Protecting local access telecommunications networks: Toward a minimum-cost solution

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.

The natural flow regime can sustain the ecological integrity of riverine ecosystems. Different reservoir operation polices differ in their effects on the degree of alteration of natural flow regimes. Dynamic programming plays an important role in developing operation policies. When using dynamic programming models to develop operation policies, the discrete number of storage states (DNSS), which is a key factor affecting the reservoirs operation policies, is always been determined based on computational efficiency and economic benefits. Little consideration has been given to the ecological disturbance caused by different DNSS‐based operation policies. To analyze the impact of DNSS, we built a deterministic dynamic programming model to explore the relationship among DNSS, the flow regime alteration (ecological disturbance), and the cumulative annual power generation (economic benefits) by setting a range of DNSS scenarios. We used three reservoirs with different storage coefficients (ratios of usable storage to annual average runoff) as examples and used the range of variability approach to assess the ecological disturbance under these scenarios. We compared the results with those of a stochastic dynamic programming (SDP) model and a Bayesian SDP (BSDP) model. We found that when DNSS is low, increasing DNSS improves economic benefits but causes a more severe ecological disturbance; when DNSS is high, increasing DNSS improves the economic benefits only slightly, without exacerbating the ecological disturbance; for a given DNSS, the BSDP model provides higher economic benefits than the SDP model and a similar disturbance of the riverine ecosystem; and larger reservoirs more often cause more severe disturbance of riverine ecosystems because monthly mean flows and annual extreme flows change more drastically. Our results will help to protect the riverine ecosystems and improve economic benefits if reservoir operation managers consider DNSS using dynamic programming models.

CARE: Heuristics for two-stage multi-product inventory routing problems with replenishments

It may be very difficult to achieve the optimal shift schedule in call centers which have highly uncertain and peaked demand during short time periods. Overlapping shift systems are usually designed for such cases. This paper studies shift scheduling and rostering problems for inbound call centers where overlapping shift systems are used. An integer programming model that determines which shifts to be opened and how many operators to be assigned to these shifts is proposed for the shift scheduling problem. For the rostering problem both integer programming and constraint programming models are developed to determine assignments of operators to all shifts, weekly days-off, and meal and relief break times of the operators. The proposed models are tested on real data supplied by an outsource call center and optimal results are found in an acceptable computation time. An improvement of 15% in the objective function compared to the current situation is observed with the proposed model for the shift scheduling problem. The computational performances of the proposed integer and constraint programming models for the rostering problem are compared using real data observed at a call center and simulated test instances. In addition, benchmark instances are used to compare our Constraint Programming (CP) approach with the existing models. The results of the comprehensive computational study indicate that the constraint programming model runs more efficiently than the integer programming model for the rostering problem. The originality of this research can be attributed to two contributions: (a) a model for shift scheduling problem and two models for rostering problem are presented in detail and compared using real data and (b) the rostering problem is considered as a task-resource allocation and considerably shorter computation times are obtained by modeling this new problem via CP.

SummaryThe estimation of finite‐horizon discrete‐choice dynamic programming (DCDP) models is computationally expensive. This limits their realism and impedes verification and validation efforts. Keane and Wolpin (Review of Economics and Statistics, 1994, 76(4), 648–672) propose an interpolation method that ameliorates the computational burden but introduces approximation error. I describe their approach in detail, successfully recompute their original quality diagnostics, and provide some additional insights that underscore the trade‐off between computation time and the accuracy of estimation results.

Prescribing product upgrades, prices and production levels over time in a stochastic environment

One most common problem in reinforcement learning systems (e.g. Q-learning) is to reduce the number of trials to converge to an optimal policy. As one of the solution to the problem, k-certainty exploration method was proposed. Miyazaki reported that this method could determine an optimal policy faster than Q-learning in Markov decision processes (MDPs). This method is very efficient learning method. But, we propose an improvement plan that makes this method more efficient. In k-certainty exploration method, in case there is no k-uncertainty rule (rules which aren’t selected more than k times) in current state, an agent sometimes walks randomly until it finds a state where it can select a k-uncertainty rule. We think that this behavior is not efficient. To reduce this useless behavior, we propose combining k-certainty exploration method with Dynamic programming (DP). Miyazaki’s system uses DP after all rules are executed at least k times. But, our method uses k-certainty exploration method along with DP during learning. Our method, takes two pattern actions. In case an agent can select k-uncertainty rules, one of these rules is selected at random as k-certainty exploration method. In another case there is no k-uncertainty rule, behavior of agent is different from the behavior of k-certainty exploration method. In that case, our method uses DP to compute an optimal policy for moving from a current state to a state in which some k-uncertainty rules remain. The model for DP is constructed by using only known states. The outline will be described below. First, an agent makes a map constructed by using only known states. In the map, goals are states in which there are k-uncertainty rules and arbitrary state values are set in these states. Point to which attention should be paid is that the map is not given from outside. It is made from only experience. Next, each state values of states in which there are only k-certainty rules in the map are computed by DP (we used Policy Iteration). Finally, an agent continues to select greedy action until it arrives at a state in which it can select a k-uncertainty rule. By this improvement, we expect it can determine an optimal policy faster than k-certainty exploration method. And we have verified that our exploration method can determine an optimal policy faster than k-certainty exploration method by computer simulation.

Certain types of engineering design optimization problems contain piecewise smooth functions. This paper deals with the dynamic programming (DP) formulation of such problems in general, and optimal design of casings used in ultra–deep drills in particular. A solution procedure for the DP formulation of the optimal casing problem is developed. The procedure lakes advantage of the piecewise nature of the recursive equation and the state transformation function. The procedure is then applied to a numerical example which previously had been solved by the discrete maximum principle. The numerical results demonstrate that the DP procedure is substantially simpler and more efficient and no less accurate than the discrete maximum principle.

Ultrasound Elastography is an emerging imaging technique that allows estimation of the mechanical characteristics of tissue. Two issues that need to be addressed before widespread use of elastography in clinical environments are real time constraints and deteriorating effects of signal decorrelation between pre- and post-compression images. Previous work has used Dynamic Programming (DP) to estimate tissue deformation. However, in case of large signal decorrelation, DP can fail. In this paper we, have proposed a novel solution to this problem by solving DP on a tree instead of a single Radio-Frequency line. Formulation of DP on a tree allows exploiting significantly more information, and as such, is more robust and accurate. Our results on phantom and in-vivo human data show that DP on tree significantly outperforms traditional DP in ultrasound elastography.

ABSTRACTThe solution to the assembly line balancing with the hierarchical worker assignment problem (ALBHWP) provides the optimal allocation of workers and tasks to the stations that minimise the total worker cost. In the ALBHWP, tasks differ in terms of the qualification requirements of workers, and the qualification levels of workers are hierarchical. In the hierarchical workforce structure, a lower qualified worker can be replaced by higher qualified ones with higher costs, while the vice versa is not applicable. This problem has only been studied for straight assembly lines so far. In this paper, we introduce the ALBHWP for U-shaped assembly lines. We developed integer and constraint programming models for solving the ALBHWP and compared their effectiveness using an extensive set of benchmark instances. We solved the ALBHWP for straight and U-shaped assembly lines comparatively. Constraint programming models have been statistically proven to provide better quality solutions faster than integer programming models. Besides, the CP model outperforms the only available metaheuristic in the literature for the S-ALBHWP in almost all problem sizes. Another observation is that a U-shaped line design is more cost-effective than a straight line design, but solving the ALBHWP for U-shaped lines is more difficult regarding computational complexity.

A MAC layer power management scheme for efficient energy delay tradeoff in a WLAN

A heuristic for scheduling problems, especially for scheduling farm operations

The study on which this article is based is hoped to be the first of a series investigating the use of dynamic programming in agricultural allocation decisions. The model presented in this article was constructed in simple form to study once-over sequences of allocation of land to some activity of long-run benefit. The activity chosen was pasture improvement, but as will be seen later the section of the model which describes pasture improvement could be altered to make the model specific to some other relevant activity if desired. The presentation of this article is as follows: First the nature of dynamic programming as an analytical tool is explained. Then the dynamic programming relationships in the model are constructed and a simple numerical example is given to illustrate the computational procedure. The second part of the model, which derives the pasture improvement return functions, is then shown. Some general computational problems are discussed, following which the properties of both parts of the model are investigated in some detail.

Since the late 1970’s the U.S. Geologic Survey (USGS) has led a program to remove abandoned logging roads in Redwood National Park. Because abandoned logging roads contribute large amounts of sediment to local fish bearing streams, the ecosystem health of these waterways suffer. Recent research has identified the effectiveness of preventing sediment from reaching the streams for different road treatments after significant storm events. However, road removal is expensive and time consuming. This research reported in this paper was part of that pilot study, and specifically reviews the feasibility of the optimization algorithm Dynamic Programming (DP), using data from recent research on road removal effectiveness. The DP sought to determine the road removal treatment that maximizes the amount of sediment saved from erosion, while meeting a budgetary constraint. The results indicate that DP is an effective tool for developing a road removal management plan. However, the order in which roads and stream crossings are treated has a large effect on the solution, indicating that the DP formulation has room for improvement. The USGS is supporting further research to reformulate the DP.

The classical problem of order acceptance/rejection in make-to-order environments, when aiming to maximise profit with machine set-ups is extended in this paper to multiple set-ups depending on manufacturing batch size. In this case, if the manufacturing batch is larger than certain product-dependent bounds, not only is the initial set-up required but also periodic reset-ups are in order, generating sub-batches of the same order, such as tool resharpening and machine recalibration. A network formulation provides the basis for identifying effective algorithms to obtain a solution to the problem. A binary programming model (BPM) and a dynamic programming formulation (DPF) are proposed to solve the problem to optimality. In addition, two heuristics are developed to obtain lower bounds on maximum profit: each attempt to maximise customer satisfaction under production time restrictions, and to provide an extension to the classical knapsack problem. Numerical experimentation shows that computational time is not an issue when BPM and heuristics are applied, but the cost of commercial solvers for BPM algorithms might be problematic. However, if the aim is to code the DPF in-house, the curse of dimensionality in dynamic programming must be addressed, although dynamic programming does yield a full sensitivity analysis, which is useful for decision-making.