Decision Analysis Based on Enterprise Production Process

Optimal load clipping with time of use rates

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.

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.

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.

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).

New wall materials alleviate the problems of high energy consumption and heavy pollution in the production process through the forms of new natural raw materials, energy conservation, land conservation, waste utilization, etc.. In this paper, design of new building wall materials is achieved through the integrated innovation method of Theory of Inventive Problem Solving (TRIZ), Technology Acceptance Model (TAM), and Quality Function Deployment (QFD). Technical contradictions and physical contradictions in various stages of product design and production are resolved from the perspectives of user survey, R & D design, manufacturing, marketing. According to the different advantages of TRIZ, TAM and QFD in various stages of product, new wall material products of Guizhou Long Life Forestry Group are used as an example, with the integrated innovation method, the company’s new wall materials products are designed, and green, environmental, economical series wall materials products are designed and marketed in China. Key words: TRIZ; TAM; QFD; New building materials; Integrated innovation method

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 aim of this study is to optimize the decision-making in the production process of a company through Monte Carlo simulation and dynamic programming methods. First, the Sequential Likelihood Ratio Test (SPRT) is designed to improve the efficiency of sampling and inspection of supplied spare parts and the performance of the method is evaluated through Monte Carlo simulation. Second, a profit model is defined and dynamic programming is applied to solve the multi-stage decision-making problem, which specifies whether or not to inspect spare parts and finished products at each decision point and how to deal with non-conforming finished products. Then, the minimum cost of each stage is calculated by exhaustively enumerating different decision combinations to obtain the maximum profit and the optimal decision combination. Finally, the objective function of maximizing profit is constructed for the increased number of spare parts and process complexity, and the dynamic programming technique is applied again to recursively calculate the optimal decision and potential revenue from the first stage, so that the profit model can be updated during the dynamic decision-making process.

We consider a variant of no-wait flowshop scheduling that is motivated by continuous casting in the multistage production process in steel manufacturing. The task is to find a feasible schedule with a minimum number of interruptions, i.e., continuous idle time intervals on the last production stage. Based on an interpretation as Eulerian Extension Problems, we fully settle the complexity status of any particular problem case: We give a very intuitive optimal algorithm for scheduling on two processing stages with one machine in the first stage, and we show that all other problem variants are strongly NP-hard. We also discuss alternative idle time related scheduling models and their justification in the considered steel manufacturing environment. Here, we derive constant factor approximations.

Loss of control prevention for aircraft remains an active area of research to improve aviation safety. Two separate numerical methods are presented here and were used to generate attitude and flight vector recovery solutions for a simulated aircraft model in an initial upset condition. The problem is posed as an optimal control problem and both methods' general approach uses a reduced-order mathematical model of a sub-scale jet airliner simulation model. The first method discussed uses a method called dynamic programming (DP) to generate a discrete closed-loop solution and the second method uses direct transcription and sequential quadratic programming (SQP) to generate an open-loop solution. The two methods' trajectory solutions are compared with an illustrative example and it was found that both methods' solutions use the same maneuver strategy to recover the aircraft model's trajectory back to wings level flight. In conclusion the DP is limited to a reduced model to remain tractable while the SQP can use a more accurate and representative model, and the DP method is computationally expensive offline while the SQP method is expensive online.

Background Systems operating in industrial environments are often exposed to two concurrent failure mechanisms: gradual degradation and sudden traumatic events. Maintenance decisions must account for these competing risks while controlling inspection, replacement, and failure costs. This study develops a quantitative framework to determine an economically efficient maintenance strategy under such conditions. Methods A discrete-state model is formulated with three operational conditions: Good, Degraded, and Failed. Transitions between states are driven by the system’s degradation trajectory and the occurrence of traumatic failures. A long-term expected cost model is established, incorporating inspection costs, preventive replacement costs, and failure-related losses. Dynamic programming is used to identify the policy that minimizes the expected cost per unit time. The optimisation evaluates how inspection intervals, degradation rates, and traumatic event probabilities influence replacement decisions. Results The optimisation results indicate that the cost-effective policy depends strongly on the interaction between degradation progression and the frequency of traumatic events. Higher rates of traumatic events lead to earlier preventive replacement, while intermediate degradation rates make the inspection interval the primary driver of cost reduction. The model delineates the parameter regions in which periodic inspection is justified and quantifies the cost effects of different maintenance schedules. Conclusions The proposed dynamic programming approach provides a structured method for selecting inspection and replacement strategies in systems subject to multiple failure mechanisms. The results offer decision-support guidance for maintenance planning, particularly in environments where degradation and traumatic events jointly affect system reliability and operating costs.

This paper provides an in-depth study on the impact of spare parts quality inspection on production costs in the electronics industry. By establishing a model based on binomial distribution, central limit theorem and right-hand side hypothesis testing, the costs, profits and losses of enterprises under different testing strategies are analysed. Firstly, for the inspection cost problem of accessory products, the minimum number of inspections is determined by assuming the number of sample defective products using binomial distribution and approximating the probability by De Moivre-Laplace theorem. Second, the simulated annealing algorithm is combined to derive 16 decision alternatives based on the analysis of control variables, and the best decision with the lowest total cost is finally determined. Finally, for the case of increasing number of spare parts and the appearance of semi-finished products, a mathematical model with minimising cost as the objective function is developed and solved using a genetic algorithm to evaluate the total cost under different inspection strategies. The study shows that the model proposed in this paper can reasonably solve the cost optimisation problem in electronic product quality inspection with high efficiency and practicality.

ABSTRACT: In this paper, the maximum principle of optimal control theory and the method of dynamic programming are discussed in relation to the minimization of fuel consumption in ship routing. The connection between the two methods is indicated for the case in which ship routing is treated as a continuous process, meaning that the sailing paths are not restricted to arcs of a grid as in the discrete dynamic programming method, but can vary continuously in the navigation area. Practical aspects are also discussed, such as the discrete approach of dynamic programming, as well as the finite version of the continuous approach and the limited predictability of the weather. Results are presented showing least-time routes, which are obtained with computational methods based on the maximum principle and the corresponding continuous type of dynamic programming.

The cement industry confronts significant challenges in raw materials, energy demands, and CO2 emissions reduction, which are global and local environmental concerns. Life cycle assessment (LCA) has been used in many studies to assess the environmental impact of cement production and investigate ways to improve environmental performance. This study aims to analyse the environmental impact of Portland cement (CEM I) on the South African cement industry using the life cycle impact assessment (LCIA), based on the Recipe 2016 v 1.04 midpoint method. The study was conducted using data modeled after the South African cement plant, considered a cradle-to-gate system boundary, starting from the extraction of the raw material to the cement production process that produces cement as the main product. The data were obtained from the Ecoinvent database v3.7.1, integrated with SimaPro 9.1.1. software, used to assess the impact categories. For simplicity, the study merged the entire production process into five processes, i.e., raw materials usage, fuel consumption, clinker production, transportation and electricity. The impact categories of the five production stages were assessed using the LCA methodology. The impact categories investigated were classified into three categories: atmospheric, resource depletion and toxicity categories. According to the results, clinker production and electricity usage stages contribute the most to atmospheric impact (global warming, which causes climatic change due to high CO2 emissions), followed by raw materials and fuel consumption, contributing to the toxicity and resource depletion impact category. These stages contribute more than 76% of CO2 eq. and 93% of CFC-11 eq. In the midpoint method, CO2 is the most significant pollutant released. Therefore, replacing fossil fuels with alternative fuels can reduce fossil fuel use and the atmospheric impact of cement kilns.