Dynamic Capacity Acquisition and Assignment under Uncertainty

Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-and-bound strategy for the problem. Encouraging preliminary computational results are provided.     

The dynamic multilevel assignment problem as a stochastic extremal process

This paper considers the multilevel assignment problem (i.e. the assignment problem where the supply alternatives are ranked in hierarchical levels) under the assumption that the utility components for each pairwise matching are stochastic. A dynamic version of the multilevel stochastic assignment model is developed, where both demand and supply evaluate alternatives according to a stochastic extremal process, i.e. a process where the maximum of a sequence of random variables is taken into account. The probability distributions of the random variables which describe the joint dynamic behaviour of demand and supply are found. It is also shown that the assignment probabilities assume the structure of a nested-logit model.     

Throughput-oriented channel assignment for opportunistic spectrum access networks

Cognitive radio (CR) is a revolutionary technology in wireless communications that enhances spectrum utilization by allowing opportunistic and dynamic spectrum access. One of the key challenges in this domain is how CR users cooperate to dynamically access the available spectrum opportunities in order to maximize the overall perceived throughput. In this paper, we consider the coordinated spectrum access problem in a multi-user single-transceiver CR network (CRN), where each CR user is equipped with only one half-duplex transceiver. We first formulate the dynamic spectrum access as a rate/power control and channel assignment optimization problem. Our objective is to maximize the sum-rate achieved by all contending CR users over all available spectrum opportunities under interference and hardware constraints. We first show that this problem can be formulated as a mixed integer nonlinear programming (MINLP) problem that is NP-hard, in general. By exploiting the fact that actual communication systems have a finite number of available channels, each with a given maximum transmission power, we transfer this MINLP into a binary linear programming problem (BLP). Due to its integrality nature, this BLP is expected to be NP-hard. However, we show that its constraint matrix satisfies the total unimodularity property, and hence our problem can be optimally solved in polynomial time using linear programming (LP). To execute the optimal assignment in a distributed manner, we then present a distributed CSMA/CA-based random access mechanism for CRNs. We compare the performance of our proposed mechanism with reference CSMA/CA channel access mechanisms designed for CRNs. Simulation results show that our proposed mechanism significantly improves the overall network throughput and preserves fairness.     

Some Fixed-Point Results for the Dynamic Assignment Problem

In previous work the authors consider the dynamic assignment problem, which involves solving sequences of assignment problems over time in the presence of uncertain information about the future. The algorithm proposed by the authors provides generally high-quality but non-optimal solutions. In this work, though, the authors prove that if the optimal solution to a dynamic assignment problem in one of two problem classes is unique, then the optimal solution is a fixed point under the algorithm.     

Frequency assignment in a SDMA satellite communication system with beam decentring feature

In satellite communication, Spatial Division Multiple Access (SDMA) has become one of the most promising techniques that can accommodate continuing increase in the number of users and traffic demands. The technology is based on radio resource sharing that separates communication channels in space. It relies on adaptive and dynamic beam-forming technology and well-designed algorithms for resource allocation among which frequency assignment is considered. This paper studies static Frequency Assignment Problem (FAP) in a satellite communication system involving a satellite and a number of users located in a service area. The objective is to maximize the number of users that the system can serve while maintaining the signal to interference plus noise ratio of each user under a predefined threshold. Traditionally, interference is treated as fixed (binary interferences or fixed minimal required separation between frequencies) . In this paper, the interference is cumulative and variable. To solve the problem, we work on both discrete and continuous optimizations. Integer linear programming formulations and greedy algorithms are proposed for solving the discrete frequency assignment problem. The solution is further improved by beam decentring algorithm which involves continuous adjustment of satellite beams and deals with non-linear change of interference.     

A two-stage model for a day-ahead paratransit planning problem

We consider a dynamic planning problem for paratransit transportation. The focus is on a decision to take one day ahead: which requests to serve with own vehicles, and which requests to subcontract to taxis? We call this problem the day-ahead paratransit planning problem. The developed model is a non-standard two-stage integer recourse model. Both stages consist of two consecutive optimization problems: the clustering of requests into routes, and the assignment of these routes to vehicles. To solve this model, a genetic algorithm approach is used. Computational results are presented for randomly generated data sets.     

Dynamic Generalized Assignment Problems with Stochastic Demands and Multiple Agent--Task Relationships

The assignment problem is a well-known operations research model. Its various extensions have been applied to the design of distributed computer systems, job assignment in telecommunication networks, and solving diverse location, truck routing and job shop scheduling problems.This paper focuses on a dynamic generalization of the assignment problem where each task consists of a number of units to be performed by an agent or by a limited number of agents at a time. Demands for the task units are stochastic. Costs are incurred when an agent performs a task or a group of tasks and when there is a surplus or shortage of the task units with respect to their demands. We prove that this stochastic, continuous-time generalized assignment problem is strongly NP-hard, and reduce it to a number of classical, deterministic assignment problems stated at discrete time points. On this basis, a pseudo-polynomial time combinatorial algorithm is derived to approximate the solution, which converges to the global optimum as the distance between the consecutive time points decreases. Lower bound and complexity estimates for solving the problem and its special cases are found.     

Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions

Mukherjee and Basu proposed a new method for solving fuzzy assignment problems. In this paper, some fuzzy assignment problems and fuzzy travelling salesman problems are chosen which cannot be solved by using the fore-mentioned method. Two new methods are proposed for solving such type of fuzzy assignment problems and fuzzy travelling salesman problems. The fuzzy assignment problems and fuzzy travelling salesman problems which can be solved by using the existing method, can also be solved by using the proposed methods. But, there exist certain fuzzy assignment problems and fuzzy travelling salesman problems which can be solved only by using the proposed methods. To illustrate the proposed methods, a fuzzy assignment problem and a fuzzy travelling salesman problem is solved. The proposed methods are easy to understand and apply to find optimal solution of fuzzy assignment problems and fuzzy travelling salesman problems occurring in real life situations.     

Fleet assignment and routing with schedule synchronization constraints

This paper introduces a new type of constraints, related to schedule synchronization, in the problem formulation of aircraft fleet assignment and routing problems and it proposes an optimal solution approach. This approach is based on Dantzig–Wolfe decomposition/column generation. The resulting master problem consists of flight covering constraints, as in usual applications, and of schedule synchronization constraints. The corresponding subproblem is a shortest path problem with time windows and linear costs on the time variables and it is solved by an optimal dynamic programming algorithm. This column generation procedure is embedded into a branch and bound scheme to obtain integer solutions. A dedicated branching scheme was devised in this paper where the branching decisions are imposed on the time variables. Computational experiments were conducted using weekly fleet routing and scheduling problem data coming from an European airline. The test problems are solved to optimality. A detailed result analysis highlights the advantages of this approach: an extremely short subproblem solution time and, after several improvements, a very efficient master problem solution time.     

Scheduling trams in the morning

In this note, we prove —›-completeness of the following problem: Given a set of trams of different types, which are stacked on sidings in their depot and an order in which trams of specified types are supposed to leave. Is there an assignment of trams to departure times without any shunting movements? In the particular case where the number of sidings is fixed, the problem is solvable in polynomial time. We derive a dynamic program and improve its performance by a state elimination scheme. We implemented three variants of the dynamic program and applied them to random data as well as to real-world data.     

Categorized Assignment Scheduling: a Tabu Search Approach

The assignment problem (AP) and bottleneck assignment problem (BAP) are well studied in operational research literature. In this paper we consider two related problems which simultaneously generalize both AP and BAP. Unlike AP and BAP, these generalizations are strongly NP-complete. We propose two heuristics to solve these generalized problems: one based on a greedy principle and the other based on tabu search. Computational results are presented which show that these heuristics, when used together, produce good quality solutions. Our adaptation of tabu search also gives some new insight into the application of tabu search on permutation problems.     

Optimal Network Design for Wireless Local Area Network

Network design for wireless local area networks is an important issue in the deployment of these networks. Research activities are presently being undertaken in two major areas: determining the location of base stations (BSs) and assigning the frequency channels for these stations. Our BS location problem selects a set of BSs to provide the best demand area coverage and maximize the signal level and physical area attendance priority. Adequate channel assignment reduces signal interference and improves network throughput. This paper reports a real world experiment where we applied the concepts of two classical outdoor problems namely the optimal BS location problem and the fixed channel assignment problem to build a WLAN into an indoor environment. We propose a mathematical model that we solve by a commercial software and report the computational results.     

弹性需求下城市公交网络服务的优化

对具有弹性需求的城市公交网络系统进行了票价结构与发车频率组合的优化。考虑到公交定价和发车频率会影响乘客需求以及乘客对路径的选择行为,将这一问题描述为一个双层规划问题,上层是寻求社会福利最大的优化问题;下层考虑了乘客的出行选择行为,为弹性需求下乘客在城市公交网络上流量分布的随机用户平衡分配模型。鉴于双层规划问题的非凸性,运用模拟退火算法对模型进行求解,并给出一个仿真算例说明提出的模型和算法的合理性。     

Batch scheduling and common due-date assignment on a single machine

We consider the problem of scheduling n groups of jobs on a single machine where three types of decisions are combined: scheduling, batching and due-date assignment. Each group includes identical jobs and may be split into batches; jobs within each batch are processed jointly. A sequence independent machine set-up time is needed between each two consecutively scheduled batches of different groups. A due-date common to all jobs has to be assigned. A schedule specifies the size of each batch, i.e. the number of jobs it contains, and a processing order for the batches. The objective is to determine a value for the common due-date and a schedule so as to minimize the sum of the due date assignment penalty and the weighted number of tardy jobs. Several special cases of this problem are shown to be ordinary NP-hard. Some cases are solved in O(n log n) time. Two pseudopolynomial dynamic programming algorithms are presented for the general problem, as well as a fully polynomial approximation scheme.     

A study of decision support models for online patient-to-room assignment planning

The present paper studies patient-to-room assignment planning in a dynamic context. To this end, an extension of the patient assignment (PA) problem formulation is proposed, for which two online ILP-models are developed. The first model targets the optimal assignment for newly arrived patients, whereas the second also considers future, but planned, arrivals. Both models are compared on an existing set of benchmark instances from the PA planning problem, which serves as the basic problem setting. These instances are then extended with additional parameters to study the effect of uncertainty on the patients’ length of stay, as well as the effect of the percentage of emergency patients. The results show that the second model provides better results under all conditions, while still being computationally tractable. Moreover, the results show that pro-actively transferring patients from one room to another is not necessarily beneficial.     

分配小于人数和任务数的指派问题的反点算法

摘要：本文对从 个人中派出 个人去完成 项任务中的 项任务使总效率最高这类指派问题给出了新算法,通过对这类指派问题引入了反点的概念,讨论了反点所具有的一些性质并证明了相关结论,利用这些结论找到了通过增加反点来解决此类指派问题的反点算法。     

Improving heuristics for the frequency assignment problem

Lower bounds for the frequency assignment problem can be found from maximal cliques and subgraphs related to cliques. In this paper we show that for many types of problem optimal assignments can be found by a process of assigning these subgraphs first, fixing the assignment and then extending the assignment to the full problem. We demonstrate the advantages of the method for some typical examples. In particular we give the first optimal assignments of several variants of the “Philadelphia” problems. These problems have been used by several authors to assess assignment methods and lower bounds.     

Effective algorithm and heuristic for the generalized assignment problem

We present new Branch-and-Bound algorithm for the generalized assignment problem. A standard subgradient method (SM), used at each node of the decision tree to solve the Lagrangian dual, provides an upper bound. Our key contribution in this paper is a new heuristic, applied at each iteration of the SM, which tries to exploit the solution of the relaxed problem, by solving a smaller generalized assignment problem. The feasible solution found is then subjected to a solution improvement heuristic. We consider processing the root node as a Lagrangian heuristic. Computational comparisons are made with new existing methods.     

Genetic Tabu search for robust fixed channel assignment under dynamic traffic data

The contribution of this work is twofold. Firstly, we introduce a new channel assignment model for GSM radio networks. In this model both spatial and temporal variations of traffic are taken into account in order to improve network capacity and robustness. Secondly, using this model, we develop an original and effective hybrid algorithm to get high quality frequency plans. This algorithm combines a problem specific crossover and a Tabu search procedure. The proposed model and hybrid algorithm are evaluated using both artificial and real data. Computational results allow us to confirm the effectiveness of the proposed approach.     

A Lagrangian relaxation-based heuristic for the vehicle routing with full container load

We address a problem of vehicle routing that arises in picking up and delivering full container load from/to an intermodal terminal. The substantial cost and time savings are expected by efficient linkage between pickup and delivery tasks, if the time of tasks and the suitability of containers for cargo allow. As this problem is NP-hard, we develop a subgradient heuristic based on a Lagrangian relaxation which enables us to identify a near optimal solution. The heuristic consists of two sub-problems: the classical assignment problem and the generalized assignment problem. As generalized assignment problem is also NP-hard, we employ an efficient solution procedure for a bin packing based problem, which replaces the generalized assignment problem. The heuristic procedure is tested on a wide variety of problem examples. The test results demonstrate that the procedure developed here can efficiently solve large instances of the problem.