Pricing and setup/closedown policies in unobservable queues with strategic customers

In this paper we study unobservable Markovian queueing systems with three types of setup/closedown policies: interruptible, skippable and insusceptible setup/closedown policies, respectively. For a system with the interruptible setup/closedown policy, service starts as soon as a customer arrives during a closedown time; However, for a system with the skippable setup/closedown policy, customers arriving in a closedown time (if any) can be served only after the closedown time finishes and the following setup time can be skipped; Then for a system with the insusceptible setup/closedown policy, customers arriving in a closedown time can??t be served until the following setup time finishes. We assume that customers need a price for service, and derive the equilibrium and socially optimal balking strategies for customers as well as the maximal social welfare. Then we make pricing control to motivate customers to adopt the optimal strategies and obtain an appropriate price that also maximizes server??s profit. Moreover, we numerically make some comparisons between the various performance measures.     

Optimal pricing for tandem queues with finite buffers

We consider optimal pricing for a two-station tandem queueing system with finite buffers, communication blocking, and price-sensitive customers whose arrivals form a homogeneous Poisson process. The service provider quotes prices to incoming customers using either a static or dynamic pricing scheme. There may also be a holding cost for each customer in the system. The objective is to maximize either the discounted profit over an infinite planning horizon or the long-run average profit of the provider. We show that there exists an optimal dynamic policy that exhibits a monotone structure, in which the quoted price is non-decreasing in the queue length at either station and is non-increasing if a customer moves from station 1 to 2, for both the discounted and long-run average problems under certain conditions on the holding costs. We then focus on the long-run average problem and show that the optimal static policy performs as well as the optimal dynamic policy when the buffer size at station 1 becomes large, there are no holding costs, and the arrival rate is either small or large. We learn from numerical results that for systems with small arrival rates and no holding cost, the optimal static policy produces a gain quite close to the optimal gain even when the buffer at station 1 is small. On the other hand, for systems with arrival rates that are not small, there are cases where the optimal dynamic policy performs much better than the optimal static policy.

     

Profit maximization in flexible serial queueing networks

We analyze the tradeoff between efficiency and service quality in tandem systems with flexible servers and finite buffers. We reward efficiency by assuming that a revenue is earned each time a job is completed, and penalize poor service quality by incorporating positive holding costs. We study the dynamic assignment of servers to tasks with the objective of maximizing the long-run average profit. For systems of arbitrary size, structured service rates, and linear or nonlinear holding costs, we determine the server assignment policy that maximizes the profit. For systems with two stations, two servers with arbitrary service rates, and linear holding costs, we show that the optimal server assignment policy is of threshold type and determine the value of this threshold as a function of the revenue and holding cost. The threshold can be interpreted as the best possible buffer size, and hence our results prove the equivalence of addressing service quality via a holding cost and via limiting the buffer size. Furthermore, we identify the optimal buffer size when each buffer space comes at a cost. We provide numerical results that suggest that the optimal policy also has a threshold structure for nonlinear holding costs. Finally, for larger systems with arbitrary service rates, we propose effective server assignment heuristics.     

Simulation and Queueing Theory Applied to a Single-Server Queue with Advertising and Balking

We use a single-server queueing model, with limited waiting room capacity, to model a situation where the manager of a facility tries to maximize the profit generated by the facility. He advertises to attract customers. The effectiveness of advertising may depend on the reputation of the facility, which is measured by the fraction of customers who balk. We assume Poisson arrivals and allow Erlang service times to study how the variance of service times affects the optimal policy, both when the efficiency of advertising is exogenous, and when it is a function of the balking rate. We conclude that the optimal policies are similar for deterministic service times, but diverge as the variance of the service time increases.     

On the order of tandem queues

We consider the optimal order of servers in a tandem queueing system withm stages, an unlimited supply of customers in front of the first stage, and a service buffer of size 1 but no intermediate storage buffers between the first and second stages. Service times depend on the servers but not the customers, and the blocking mechanism at the first two stages is manufacturing blocking. Using a new characterization of reversed hazard rate order, we show that if the service times for two servers are comparable in the reversed hazard rate sense, then the departure process is stochastically earlier if the slower server is first and the faster server is second than if the reverse is true. This strengthens earlier results that considered individual departure times marginally. We show similar results for the last two stages and for other blocking mechanisms. We also show that although individual departure times for a system with servers in a given order are stochastically identical to those when the order of servers is reversed, this reversibility property does not hold for the entire departure process.     

Make waiting not to seem like waiting: Capacity management of waiting-area entertainment

To operationalize the psychological principle that “occupied time feels shorter than unoccupied time”, it is common for service providers to offer entertainment options in the waiting areas. Typical examples that put in practice this mechanism include amusement parks, car dealers, airports, hospitals, restaurants, etc. In this paper, we study a queueing system where the server provides entertainment services to waiting customers. Assuming customers are strategic and delay-sensitive, we formulate a game-theoretical model and study customers' equilibrium behavior in response to this mechanism. Because offering waiting-area entertainment incurs extra operational costs, we discuss whether and when this option will benefit the service provider and obtain the optimal entertainment capacity that maximizes the system's profit. Our analysis reveals that this option is appealing if and only if the market size is intermediate and that the optimal capacity of the entertainment is a unimodal function in the market size. Our insights continue to remain valid when the service fee becomes endogenous.     

The uncapacitated facility location problem with demand-dependent setup and service costs and customer-choice allocation

We consider a generalization of the uncapacitated facility location problem, where the setup cost for a facility and the price charged for service may depend on the number of customers patronizing the facility. Customers are represented by the nodes of the transportation network, and facilities can be located only at nodes; a customer selects a facility to patronize so as to minimize his (her) expenses (price for service + the part of transportation costs paid by the customer). We assume that transportation costs are paid partially by the service company and partially by customers. The objective is to choose locations for facilities and balanced prices so as to either minimize the expenses of the service company (the sum of the total setup cost and the total part of transportation costs paid by the company), or to maximize the total profit. A polynomial-time dynamic programming algorithm for the problem on a tree network is developed.     

Optimizing capacity,pricing and location decisions on a congested network with balking

In this paper, we consider the problem of making simultaneous decisions on the location, service rate (capacity) and the price of providing service for facilities on a network. We assume that the demand for service from each node of the network follows a Poisson process. The demand is assumed to depend on both price and distance. All facilities are assumed to charge the same price and customers wishing to obtain service choose a facility according to a Multinomial Logit function. Upon arrival to a facility, customers may join the system after observing the number of people in the queue. Service time at each facility is assumed to be exponentially distributed. We first present several structural results. Then, we propose an algorithm to obtain the optimal service rate and an approximate optimal price at each facility. We also develop a heuristic algorithm to find the locations of the facilities based on the tabu search method. We demonstrate the efficiency of the algorithms numerically.     

Optimizing pricing and location decisions for competitive service facilities charging uniform price

In this paper, we present the problem of optimizing the location and pricing for a set of new service facilities entering a competitive marketplace. We assume that the new facilities must charge the same (uniform) price and the objective is to optimize the overall profit for the new facilities. Demand for service is assumed to be concentrated at discrete demand points (customer markets); customers in each market patronize the facility providing the highest utility. Customer demand function is assumed to be elastic; the demand is affected by the price, facility attractiveness, and the travel cost for the highest-utility facility. We provide both structural and algorithmic results, as well as some managerial insights for this problem. We show that the optimal price can be selected from a certain finite set of values that can be computed in advance; this fact is used to develop an efficient mathematical programming formulation for our model.     

Optimal inventory replenishment policy for a queueing system with finite waiting room capacity

We treat an inventory control problem in a facility that provides a single type of service for customers. Items used in service are supplied by an outside supplier. To incorporate lost sales due to service delay into the inventory control, we model a queueing system with finite waiting room and non-instantaneous replenishment process and examine the impact of finite buffer on replenishment policies. Employing a Markov decision process theory, we characterize the optimal replenishment policy as a monotonic threshold function of reorder point under the discounted cost criterion. We present a simple procedure that jointly finds optimal buffer size and order quantity.     

Optimal pricing for service facilities with self-optimizing customers

Many service industries (e.g., walk-in clinics, vehicle inspection facilities, and data-processing centers) have customers who choose among congested facilities, and select the facility with the lowest combination of travel cost plus congestion cost at the facility. In general, customers over-utilize attractive facilities, causing higher costs than if customers were assigned to facilities to minimize total costs. Optimal facility prices induce customers to select facilities that minimize total cost. We find optimal facility prices and show they equal charging customers for the impact (net costs and benefits) they cause for others. We explore a rich flexibility that allows a range of optimal prices, useful when negotiating the implementation of facility fees. Facility prices can be positive or negative (price discounts), and can be adjusted to be all positive, or to provide net subsidy or net revenue. We contribute to unifying and generalizing several disparate streams of research.     

Optimal admission and pricing control problem with deterministic service times and sideline profit

We consider a discrete-time admission control problem in a company operating in service industries with two classes of customers. For the first class of customers, the company then (1) has an option to accept or reject him/her (admission control), or (2) decides on an offering price (pricing control). The second-class (sideline) customers are only served if no first-class customers are in the system, and this yields the sideline profit. In this paper, we discuss both admission control and pricing control problems within an identical framework, and we examine the properties of the optimal policies to maximize the total expected present discounted net profits. We show that when the sideline profit is large, the optimal policies may not be monotone in the number of first-class customers in the system.     

专有服务机制下提供免费体验服务的服务系统优化设计研究

通过提供免费的体验服务,服务系统可以吸引潜在顾客成为忠实顾客。本文考虑专有服务机制下提供免费体验服务和付费(常规)服务的服务系统,基于顾客的延时敏感特性,利用排队论的矩阵分析方法和谱扩展方法,研究服务系统的相关性能指标以及服务系统的优化设计,进而构建服务提供商利润函数并通过数值实例来获得免费体验服务的最优服务速率以及常规服务收取的最优服务费用,并为服务提供商提供相应的管理启示。研究表明,当越来越多的体验顾客转为付费顾客时,服务提供商需要降低体验服务的服务速率,来缓解系统的拥堵情况,减少顾客的逗留时间,并且服务提供商需要降低常规服务的服务费来弥补顾客因拥堵而造成的服务延迟。新到达顾客选择体验服务的人数越多时,服务提供商需要大幅度降低常规服务的收费标准,来吸引体验顾客成为付费顾客。     

Expulsion and scheduling control for multiclass queues with heterogeneous servers

We consider an M/M/2 system with nonidentical servers and multiple classes of customers. Each customer class has its own reward rate and holding cost. We may assign priorities so that high priority customers may preempt lower priority customers on the servers. We give two models for which the optimal admission and scheduling policy for maximizing expected discounted profit is determined by a threshold structure on the number of customers of each type in the system. Surprisingly, the optimal thresholds do not depend on the specific numerical values of the reward rates and holding costs, making them relatively easy to determine in practice. Our results also hold when there is a finite buffer and when customers have independent random deadlines for service completion.     

Equilibrium balking strategies for a clearing queueing system in alternating environment

We consider a Markovian clearing queueing system, where the customers are accumulated according to a Poisson arrival process and the server removes all present customers at the completion epochs of exponential service cycles. This system may represent the visits of a transportation facility with unlimited capacity at a certain station. The system evolves in an alternating environment that influences the arrival and the service rates. We assume that the arriving customers decide whether to join the system or balk, based on a natural linear reward-cost structure. We study the balking behavior of the customers and derive the corresponding Nash equilibrium strategies under various levels of information.     

Capacity and price setting for dispersed,time-sensitive customer segments

We consider joint pricing and capacity decisions for a facility serving heterogeneous consumers that span a continuous range of locations, and are sensitive to time delays. Within this context, we analyze two contrasting service strategies: segmentation and pooling. Consumer segments differ with respect to their reservation prices and time sensitivities, and are dispersed over a single distance dimension. The firm serves these consumers using a process that we initially model as an M/M/1 queuing system. We analyze profit-maximizing price and capacity levels for a monopolist, and contrast the optimal segmentation and pooling policies. We find that when consumers are time sensitive, and can expect queuing delays at the firm’s facility (due to random arrival and service times), then scale economies from pooling can outweigh segmentation benefits. Yet, segmentation outperforms pooling when consumer segments differ substantively, in which case the firm can use capacity as a lever to price discriminate between the segments. Moreover, by contrasting a dedicated-services strategy, which directly targets specific segments and serves them separately, with the alternative of allowing consumers to self-select, we find that self-selection has a moderate negative influence on profits. We also examine the profit impact of employing alternative queuing systems, and find that a hybrid strategy based on a prioritized queuing discipline, that combines elements of segmentation (by offering different waiting times) and pooling (by sharing capacity across consumer segments), can outperform both the pure segmentation and pooling strategies.     

Optimal (d, c) vacation policy for a finite buffer M/M/c queue with unreliable servers and repairs

This paper considers a finite buffer M/M/c queueing system in which servers are unreliable and follow a (d, c) vacation policy. With such a policy, at a service completion instant, if the number of customers is reduced to c − d (c > d), the d idle servers together take a vacation (or leave for a random amount of time doing other secondary job). When these d servers return from a vacation and if still no more than c − d customers are in the system, they will leave for another vacation and so on, until they find at least c − d + 1 customers are in the system at a vacation completion instant, and then they return to serve the queue. This study is motivated by the fact that some practical production and inventory systems or call centers can be modeled as this finite-buffer Markovian queue with unreliable servers and (d, c) vacation policy. Using the Markovian process model, we obtain the stationary distribution of the number of customers in the system numerically. Some cost relationships among several related systems are used to develop a finite search algorithm for the optimal policy (d, c) which maximizes the long-term average profit. Numerical results are presented to illustrate the usefulness of such a algorithm for examining the effects of system parameters on the optimal policy and its associated average profit.     

The Clustered Orienteering Problem

In this paper we study a generalization of the Orienteering Problem (OP) which we call the Clustered Orienteering Problem (COP). The OP, also known as the Selective Traveling Salesman Problem, is a problem where a set of potential customers is given and a profit is associated with the service of each customer. A single vehicle is available to serve the customers. The objective is to find the vehicle route that maximizes the total collected profit in such a way that the duration of the route does not exceed a given threshold. In the COP, customers are grouped in clusters. A profit is associated with each cluster and is gained only if all customers belonging to the cluster are served. We propose two solution approaches for the COP: an exact and a heuristic one. The exact approach is a branch-and-cut while the heuristic approach is a tabu search. Computational results on a set of randomly generated instances are provided to show the efficiency and effectiveness of both approaches.     

Complexity of flow shop scheduling problems with transportation constraints

In most manufacturing and distribution systems, semi-finished jobs are transferred from one processing facility to another by transporters such as Automated Guided Vehicles, robots and conveyors, and finished jobs are delivered to warehouses or customers by vehicles such as trucks.This paper investigates two-machine flow shop scheduling problems taking transportation into account. The finished jobs are transferred from the processing facility and delivered to customers by truck. Both transportation capacity and transportation times are explicitly taken into account in these models. We study the class of flow shop problems by analysing their complexity. For the makespan objective function, we prove that this problem is strongly NP-hard when the capacity of a truck is limited to two or three parts with an unlimited buffer at the output of the each machine. This problem with additional constraints, such as blocking, is also proven to be strongly NP-hard.