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The decision making of a suitable heating, ventilating and air conditioning system's set-point temperature is an energy and environmental challenge in our society. In the present paper, a general framework to define such temperature based on a dynamic adaptive comfort algorithm is proposed. Due to the fact that the thermal comfort of the occupants of a building has different ranges of acceptability, this method is applied to learn such comfort temperature with respect to the running mean temperature and therefore to decide the suitable range of indoor temperature. It is demonstrated that this solution allows to dynamically build an adaptive comfort algorithm, an algorithm based on the human being's thermal adaptability, without applying the traditional theory. The proposed methodology based on the K-Nearest-Neighbour algorithm was tested and compared with data from an experimental thermal comfort field study carried out in a mixed mode building in the south-western area of Spain and with the Support Vector Machine method. The results show that K-Nearest-Neighbour algorithm represents the pattern of thermal comfort data better than the traditional solution and that it is a suitable method to learn the thermal comfort area of a building and to define the set-point temperature for a heating, ventilating and air-conditioning system. [ABSTRACT FROM AUTHOR]

In this paper we consider a coordinated in-house production scheduling and outsourcing model, where a manufacturer might outsource part of the production to a subcontractor so as to achieve a tight production due date. The manufacturer pays a specific outsourcing cost for each job that is outsourced. To encourage the manufacturer to outsource more jobs, the subcontractor provides a specific discount scheme on the total outsourcing cost. Previous studies focus on the balance between in-house production performance and the total outsourcing cost. Our model is the first to investigate the impact on the manufacturer's decision-making under different discount schemes on the total outsourcing cost. Four distinct discount schemes on the total outsourcing cost are studied. We either show the intractability of those problems, or provide efficient exact or approximation algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an additional constraint to the one-dimensional variable sized bin packing problem. Practically, some of items have to be packed separately in different bins due to their specific requirement. Therefore, these items are labelled as different types. The bins can be used to pack either any type of items if they are empty originally or the same type of items as what they already have. We model the problem as a type-constrained and variable sized bin packing problem (TVSBPP), and solve it via a branch and bound method. An efficient backtracking procedure is proposed to improve the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

In location-routing problems, the objective is to locate one or many depots within a set of sites (representing customer locations or cities) and to construct delivery routes from the selected depot or depots to the remaining sites at least system cost. The objective function is the sum of depot operating costs, vehicle acquisition costs and routing costs. This paper considers one such problem m which a weight is assigned to each site and where sites are to be visited by vehicles having a given capacity. The solution must be such that the sum of the weights of sites visited on any given route does not exceed the capacity of the visiting vehicle. The formulation of an integer linear program for this problem involves degree constraints generalized subtour elimination constraints, and chain baring constraints. An exact algorithm, using initial relaxation of most of the problem constraints, is presented which is capable of solving problems with up to twenty sites within a reasonable number of iterations. [ABSTRACT FROM AUTHOR]

In this paper we study multiprocessor and open shop scheduling problems from several points of view. We explore a tight dependence of the polynomial solvability/intractability on the number of allowed preemptions. For an exhaustive interrelation, we address the geometry of problems by means of a novel graphical representation. We use the so-called preemption and machine-dependency graphs for preemptive multiprocessor and shop scheduling problems, respectively. In a natural manner, we call a scheduling problem acyclic if the corresponding graph is acyclic. There is a substantial interrelation between the structure of these graphs and the complexity of the problems. Acyclic scheduling problems are quite restrictive; at the same time, many of them still remain NP-hard. We believe that an exhaustive study of acyclic scheduling problems can lead to a better understanding and give a better insight of general scheduling problems. We show that not only acyclic but also a special non-acyclic version of periodic job-shop scheduling can be solved in polynomial (linear) time. In that version, the corresponding machine dependency graph is allowed to have a special type of the so-called parti-colored cycles. We show that trivial extensions of this problem become NP-hard. Then we suggest a linear-time algorithm for the acyclic open-shop problem in which at most m−2 preemptions are allowed, where m is the number of machines. This result is also tight, as we show that if we allow one less preemption, then this strongly restricted version of the classical open-shop scheduling problem becomes NP-hard. In general, we show that very simple acyclic shop scheduling problems are NP-hard. As an example, any flow-shop problem with a single job with three operations and the rest of the jobs with a single non-zero length operation is NP-hard. We suggest linear-time approximation algorithm with the worst-case performance of $\|\mathcal{M}\|+2\|\mathcal{J}\|$ ( $\|\mathcal{M}\|+\|\mathcal{J}\|$ , respectively) for acyclic job-shop (open-shop, respectively), where $\|\mathcal{J}\|$ (|ℳ|, respectively) is the maximal job length (machine load, respectively). We show that no algorithm for scheduling acyclic job-shop can guarantee a better worst-case performance than $\|\mathcal{M}\|+\|\mathcal{J}\|$ . We consider two special cases of the acyclic job-shop with the so-called short jobs and short operations (restricting the maximal job and operation length) and solve them optimally in linear time. We show that scheduling m identical processors with at most m−2 preemptions is NP-hard, whereas a venerable early linear-time algorithm by McNaughton yields m−1 preemptions. Another multiprocessor scheduling problem we consider is that of scheduling m unrelated processors with an additional restriction that the processing time of any job on any machine is no more than the optimal schedule makespan C . We show that the (2 m−3)-preemptive version of this problem is polynomially solvable, whereas the (2 m−4)-preemptive version becomes NP-hard. For general unrelated processors, we guarantee near-optimal (2 m−3)-preemptive schedules. The makespan of such a schedule is no more than either the corresponding non-preemptive schedule makespan or max { C , p max }, where C is the optimal (preemptive) schedule makespan and p max is the maximal job processing time. [ABSTRACT FROM AUTHOR]

Computer game-playing programs repeatedly calculate minimax elements μ = mii maxj Mij of large payoff matrices Mij. A straightforward row-by-row calculation of μ scans rows of Mij one at a time, skipping to a new row whenever an element is encountered that exceeds a current minimax. An optimal calculation, derived here, scans the matrix more erratically but finds ii after testing the fewest possible matrix elements. Minimizing the number of elements tested is reasonable when elements must be computed as needed by evaluating future game positions. This paper obtains the expected number of tests required when the elements are independent, identically distributed, random variables. For matrices 50 by 50 or smaller, the expected number of tests required by the row-by-row calculation can be at most 42% greater than the number for the optimal calculation. When the numbers R, C of rows and columns are very large, both calculations require an expected number of tests near RC/InR. [ABSTRACT FROM AUTHOR]

Linear optimization problems are investigated that have random parameters in their $$m\ge 1$$ constraints. In constructing a robust solution $${\mathbf {x}}\in \mathbb {R}^d$$ , we control the risk arising from violations of the constraints. This risk is measured by set-valued risk measures, which extend the usual univariate coherent distortion (=spectral) risk measures to the multivariate case. To obtain a robust solution in $$d$$ variables, the linear goal function is optimized under the restrictions holding uniformly for all parameters in a $$d$$ -variate uncertainty set. This set is built from uncertainty sets of the single constraints, each of which is a weighted-mean trimmed region in $$\mathbb {R}^d$$ and can be efficiently calculated. Furthermore, a possible substitution of violations between different constraints is investigated by means of the admissable set of the multivariate risk measure. In the case of no substitution, we give an exact geometric algorithm, which possesses a worst-case polynomial complexity. We extend the algorithm to the general substitutability case, that is, to robust polyhedral optimization. The consistency of the approach is shown for generally distributed parameters. Finally, an application of the model to supervised machine learning is discussed. [ABSTRACT FROM AUTHOR]

The purpose of this research is to develop two manpower supply planning models and a solution algorithm for mass rapid transit carriage maintenance under mixed deterministic and stochastic demands. These models are formulated as mixed integer programs that are characterized as NP-hard. We employ problem decomposition techniques, coupled with the CPLEX mathematical programming solver, to develop an algorithm that is capable of efficiently solving the problems. The models and the method used currently in actual operations are evaluated by a simulation-based evaluation method. Finally, we perform a case study using real operating data from a Taiwan MRT maintenance facility. The preliminary results are good, showing that the models could be useful for planning carriage maintenance manpower supply. [ABSTRACT FROM AUTHOR]

In this work, we consider a public facility allocation problem decided through a voting process under the majority rule. A location of the public facility is a majority rule winner if there is no other location in the network where more than half of the voters would have been closer to than the majority rule winner. We develop fast algorithms for interesting cases with nice combinatorial structures. We show that the computing problem and the decision problem in the general case, where the number of public facilities is more than one and is considered part of the input size, are all NP-hard. Finally, we discuss majority rule decision making for related models. [ABSTRACT FROM AUTHOR]

We give a complement note on the proof of the NP-hardness of preemptive acyclic open-shop problem presented earlier by the authors in Ann. Oper. Res. 159:183-213, . [ABSTRACT FROM AUTHOR]