Customer Locations Research Articles

The CallManager system: A platform for intelligent telecommunications services

Bellcore's CallManager system is an experimental prototype of a call screening and `follow-me anywhere' service platform that makes use of a personal appointment calendar and a personal phonebook (accessed through the customer's wireline or wireless PDA) to determine the customer's current location and the importance of each caller to the customer. This is an example of a future class of network-provided services that utilize advanced speech processing and customer specific data to greatly enhance the value of the telephone network to the customer. Such services allow important calls to reach the customer while screening out unwanted or unimportant calls. These services can potentially also proactively provide information to a customer `as it happens' wherever the customer may happen to be.

A dynamic programming heuristic for the P-median problem

A new heuristic algorithm is proposed for the P-median problem. The heuristic restricts the size of the state space of a dynamic programming algorithm. The approach may be viewed as an extension of the myopic or greedy adding algorithm for the P-median model. The approach allows planners to identify a large number of solutions all of which perform well with respect to the P-median objective of minimizing the demand weighted average distance between customer locations and the nearest of the P selected facilities. In addition, the results indicate regions in which it is desirable to locate facilities. Computational results from three test problems are discussed.

Probabilistic Analysis of a Combined Aggregation and Math Programming Heuristic for a General Class of Vehicle Routing and Scheduling Problems

We propose and analyze a heuristic that uses region partitioning and an aggregation scheme for customer attributes (load size, time windows, etc.) to create a finite number of customer types. A math program is solved based on these aggregated customer types to generate a feasible solution to the original problem. The problem class we address is quite general and defined by a number of general consistency properties. Problems in this class include VRPs with general distance norms, capacitated problems, time window VRPs, pick-up and delivery problems, combined inventory control and routing problems and arc routing. We provide a probabilistic analysis of this heuristic under very general probabilistic assumptions. In particular, we do not require independence between customer locations and their various attributes. The heuristic is (a.s.) ϵ-optimal as the number of customers n tends to infinity. Further, it runs in O(n log n) time for a fixed relative error, and can be designed to be asymptotically optimal while still running in polynomial time. We characterize the asymptotic average value of the heuristic and the optimal solution as the limit of a sequence of linear program values. We also provide bounds on the rate of convergence to the asymptotic value and bounds on tail probabilities. Finally, we discuss numerical issues involved in implementing our heuristic.

A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows

This paper describes a tabu search heuristic for the vehicle routing problem with soft time windows. In this problem, lateness at customer locations is allowed although a penalty is incurred and added to the objective value. By adding large penalty values, the vehicle routing problem with hard time windows can be addressed as well. In the tabu search, a neighborhood of the current solution is created through an exchange procedure that swaps sequences of consecutive customers (or segments) between two routes. The tabu search also exploits an adaptive memory that contains the routes of the best previously visited solutions. New starting points for the tabu search are produced through a combination of routes taken from different solutions found in this memory. Many best-known solutions are reported on classical test problems.

Planning and consolidating shipments from a warehouse

A typical warehouse or distribution centre ships material to various customer locations across the country, using various modes of transportation. Each mode has different constraints on size of shipment, different cost structures and different transportation times. Typically, for a given warehouse there are certain customer locations that receive frequent shipments of material. It is often possible, therefore, for the warehouse to consolidate different orders for the same customer location into a single shipment. The transportation mode and the day of shipment must be chosen such that the consolidated shipment meets the size constraints and arrives within an agreed-upon ‘delivery window’. In preparing a warehouse distribution plan, a planner seeks to achieve transportation economies of scale (by consolidating two or more orders into fewer shipments) while levelling the workload on warehouse resources and ensuring that material arrives at a customer location during the acceptable delivery window.The problem of deciding what shipments to make daily can be formulated as a set partitioning problem with side constraints. This paper describes a heuristic solution approach for this problem. Computational experiments using actual warehouse select activity indicate that, for moderate-size problems, the heuristic produces solutions with transportation costs that are within a few percent of optimal. Larger problems found in practice are generally too large to be solved by optimal algorithms; the heuristic easily handles such problems. The heuristic has been integrated into the transportation planning system of a leading distributor of telecommunications products.

Putting the Squeeze on Flexible Pipe

Clark Public Utilities in Vancouver, Washington, uses polyethylene (PE) pipe to provide water from the main water lines to the water meter at each customer location. During the process of installing water distribution mains and providing service for new construction, it sometimes is necessary to shut off the water service line connected to the meter. It also is necessary to shut off the flow of water when repairs, pipe maintenance, or pipe damage are encountered at an existing site. This article discusses the procedure used for squeezing off the flow in polyethylene pipe, including choosing a proper clamp and how to stop a water leak in the field.

A Tabu Search Heuristic for the Vehicle Routing Problem with Backhauls and Time Windows

This article describes a tabu search heuristic for the vehicle routing problem with backhauls and time windows. In this problem, the set of customers is partitioned into two subsets: linehaul customers where a given quantity of goods is delivered from a central depot, and backhaul customers where a given quantity of goods is collected and transported to the depot. Mixed routes with both linehaul and backhaul customers are constructed. A variant of this problem is examined where linehauls must precede bachhauls on each route. Furthermore, the time of beginning of service at each customer location must occur within a particular time interval. Computational results are reported on a standard set of test problems, and comparisons are made with other heuristic approaches and with optimal solutions.

Heuristic approaches to vehicle routing with backhauls and time windows

The vehicle routing problem with backhauls and time windows (VRPBTW) involves the pickup and delivery of goods at different customer locations, with earliest and latest time deadlines, and varying demands. The demands are serviced using capacitated vehicles with limited route time. Moreover, all deliveries (linehauls) must be done before the pickups (backhauls). The objective of the problem is to service all customers while minimizing the number of vehicles and distance traveled. In doing so, the capacity and route time constraints of the vehicles and the time window constraint at each customer should not be violated. In this paper, we describe a route construction heuristic for the VRPBTW, as well as different local search heuristics to improve the initial solutions. The heuristics were tested on 45 problems of size 25, 50 and 100 previously reported in the literature and whose optimum is known in most cases. In addition, the heuristic was tested on 24 newly created problems of size 250 and 500. The solutions produced by the heuristics are within 2.5% of the known optimal solutions on average.

A new subtour elimination constraint for the vehicle routing problem

Vehicle Routing Problems (VRP) are concerned with the delivery of a single commodity from a centralized depot to a number of specified customer locations with known demands. In this paper we consider the VRP characterized by: fixed or variable number of vehicles, common vehicle capacity, distance restrictions, and minimization of total distance travelled by all vehicles as the objective. We develop an exact algorithm based on a new subtour elimination constraint. The algorithm is implemented using the CPLEX package for solving the relaxed subproblems. Computational results on 1590 simulated problems and 10 literature problems (without distance restrictions) are reported and a comparative analysis is carried out.

Projecting the growth of cellular communications

The tremendous success of cellular technology has fundamentally changed the way people communicate and prompted the evolution of a new multibillion dollar wireless communications industry. Linking service areas, wireless communications has altered the way business is conducted. For instance, with a laptop computer, a PCMCIA modem and a cellular phone, a real estate agent can contact his or her office and clients, check sales listings and arrange appointments while traveling. Field service and sales people can, from customer locations, access corporate databases to check inventory status, prepare up-to-the-minute price and delivery quotes, and cut orders directly to the factory. Two-way paging services allow a firm's workforce to stay in close contact, even when traditional wired communication services are not available. Hand-held hybrids of phone-computer-fax machines feed information to wireless communication networks, allowing an executive to make decisions while watching a little league baseball game.

A Location Based Heuristic for General Routing Problems

We present a general framework for modeling routing problems based on formulating them as a traditional location problem called the capacitated concentrator location problem. We apply this framework to two classical routing problems: the capacitated vehicle routing problem and the inventory routing problem. In the former case, the heuristic is proven to be asymptotically optimal for any distribution of customer demands and locations. Computational experiments show that the heuristic performs well for both problems and, in most cases, outperforms all published heuristics on a set of standard test problems.

Queueing in space

We consider a problem in which a single server must serve a stream of customers whose arrivals are distributed over a finite-size convex space. Under the assumption that the server has full information on the customer location, obvious service policies are the FCFS and the greedy (serve-the-closest-customer) approaches. These algorithms are, however, either inefficient (FCFS) or ‘unfair' (greedy). We propose and study two alternative algorithms, the gated-greedy policy and the gated-scan policy, which are more ‘fair' than the pure greedy method. We show that the stability conditions of the gated-greedy are p < 1 (where p is the expected rate at which work arrives at the system), implying that the method is at least as efficient (in terms of system stability) as any other discipline, in particular the greedy one. For the gated-scan policy we show that for any p < 1 one can design a stable gated-scan policy; however, for any fixed gated-scan policy there exists p < 1 for which the policy is unstable. We evaluate the performance of the gated-scan policy, and present bounds for the performance of the gated-greedy policy. These results are derived for systems in which the arrivals occur on a two-dimensional space (a square) but they are not limited to this configuration; rather they hold for more complex N-dimensional spaces, in particular for serving customers in (three-dimensional) convex space and serving customers on a line.

Queueing in space

We consider a problem in which a single server must serve a stream of customers whose arrivals are distributed over a finite-size convex space. Under the assumption that the server has full information on the customer location, obvious service policies are the FCFS and the greedy (serve-the-closest-customer) approaches. These algorithms are, however, either inefficient (FCFS) or ‘unfair' (greedy).We propose and study two alternative algorithms, the gated-greedy policy and the gated-scan policy, which are more ‘fair' than the pure greedy method. We show that the stability conditions of the gated-greedy are p < 1 (where p is the expected rate at which work arrives at the system), implying that the method is at least as efficient (in terms of system stability) as any other discipline, in particular the greedy one. For the gated-scan policy we show that for any p < 1 one can design a stable gated-scan policy; however, for any fixed gated-scan policy there exists p < 1 for which the policy is unstable. We evaluate the performance of the gated-scan policy, and present bounds for the performance of the gated-greedy policy.These results are derived for systems in which the arrivals occur on a two-dimensional space (a square) but they are not limited to this configuration; rather they hold for more complex N-dimensional spaces, in particular for serving customers in (three-dimensional) convex space and serving customers on a line.

Probabilistic Analysis of a Capacitated Vehicle Routing Problem II

A fleet of vehicles located at a common depot must serve customers located throughout the plane. Without loss of generality, the depot will be located at the origin. Each vehicle must start at the depot, travel in turn to each customer its serves and go back to the depot. Each vehicle can serve at most $k$ customers. The objective is to minimize the total distance traveled by the fleet. In our model, the customers $X_1, \ldots, X_n$ are independent and uniformly distributed over the unit disc. If $R'(X_1, \ldots, X_n)$ denotes the optimal solution with these customer locations, we show that with overwhelming probability we have $\big|R'(X_1, \ldots, X_n) - \frac{2}{k} \sum_{i \leq n} \|X_i\| - \xi \sqrt{n} big| \leq K(n \log n)^{1/3},$ where $\xi$ and $K$ are constants that depend on $k$ only.

Stage of the organizational life cycle and competition as mediators of problem perception for small businesses

AbstractAn empirical study based upon a sample of 645 small businesses assesses the relationship that life cycle stage and level of competition exhibit with the problems perceived to constrain small business strategic planning. Problems have been identified as either internal (cash flow) or external (competition); they have further been classified as either situational or core problems. Among the most prevalent problems reported by decision makers are customer contact, market knowledge, marketing planning, location, and adequacy of capital. A total of 16 problem areas were identified. Traditional wisdom offers the scenario where problems faced will vary as the organization progresses through the life cycle. Much of this research refutes conventional wisdom in that level of competition was determined to have more of an impact on problem perception.

Queueing systems on a circle

Consider a ring on which customers arrive according to a Poisson process. Arriving customers drop somewhere on the circle and wait there for a server who travels on the ring. Whenever this server encounters a customer, he stops and serves the customer according to an arbitrary service time distribution. After the service is completed, the server removes the client from the circle and resumes his journey. We are interested in the number and the locations of customers that are waiting for service. These locations are modeled as random counting measures on the circle. Two different types of servers are considered: The polling server and the Brownian (or drunken) server. It is shown that under both server motions the system is stable if the traffic intensity is less than 1. Furthermore, several earlier results on the configuration of waiting customers are extended, by combining results from random measure theory, stochastic integration and renewal theory.

A Dynamic Distribution Model with Warehouse and Customer Replenishment Requirements

This paper addresses a multiperiod integrated model that plans deliveries to customers based upon inventories (at warehouse and customer locations) and vehicle routes. The model determines replenishment quantities and intervals at the warehouse, and distribution lots and delivery routes at customer locations. We investigate coordination of customer and warehouse replenishment decisions and illustrate their interdependence. Computational experience on randomly generated problems is reported. We show that ordering policy at the warehouse is a function of how goods are distributed to lower echelons and that coordination leads to cost reduction.

A Dynamic Distribution Model with Warehouse and Customer Replenishment Requirements

This paper addresses a multiperiod integrated model that plans deliveries to customers based upon inventories (at warehouse and customer locations) and vehicle routes. The model determines replenishment quantities and intervals at the warehouse, and distribution lots and delivery routes at customer locations. We investigate coordination of customer and warehouse replenishment decisions and illustrate their interdependence. Computational experience on randomly generated problems is reported. We show that ordering policy at the warehouse is a function of how goods are distributed to lower echelons and that coordination leads to cost reduction.

Probabilistic Analysis of a Vehicle Routing Problem with Time Windows

SYNOPTIC ABSTRACTIn the Vehicle Routing Problem with Time Windows, a set of customers requests service by vehicles initially located at a central depot. Each customer provides a period of time in which they must be served. The service may consist of repair work or loading/unloading of the vehicle. The objective is to find tours for the vehicles, such that each customer is served in its specified time window and the total distance traveled by the vehicles is as small as possible. In this paper, we present a new polynomial-time heuristic for a stylized version of the problem, and show it is asymptotically optimal when customer locations are independent and identically distributed in a given region. We also describe the implementation of the heuristic and present computational results.

Probabilistic analysis of a capactiated vehicle routing problem—I

A fleet of vehicles located at a service center must serve the demands of a set of customers. The amount delivered by each vehicle cannot exceed its capacity and a customer’s demand may not be split over more than one vehicle. In our model, customers locations, as well as their demands are independent identically distributed. Simchi-Levi and Bramel [10] determined the asymptotic value of the optimal solution in this model. We prove here a sharp rate of convergence to the asymptotic value