain data. The first part a) applies DTW to successfully find locally interesting signal changes in EEG and functional magnetic resonance imaging (fMRI) data. In the second part b) we focused on harmonic analysis. Harmonic analysis as conducted via Fourier Transform (FT) or Wavelet Transform (WT) is extremely widespread in analyzing brain data, especially electroencephalography (EEG) data. The fundamental assumption of these methods is that a complex function (the time series waveform) can be represented as a superposition of sinusoidal oscillations. While comparing spectra is useful, it is incorrect to assume that the entirety of the spectral density is due to oscillatory activity proper (especially sinusoidal) [5]. We wanted to get some idea of the amount and effects of non-sinusoidal oscillations in EEG data. In a) we quantify the amount of local signal dissimilarity, which is often equivalent to where there is interesting sudden activity, and in b) we quantify how much non-sinusoidal activity there is in spectra computed in a standard way. For a) we apply the method on a data set from a simultaneous EEG/fMRI session with 18 subjects that has been used in other published works before [6] and show that we can easily detect movement, changes in brain state accompanying large reaction time changes during a choice reaction time task, and other interesting events in the EEG and fMRI data sets. The method is applicable to both modalities, as DTW is very general and can be used with any type of time series. The method we used works by either running DTW on a selected time interval (or volume) against sequential intervals (or volumes), or by running it as a sliding-window for detecting sudden local signal changes in the EEG or fMRI. For b) we show that the spectral power, as it's typically computed, includes non-sinusoidal activity, when compared to the signal compared against a series of equal-length (to the signal) sinusoidal waves of varying frequencies. We also found when the sinusoidal-oscillation deviations occurred during an EEG time series extrapolation which we performed using a deep learning Toolbox. The EEG time series prediction gave another point of view for the oscillation changes. We find that the prediction breakdown points are related to sudden oscillation changes, which are presumably time points when other neural oscillator generators become active and mixed in the signal. We interpret both prediction breakdowns and momentary oscillatory deviations as being possible reflections of sudden phase changes in the local or global brain state related, which may be related to EEG microstate changes. We hope to bring to attention the flexibility and power of DP to the neuroscientific community.

The mathematical model of optimal water quantity allocation for a single main canal in a large-scale irrigation area was constructed that took the minimal sum of the squared deviation of water shortage for water receiving areas controlled by the single main canal in one given irrigation period as the study target, and the total irrigation quantity of the single main canal as a constraint condition. Taking the optimal allocation of water quantity of each branch canal as decision variables, and several branch canals under the irrigation sequence of the main canal as a state variable, this model was solved by the one-dimensional dynamic programming (DP) method, by which the minimal water shortage and corresponding optimal water quantity allocation of each branch canal was calculated. The proposed method could provide a decision-making reference for optimal water resources allocation of single main canal irrigation areas, and also provide the theoretical basis for optimal water quantity allocation of a main canal with rotation irrigation by strips or with segmented rotation irrigation mode in China’s large-scale irrigation areas. Taking Hengliu Main Canal of Zhouqiao Irrigation Area in Jiangsu Province as a study case, optimization results showed that in a medium drought year (p = 75%) and a special drought year (p = 95%), minimal water shortage for water receiving areas controlled by Hengliu Main Canal was respectively 2.57 × 104 m3 and 23.31 × 104 m3 during the ponding period of rice. The corresponding water quantity allocation for each branch canal has reflected a compellent model solution precision and efficiency.

This paper mainly studies the decision-making problems encountered by enterprises in the production process, including whether to inspect parts and finished products, and how to handle unqualified parts and finished products. By applying operations research and statistical knowledge, and adopting dynamic programming and one-sided hypothesis testing methods, relevant decision-making problems are effectively solved. In this paper, the authors propose a sampling inspection method to parameterize the defect rate of parts and optimize decision-making schemes for different production stages. Finally, the study analyzes the impact of various decisions on the economic benefits of enterprises, constructs corresponding models using dynamic programming, and derives optimal solutions under various decisions. For the first problem, based on the basic principles of statistics, this paper uses one-sided hypothesis testing to detect whether the defect rate of parts exceeds the nominal value. In the case of a large sample size, the central limit theorem is cleverly applied to approximate the binomial distribution to the normal distribution, thereby simplifying the calculation process. And based on the principle of sampling inspection, detailed judgments are made on whether to accept or reject parts under different confidence levels. When studying the second problem, this paper cleverly adopts the dynamic programming method to conduct detailed decision analysis on the three key stages of the enterprise production process: part inspection, finished product inspection, and unqualified product handling. And through the reverse analysis method, starting from the final product, the decision-making of each stage is gradually optimized to ensure that the risk is minimized while controlling costs. By evaluating the relationship between inspection costs and potential losses, as well as the specific impact of different handling methods for unqualified products on the economic benefits of enterprises, the goal is to maximize economic benefits while ensuring product quality. The third problem further enhances the complexity of decision-making based on the second problem, considering multiple processes and multiple parts to optimize decision-making in the multi-stage production process. This problem still adopts the reverse analysis method of dynamic programming to construct a more complex dynamic programming model, comprehensively considering the inspection costs, unqualified product handling costs, and potential market risks of each production stage. In the process of model construction, in-depth analysis is conducted on how to effectively handle parts, semi-finished products, unqualified semi-finished products, finished products, and unqualified finished products at different production stages, including different decisions for each stage. Through careful analysis, it provides enterprises with an optimal decision-making scheme for multiple processes and multiple parts.

Recently, as the market share of electric vehicles (EVs) has increased, how to handle the increased electricity demand for EV charging in the power grid and how to use EV batteries from a grid-operating aspect have become more important. Also, from the perspective of individual EVs, Vehicle-to-Grid (V2G) technologies that reduce the cost for each vehicle’s charging in conjunction with the power grid are significant. In this paper, the V2G control problem at the individual vehicle level is studied using a Dynamic Programming (DP) algorithm that considers EVs’ charging efficiency. The DP algorithm is developed to generate an optimized charging/discharging power profile that minimizes electricity costs, while satisfying the constraints of the initial and final battery states of charge, for given a time-of-use electricity price. To show the effectiveness of the proposed algorithm, simulation is conducted for three different charging scenarios (unidirectional charging, bidirectional charging, and unidirectional charging with cost variations based on electricity usage), and the results showed that DP can achieve significant cost savings of about 30% compared to the normal charging method. Also, the result of DP is compared with that of Linear Programming, demonstrating that DP outperforms Linear Programming in cost savings for the V2G control problem.

The industry and academe broadly use linear programming to analyze the logistics or supply chain solutions, which is based on the hypothesis of fixed environment and restricted procedures. However, in the dynamic market, the supply chain driven by the market faces multi units such as customers, suppliers, manufactures, distributors and carriers and multi uncertain factors such as physical distribution, manufacturing support and purchase. Through a comparative analysis of application of linear programming and dynamic programming in supply chain policy decision, the paper concludes that dynamic programming is more suitable for logistics and supply chain system policy decision study under changing market environments.

To improve the operational efficiency of automated container terminals and the coordination between multiple operations, this article studies the integrated scheduling optimization problem of automated guided vehicles (AGVs) and yard cranes. The impact of charging constraints on AGV task allocation and scheduling is considered. With the goal of minimizing the maximum completion time of all tasks, a mixed integer programming model is proposed. A solution method based on a dynamic programming algorithm is designed, where a heuristic algorithm is used to assign tasks to the yard cranes, and the dynamic programming method is used to assign tasks to the AGVs based on the task assignment results of the yard cranes. Finally, the validity of the model and algorithm is tested by numerical experiments. Furthermore, the influence of the quantity of AGVs on the terminal operational efficiency and the impact of AGV charging strategies on AGV scheduling are analysed.

Increasing the efficiency of loading container ships, especially in wartime, is one of the most important problems. The paper examines elimination of safety issues in marine transportation of containerized goods at the stowage planning stage. The article examines well-known stowage planning software that was developed in order to help with the stowage planning process. This paper presents a Boolean mathematical model of integer linear programming, which considers structural and operational constraints of a vessel and containers likewise, including hazardous cargoes compatibility constraints (according to the International Maritime Dangerous Cargoes Code) and container loading sequences (that depends on discharging port order). The proposed approach for solving the task mentioned above consists of dividing it into two stages. At the first stage, a preliminary stowage arrangement is calculated using a simple heuristic, which takes into account structural and operational limitations, container loading sequence and compatibility of dangerous cargoes as well as certain safety parameters (stability, durability, etc.). At the second stage, the arrangement is optimized using the safety parameters using a steady-state genetic algorithm. Developments on the subject include - data structures for application in container vessel stowage planning software; - interface that allows a user to graphically display a stowage plan of a container ship; - interface that allows a user to display safety parameters of a container ship (stability, durability, etc.); - interface that allows to input and edit containers and vessel data, as well as dangerous goods segregation provisions according to the International Maritime Dangerous Cargoes Code, and displays a notification if those are not satisfied.

Purpose. To develop a new approach to the design of mining production processes with limited resources. Methods. Combinatorial optimisation methods were used to develop a new approach. The problem of designing technological processes can be solved by interpreting the problem “knapsack problem” with a private solution “backpack 0-1”. Dynamic programming algorithms are used to find the optimal solution. Findings. A new approach to the design of mining production management processes with limited resources has been developed. If the target goal is to obtain the maximum effect at minimum costs, then the direct run method is used. If there are restrictions on bandwidth, energy characteristics, specific cost, then the reverse run method is used. In the final part of the study, the proposed approach was verified. The task consisted in the development of recommendations regarding the choice of the structure of the technological chain of the cleaning pit under the given technological and mining-geological development parameters. The amount of specific production cost was imposed as a limitation. As a result of solving the design problem by the reverse run method, recommendations for replacing the cleaning equipment were developed. This made it possible to ensure the specified level of productivity and reduce the unit cost by 10.6%. The use of combinatorial optimisation methods made it possible to obtain an optimal solution in the field of given parameters. Originality. The scientific novelty of the work consists in establishing regularities in the formation of the efficiency of mineral deposit development processes. For the first time, combinatorial optimization methods were used to design the processes that accompany the development of mineral deposits, and the scope of their application was determined, as well as a number of dynamic programming tasks and algorithms were formalised: backtracking, spanning tree. Practical implication. Verification of the developed approach was carried out in relation to the design of mining production processes with limited resources. The obtained approach makes it possible to find optimal solutions under the constraints set at the design stage. As limitations can be: throughput capacity of the transport chain, energy characteristics of technological processes accompanying mining, specific cost of mining, etc. The design problem can be solved in a direct order – if the objective function is to maximise the parameter, or in the opposite way – if there are restrictions.

In any complex or large scale sequential decision making problem, there is a crucial need to use function approximation to represent the relevant functions such as the value function or the policy. The Dynamic Programming (DP) and Reinforcement Learning (RL) methods introduced in previous chapters make the implicit assumption that the value function can be perfectly represented (i.e. kept in memory), for example by using a look-up table (with a finite number of entries) assigning a value to all possible states (assumed to be finite) of the system. Those methods are called exact because they provide an exact computation of the optimal solution of the considered problem (or at least, enable the computations to converge to this optimal solution). However, such methods often apply to toy problems only, since in most interesting applications, the number of possible states is so large (and possibly infinite if we consider continuous spaces) that a perfect representation of the function at all states is impossible. It becomes necessary to approximate the function by using a moderate number of coefficients (which can be stored in a computer), and therefore extend the range of DP and RL to methods using such approximate representations. These approximate methods combine DP and RL methods with function approximation tools.

The applicability of the dynamic programming method to two-dimensional slope stability analyses is studied. The critical slip surface is defined as the slip surface that yields the minimum value of an optimal function. The only assumption regarding the shape of the critical slip surface is that the surface is an assemblage of linear segments. Stresses acting along the critical slip surface are computed using a finite element stress analysis. Assumptions associated with limit equilibrium methods of slices related to the shape of the critical slip surface and the relationship between interslice forces are no longer required. A computer program named DYNPROG was developed based on the proposed analytical procedure, and numerous example problems have been analyzed. Results obtained when using DYNPROG were compared with those obtained when using several well-known limit equilibrium methods. The comparisons demonstrate that the dynamic programming method provides a superior solution when compared with conventional limit equilibrium methods. Analyses conducted also show that factors of safety computed when using the dynamic programming method are generally slightly lower than those computed using conventional limit equilibrium methods of slices; however, as Poisson's ratio approaches 0.5, the computed factors of safety from the dynamic programming method and the limit equilibrium method appear to become similar.Key words: dynamic programming, slope stability, stress analysis, optimization theory, limit equilibrium methods of slices.