Optimum workforce-size model using dynamic programming approach

This research is about the development of a dynamic programming model for solving fuzzy linear programming problems. Initially, fuzzy dynamic linear programming model FDLP is developed. This research revises the established dynamic programming model for solving linear programming problems in a crisp environment. The mentioned approach is upgraded to address the problem in an uncertain environment. Dynamic programming model can either be passing forward or backward. In the proposed approach backward dynamic programming approach is adopted to address the problem. It is then followed by implementing the proposed method on the education system of Pakistan. The education system of Pakistan comprises of the Primary, Middle, Secondary, and Tertiary education stages. The problem is to maximize the efficiency of the education system while achieving the targets with minimum usage of the constrained resources. Likewise the model tries to maximize the enrollment in the Primary, Middle, Secondary and Tertiary educational categories, subject to the total available resources in a fuzzy uncertain environment. The solution proposes that the enrollment can be increased by an amount 9997130, by increasing the enrollment in the Middle and Tertiary educational categories. Thus the proposed method contributes to increase the objective function value by 30%. Moreover, the proposed solutions violate none of the constraints. In other words, the problem of resources allocation in education system is efficiently managed to increase efficiency while remaining in the available constrained resources. The motivation behind using the dynamic programming methodology is that it always possesses a numerical solution, unlike the other approaches having no solution at certain times. The proposed fuzzy model takes into account uncertainty in the linear programming modeling process and is more robust, flexible and practicable.

This study formulates and solves an advertising pulsation problem for a monopolistic firm using dynamic programming (DP). The firm aims at maximising profit through an optimal allocation of the advertising budget in terms of rectangular pulses over a finite planning horizon. Aggregate sales response to the advertising effort is assumed to be governed by a modified version of the Vidale–Wolfe model in continuous time proposed by Little. Using a numerical example in which a planning horizon of one year is divided into one, two through ten equal time periods, computing routines are developed to solve 150 DP problems. Computational results show among other findings that the performance yielded by the DP policy dominates the uniform advertising policy (constant spending) for a concave advertising response function and the advertising pulsing policy (turning advertising on and off) for a linear or convex response function.

In this paper, the application of the dynamic programming approach to constrained stochastic control problems with expected value constraints is demonstrated. Specifically, two such problems are analyzed using this approach. The problems analyzed are the problem of minimizing a discounted cost infinite horizon expectation objective subject to an identically structured constraint, and the problem of minimizing a discounted cost infinite horizon minimax objective subject to a discounted expectation constraint. Using the dynamic programming approach, optimality equations, which are the chief contribution of this paper, are obtained for these problems. In particular, the dynamic programming operators for problems with expectation constraints differ significantly from those of standard dynamic programming and problems with worst-case constraints. For the discounted cost infinite horizon cases, existence and uniqueness of solutions to the dynamic programming equations are explicitly shown by using the Banach fixed point theorem to show that the corresponding dynamic programming operators are contractions. The theory developed is illustrated by numerically solving the constrained stochastic control dynamic programming equations derived for simple example problems. The example problems are based on a two-state Markov model that represents an error prone system that is to be maintained.

Optimal Consumption Plans—A Dynamic Programming Approach

In the next decades, many public infrastructure assets will reach the end of their life that they were originally designed for. Replacement costs are high, and therefore increasing effort is put into lifetime-extending maintenance, including major overhauls and renovations. A key question is whether the investments in lifetime-extending maintenance justify the postponement of a full replacement. This question becomes more complicated when future life cycle cash flows are non-repeatable. Differential inflation and technological change, including multiple intervention strategies to maintain a desired functionality, cause such non-repeatability. In this case, classic replacement analysis techniques will not suffice in answering this question. Literature demonstrates that case-specific modelling with dynamic or linear programming techniques is required to find economic optimisation. However, such literature primarily addresses replacement interval optimisation of new investments within relative short time horizons, whereas the current research develops a nested dynamic programming (DP) approach for typical ageing infrastructure assets over long service life periods. The model can deal with multiple and various successive intervention strategies and addresses differential inflation and age-related cost increases. Finally, it is shown in an infrastructure case study that this DP approach leads to a better decision in comparison to the application of classical replacement techniques.

This paper considers optimal feedback control for a general continuous time finite-dimensional deterministic system with finite horizon cost functional. A practically feasible algorithm to calculate the numerical solution of the optimal feedback control by dynamic programming approach is developed. The highlights of this algorithm are: a) It is based on a convergent constructive algorithm for optimal feedback control law which was proposed by the authors before through an approximation for the viscosity solution of the time-space discretization scheme developed by dynamic programming method; b) The computation complexity is significantly reduced since only values of viscosity solution on some local cones around the optimal trajectory are calculated. Two numerical experiments are presented to illustrate the effectiveness and fastness of the algorithm.

The basic procedures for solving different types of dynamic programming problem were explained in Part II. This was followed in Parts III and IV by an examination of how some of the problems encountered in agriculture and natural resource industries can be solved by dynamic programming. In this final chapter some reflections are presented on the usefulness of the dynamic programming approach, the extent to which the technique has been applied in agriculture and natural resource industries to date, and the scope for its use in the future.

Ship voyage optimization for safe and energy-efficient navigation: A dynamic programming approach

Dynamic programming is a mathematical technique for optimizing decisions in stages by breaking a problem inton stages mthat solve recursively. It display the quantity and arrangement of invemtory to maintain production and ,businness revenue efficiently when used in inventory control management. This production planning uses a dynamic programming method based on the results of advanced calculations start from stage 1 and move forward to stage 12. the dynamic programming approach in this writing is deterministic because the pattern of the number of requests for bread is known absolutely. Decisions involving a problem are simplified little by little rather than directly. This research uses linear regression with a mathematical formula that is: followed by the defect percetage formula to forecast demand for the next 12 months and apply a dynamic program to achieve the minimum total quantity.

The most significant issue in cities is garbage collection. The average amount of waste a person produces daily rises as the population grows, creating severe waste management issues. Any municipality's most pressing issues are bin status monitoring, locating the shortest route, and vehicle costs. The problem's consequences result in inadequate waste monitoring and management procedures. An effective garbage collection system that periodically measures the amount of garbage in the bins is used to solve these issues. The shortest route can be determined using this bin's status. The vehicle only went to the places where the bins in the city are full. The Wi-Fi module will transmit all of the information to the municipality. The main objective of the proposed work is to create a flexible application that dynamically solve the issue of late bin clearance, poor management of bins etc. The path selection is made by using the Travelling Salesman Algorithm in the Dynamic programming approach. The sensor network is utilized to gather information regarding the garbage contents in the bins and remotely trigger the request for a cleaning process using the Internet of Things. The internet is connected with microcontroller hardware using a Node-MCU device, or ESP8266, a small internet-supporting module that works as a plug-and-play module to any microcontroller. The primary objective of this system is to send information to the municipality and the mobile application regarding the status of the bin, the minimum cost path, the total travel distance, and the kind of vehicle required. This system aims to shorten travel time, save money on diesel and human resources for garbage collection, and improve waste collection and monitoring.

This article presents a novel dynamic programming approach to determine the robust controllability of Boolean control networks (BCNs) subject to stochastic disturbances. By applying Bellman's optimality principle, we derive the recurrence relation for computing the optimal time matrix, a crucial concept characterizing robust reachability between two arbitrary states. We develop a finite-termination dynamic programming algorithm to calculate the optimal time matrix exactly and efficiently, with a rigorously certified iteration count. Sufficient and necessary conditions for robust controllability are then established based on the optimal time matrix. Furthermore, for any pair of reachable states, we construct time-optimal state feedback control laws to steer the system from the initial state to the target state, regardless of disturbances. Finally, extensive numerical experiments with biological networks validate the effectiveness of the proposed approach, showing significant improvements in computational efficiency. Additionally, we introduce a Q-learning-based algorithm and compare its performance, highlighting the advantages of our dynamic programming approach in terms of both efficiency and solution quality.

This paper reports on the successful development and implementation of an interactive manpower scheduling and planning system for a children’s mental health facility in a large urban hospital centre in Montreal, Canada. This service employs approximately 120 professionals who meet the nursing and therapy needs of between 70 and 100 children at any one time, with a yearly through-put of approximately 120 patients. The system is based on the patient as a central entity and is designed to improve the patient flow and resource scheduling process and to permit the evaluation of policy options in real time.

In the future, automated smart home energy management systems (SHEMSs) will assist residential energy users to schedule and coordinate their energy use. In order to undertake efficient and robust scheduling of distributed energy resources, such a SHEMS needs to consider the stochastic nature of the household's energy use and the intermittent nature of its distributed generation. Currently, stochastic mixed-integer linear programming (MILP), particle swarm optimization and dynamic programming approaches have been proposed for incorporating these stochastic variables. However, these approaches result in a SHEMS with very costly computational requirements or lower quality solutions. Given this context, this paper discusses the drawbacks associated with these existing methods by comparing a SHEMS using stochastic MILP with heuristic scenario reduction techniques to one using a dynamic programming approach. Then, drawing on analysis of the two methods above, this paper discusses ways of reducing the computational burden of the stochastic optimization framework by using approximate dynamic programming to implement a SHEMS.

In this paper, we present a new scheduling problem and describe a shortest path-based heuristic as well as a dynamic programming-based exact optimization algorithm to solve it. The selective multi-category parallel-servicing problem arises when a set of jobs has to be scheduled on a server (machine) with limited capacity. Each job requests service in a prespecified time window and belongs to a certain category. Jobs may be serviced partially, incurring a penalty; however, only jobs of the same category can be processed simultaneously. One must identify the best subset of jobs to process in each time interval of a given planning horizon, while respecting the server capacity and scheduling requirements. We compare the proposed solution methods with a Mixed Integer Linear Programming (MILP) formulation and show that the dynamic programming approach is faster when the number of categories is large, whereas the MILP can be solved faster when the number of categories is small.

A stochastic simulation-optimization model for base-warranty and extended-warranty decision-making of under- and out-of-warranty products