Assignment Of Customers Research Articles

Algorithmic analysis of the BMAP/D/k system in discrete time

We exploit the structural properties of the BMAP/D/k system to carry out its algorithmic analysis. Specifically, we use these properties to develop algorithms for studying the distributions of waiting times in discrete time and the busy period. One of the structural properties used results from considering the system as having customers assigned in a cyclic order—which does not change the waiting-time distribution—and then studying only one arbitrary server. The busy period is defined as the busy period of an arbitrary single server based on this cyclic assignment of customers to servers. Finally, we study the marginal distribution of the joint queue length and phase of customer arrival. The structural property used for studying the queue length is based on the observation of the system every interval that is the length of one customer service time.

Algorithmic analysis of the BMAP/D/k system in discrete time

We exploit the structural properties of the BMAP/D/k system to carry out its algorithmic analysis. Specifically, we use these properties to develop algorithms for studying the distributions of waiting times in discrete time and the busy period. One of the structural properties used results from considering the system as having customers assigned in a cyclic order—which does not change the waiting-time distribution—and then studying only one arbitrary server. The busy period is defined as the busy period of an arbitrary single server based on this cyclic assignment of customers to servers. Finally, we study the marginal distribution of the joint queue length and phase of customer arrival. The structural property used for studying the queue length is based on the observation of the system every interval that is the length of one customer service time.

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.

A heuristic method for large-scale multi-facility location problems

A heuristic method for solving large-scale multi-facility location problems is presented. The method is analogous to Cooper's method (SIAM Rev. 6 (1964) 37), using the authors’ single facility location method (Comput. Optim. Appl. 21 (2002) 213) as a parallel subroutine, and reassigning customers to facilities using the heuristic of nearest center reclassification. Numerical results are reported. Scope and purpose We study the multiple facility location problem (MFLP). The objective in MFLP is to locate facilities to serve optimally a given set of customers. MFLPs have many applications in Operations Research, and a rich literature, see Drezner (Location Sci. 3(4) (1995) 275) for a recent survey. MFLPs involve, in addition to the location decision, also the assignment of customers to facilities. The MFLP is therefore a special clustering problem, the clusters here are the sets of customers assigned to the same facility. We propose a parallel heuristic method for solving MFLPs, using ideas from cluster analysis (nearest mean reclassification (Cluster Analysis, 3rd Edition, Edward Arnold, London, 1993)), and the authors’ Newton bracketing method for convex minimization (Comput. Optim. Appl. 21 (2002) 213) as a subroutine. The method is suitable for large-scale problems, as illustrated by numerical examples.

An asymptotically optimal greedy heuristic for the multiperiod single‐sourcing problem: The cyclic case

AbstractThe dynamics of the environment in which supply chains evolve requires that companies frequently redesign their logistics distribution networks. In this paper we address a multiperiod single‐sourcing problem that can be used as a strategic tool for evaluating the costs of logistics network designs in a dynamic environment. The distribution networks that we consider consist of a set of production and storage facilities, and a set of customers who do not hold inventories. The facilities face production capacities, and each customer's demand needs to be delivered by a single facility in each period. We deal with the assignment of customers to facilities, as well as the location, timing, and size of inventories. In addition, to mitigate start and end‐of‐study effects, we view the planning period as a typical future one, which will repeat itself. This leads to a cyclic model, in which starting and ending inventories are equal. Based on an assignment formulation of the problem, we propose a greedy heuristic, and prove that this greedy heuristic is asymptotically feasible and optimal in a probabilistic sense. We illustrate the behavior of the greedy heuristic, as well as some improvements where the greedy heuristic is used as the starting point of a local interchange procedure, on a set of randomly generated test problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 412–437, 2003

Load profile assignment of low voltage customers for power retail market applications

To facilitate retail choice in a competitive power market, the knowledge of hourly load shape by customer class is necessary. Requiring a meter as a prerequisite for lower voltage customers to choose a power supplier is not considered practical at the present time. A technique which uses load research and customers’ monthly energy usage data for a preliminary screening of customer load profiles is presented. Two data mining techniques, namely, the fuzzy c-means (FCM) method and an artificial neural network (ANN) based pattern recognition technique, are utilised in this work. The proposed method can be used by the Energy Service Provider (ESP) to assign customers to specific load profiles with certainty factors. Customers with less certainty in the assignment will need meter installation or further investigation in order to determine which classes they belong to. Test data are from actual measurement and the customer information system (CIS) of Taiwan Power Company (TPC). Promising results on assigning existing under 220 V customers to their proper load profiles are illustrated.

New assignment algorithms for the multi-depot vehicle routing problem

This paper considers the design and analysis of algorithms for the multi-depot vehicle routing problem with time windows (MDVRPTW). Given the intrinsic difficulty of this problem class, approximation methods of the type ‘cluster first, route second’ (two-step approaches) seem to offer the most promise for practical size problems. After describing six heuristics for the cluster part (assignment of customers to depots) an initial computational study of their performance is conducted. Finding, as expected, that the heuristics with the best results (in terms of the routing results) are those with the largest computational efforts.

A Lagrangean relax-and-cut approach for the two-stage capacitated facility location problem

The two-stage capacitated facility location problem is to find the optimal locations of depots to serve customers with a given demand, the optimal assignment of customers to depots and the optimal product flow from plants to depots. In order to solve this problem, a Lagrangean heuristic is proposed which is based on the relaxation of the capacity constraints. The resulting Lagrangean subproblem is an uncapacitated facility location problem with an aggregate capacity constraint and can be solved efficiently by branch-and-bound methods. The best bound available from this relaxation is computed by means of a “weighted” Dantzig–Wolfe decomposition approach. Feasible solutions are constructed from those of the Lagrangean subproblems by applying simple reassignment procedures. Furthermore, the relaxation is strengthened by adding and dualizing valid inequalities which are violated by the fractional primal solution of the dual master program. Computational results and comparisons with some other bounds and heuristics for this problem are presented.

A two-phased approach to the supply network reconfiguration problem

This study focuses on a supply network problem where resource inputs are constrained to achieve performance goals for the reconfigured distribution system. Simulated annealing is applied for solving this reconfiguration problem. The supply network is comprised of distribution centers that are geographically distributed and have differing operating and maintenance cost structures on distribution-related resources. The distribution planning methodology employed in the heuristics has two phases: Phase one incorporates a strategic-based decision making step in which the `best' set of distribution centers are selected open; Phase two incorporates an operationally-based decision making step in which the heuristics perturb the customer assignments and resource assignments. The heuristics are tested on a set of 450 problems of various sizes and structures. Computational results suggest that the simulated annealing heuristics generate near optimal solutions quickly and are well suited for evaluating supply network reconfiguration. Computational results also suggest that enhanced annealing heuristics proposed in this paper are better than the standard annealing approach. The supply network problem structure was exploited to achieve very good solution results.

A simple approach to the map/d/s queue

We provide a simple approach to analyze the stationary MAP/D/s queue, where customers are served under the FCFS discipline. Assuming a cyclic assignment of customers to servers, we first characterize the sojourn time distribution, and with this, the queue length distribution immediately after departures is obtained. Further, utilizing the relationship between the time-average queue length distribution and the customer-average queue length distribution at departures, we obtain a numerically feasible formula for the stationary queue length mass function

Tactical and strategic models for satellite customer assignment

In this paper we develop tactical and strategic models for assignments of customers to satellite channels. We solve this problem using mixed integer–linear programming, and study the managerial impacts of our models. As a managerial tool, the optimal placement of customer channels to minimize transponder re-balancing was found to have a real and observable profit potential in excess of $54 million for the GE Spacenet series geosynchronous orbit satellites. Further managerial findings and computational results are presented.

Tactical and Strategic Models for Satellite Customer Assignment

Tactical and Strategic Models for Satellite Customer Assignment

Fuzzy assignment of customers for a queueing network

This paper considers a queueing network with two parallel heterogeneous servers. Each server has its own queue and customers arrive at each queue according to independent Poisson processes. Service times are independent and exponentially distributed. When a customer arrives at queue 1, the customer can be transferred to queue 2 by paying an assignment cost. Each customer in queue pays a holding cost per unit time. The objective is to dynamically determine the optimal assignment policy so as to minimize the average cost. In this paper, a novel approach is presented using fuzzy control to solve the problem.

An LP-based heuristic for two-stage capacitated facility location problems

In this paper, a linear programming based heuristic is considered for a two-stage capacitated facility location problem with single source constraints. The problem is to find the optimal locations of depots from a set of possible depot sites in order to serve customers with a given demand, the optimal assignments of customers to depots and the optimal product flow from plants to depots. Good lower and upper bounds can be obtained for this problem in short computation times by adopting a linear programming approach. To this end, the LP formulation is iteratively refined using valid inequalities and facets which have been described in the literature for various relaxations of the problem. After each reoptimisation step, that is the recalculation of the LP solution after the addition of valid inequalities, feasible solutions are obtained from the current LP solution by applying simple heuristics. The results of extensive computational experiments are given.

Efficient Solution of a Multi‐commodity, Two‐stage Distribution Problem with Constraints on Assignment of Customers to Distribution Centres

A two‐stage, distribution‐planning problem is addressed. Customers are to be served with different commodities from a number of plants, through a number of intermediate distribution centres (DCs). The possible locations for the DCs are given. For each location, there is a fixed cost for opening the DC concerned, as well as an operating cost and a maximum capacity. The demand of each customer for each commodity is known, as well as shipping costs throughout. There are also two additional important requirements. First, each customer must be served with all the products it requires from a single distribution centre. Secondly, it must be possible to ascertain the plant origin of each product quantity delivered. The objective is to choose the locations for opening DCs such that the total cost is minimised. The problem is modelled as a mixed‐integer‐programming problem and solved by branch and bound. Lower bounds are calculated through a series of structural transformations. Much of the power of the solution scheme also stems from frequent generation of good upper bounds. Results of extensive computational experiments are given and discussed.

Efficient solution of a multi-commodity, two-stage distribution problem with constraints on assignment of customers to distribution centres

A two-stage, distribution-planning problem is addressed. Customers are to be served with different commodities from a number of plants, through a number of intermediate distribution centres (DCs). The possible locations for the DCs are given. For each location, there is a fixed cost for opening the DC concerned, as well as an operating cost and a maximum capacity. The demand of each customer for each commodity is known, as well as shipping costs throughout. There are also two additional important requirements. First, each customer must be served with all the products it requires from a single distribution centre. Secondly, it must be possible to ascertain the plant origin of each product quantity delivered. The objective is to choose the locations for opening DCs such that the total cost is minimised. The problem is modelled as a mixed-integer-programming problem and solved by branch and bound. Lower bounds are calculated through a series of structural transformations. Much of the power of the solution scheme also stems from frequent generation of good upper bounds. Results of extensive computational experiments are given and discussed.

A Dynamic Programming Model For Assigning Customers To Priority Service Classes

A dynamic programming model is presented which optimally assigns n customers to m priority service classes, where customers have heterogeneous demand rates and waiting costs. The model is used to find the vertically efficient assignment of customers to priority classes for both a general service facility and a facility modeled as a M/M/l priority queue. If the priority model is M/M/l, we prove that all the demand for each customer will be assigned to a single class.

Analysis of a finite-source customer assignment model with no state information

In this paper we analyse a closed queueing network in which customers have to be assigned to parallel queues. The routing decision may not depend on the numbers of customers in the queues. We present an algorithm and we show that it computes an average optimal policy in case of exponential service times. The algorithm also works for non-exponential service times, in which case periodic policies are found.

On a Conjecture of Koole

In this short note, we give a counterexample to a conjecture of Koole (1995, Stochastic scheduling and dynamic programming) concerning the equivalence of two orderings arising in the context of a customer assignment model with asymmetric service times.

Pricing, routing, and incentive compatibility in multiserver queues

This paper studies pricing and incentive issues in the assignment of customers to servers in a system that suffers congestion effects. When customers have private information about their waiting costs, a system administrator who wishes to maximize steady-sate net benefits per unit of time (i.e. total benefits from service minus total waiting costs) may do so using a pricing and routing scheme that is incentive compatible; that is, no customer has any incentive to reveal his private information untruthfully. When the system administrator wants to maximize toll revenue, the optimal scheme involves higher tolls, and hence lower congestion, than is socially optimal.