Online scheduling policies for multiclass call centers with impatient customers

We consider a call center with two classes of impatient customers: premium and regular classes. Modeling our call center as a multiclass GI/GI/s+M$\mathit{GI}/\mathit{GI}/s+M$ queue, we focus on developing scheduling policies that satisfy a target ratio constraint on the abandonment probabilities of premium customers to regular ones. The problem is inspired by a real call center application in which we want to reach some predefined preference between customer classes for any workload condition. The motivation for this constraint comes from the difficulty of predicting in a quite satisfying way the workload. In such a case, the traditional routing problem formulation with differentiated service levels for different customer classes would be useless. For this new problem formulation, we propose two families of online scheduling policies: queue joining and call selection policies. The principle of our policies is that we adjust their routing rules by dynamically changing their parameters. We then evaluate the performance of these policies through a numerical study. The policies are characterized by simplicity and ease of implementation.     

A stochastic programming model for scheduling call centers with global Service Level Agreements

We consider the issue of call center scheduling in an environment where arrivals rates are highly variable, aggregate volumes are uncertain, and the call center is subject to a global service level constraint. This paper is motivated by work with a provider of outsourced technical support services where call volumes exhibit significant variability and uncertainty. The outsourcing contract specifies a Service Level Agreement that must be satisfied over an extended period of a week or month. We formulate the problem as a mixed-integer stochastic program. Our model has two distinctive features. Firstly, we combine the server sizing and staff scheduling steps into a single optimization program. Secondly, we explicitly recognize the uncertainty in period-by-period arrival rates. We show that the stochastic formulation, in general, calculates a higher cost optimal schedule than a model which ignores variability, but that the expected cost of this schedule is lower. We conduct extensive experimentation to compare the solutions of the stochastic program with the deterministic programs, based on mean valued arrivals. We find that, in general, the stochastic model provides a significant reduction in the expected cost of operation. The stochastic model also allows the manager to make informed risk management decisions by evaluating the probability that the Service Level Agreement will be achieved.     

Robust and data-driven approaches to call centers

We propose both robust and data-driven approaches to a fluid model of call centers that incorporates random arrival rates with abandonment to determine staff levels and dynamic routing policies. We test the resulting models with real data obtained from the call center of a US bank. Computational results show that the robust fluid model is significantly more tractable as compared to the data-driven one and produces overall better solutions to call centers in most experiments.     

Exact tail asymptotics for the Israeli queue with retrials and non-persistent customers

In this paper, we consider the Israeli queue which consists of a main queue with at most N groups and an infinite capacity retrial orbit. The retrial customers may become non-persistent before receiving service. This model was considered before and the decay rate function of the stationary distribution was obtained. To strengthen the result, we characterize the exact tail asymptotics by calculating the coefficient before the decay rate function.     

On the computation of weighted analytic centers and dual ellipsoids with the projective algorithm

The primal projective algorithm for linear programs with unknown optimal objective function value is extended to the case where one uses a weighted Karmarkar potential function. This potential is defined with respect to a strict lower bound to the optimum. The minimization of this potential when the lower bound is kept fixed, yields a primal and a dual feasible solution. The dual solution is the weighted analytic center of a certain dual polytope. Finally one exhibits a pair of homothetic dual ellipsoids that extends results obtained by Sonnevend, Todd, Ye, Freund and Anstreicher.This research has been supported by NSERC-Canada, FCAR-Quebec and FNRS-Switzerland.     

Buffer sizing in multi-product multi-reactor batch processes: Impact of allocation and campaign sizing policies

This paper studies the impact of management policies, such as product allocation and campaign sizing, on the required size of the finished goods inventories in a multi-product multi-reactor batch process. Demand, setup and batch processing times for these products are assumed to be stochastic, and the inventory buffer for every product type needs to be such that target customer service levels are met. To perform this analysis, we develop a queueing model that allows us to explicitly estimate service levels as a function of the buffer size, and the allocation/campaign sizing policies. This model can be used to evaluate the service level given an existing buffer configuration, as well as to determine the buffer sizes required across products to meet a pre-specified service level. It also allows us to formulate a number of insights into how product allocation decisions and campaign planning policies affect buffer sizing decisions in symmetric production systems.     

On the distribution of the number of retrials

We consider queuing systems where customers are not allowed to queue, instead of that they make repeated attempts, or retrials, in order to enter service after some time. We obtain the distribution of the number of retrials produced by a tagged customer, until he finds an available server.     

On equilibrium threshold strategies when choosing between observable and unobservable queues

We consider threshold equilibrium strategies in a two-server memoryless queueing system where customers inspect one queue before deciding which queue to join. We show that such an equilibrium may not exist. A numerical study indicates that if threshold equilibria exist, the effective arrival rate to the unobserved queue is higher when the regime there is last-come first-served rather than first-come first-served.     

On polynomiality of the method of analytic centers for fractional problems

We establish polynomial time convergence of the method of analytic centers for the fractional programming problemt→min |x∈G, tB(x)−A(x)∈K, whereG ⊂ ℝ ⁿ is a closed and bounded convex domain,K ⊂ ℝ ^m is a closed convex cone andA(x):G → ℝ ⁿ ,B(x):G→K are regular enough (say, affine) mappings. This research was partly supported by grant #93-012-499 of the Fundamental Studies Foundation of Russian Academy of Sciences     

L-orthogonality in Daugavet centers and narrow operators

We study the presence of L-orthogonal elements in connection with Daugavet centers and narrow operators. We prove that if $\mathrm{dens}(Y)?{\omega }_1$ and $G:X?Y$ is a Daugavet center with separable range then, for every non-empty $w^{?}$-open subset W of $B_{X^{??}}$, it follows that $G^{??}(W)$ contains some L-orthogonal to Y. In the context of narrow operators, we show that if X is separable and $T:X?Y$ is a narrow operator, then given $y\in B_X$ and any non-empty $w^{?}$-open subset W of $B_{X^{??}}$ then W contains some L-orthogonal u so that $T^{??}(u)=T(y)$. In the particular case that $T^{?}(Y^{?})$ is separable, we extend the previous result to $\mathrm{dens}(X)={\omega }_1$. Finally, we prove that none of the previous results holds in larger density characters (in particular, a counterexample is shown for ${\omega }_2$ under the assumption $2^c={\omega }_2$).     

A general class of centers for the Poincaré problem

We consider the classical Poincaré problem of a linear center perturbed by homogeneous polynomials of degree n?2. Using certain parity properties of a related differential equation, we develop a technique for obtaining center conditions for an arbitrary value of n and use it to exhibit explicitly new center conditions for n=4,…,8.     

Characterizing the performance of process flexibility structures

The objective is to identify preferred flexibility structures in service or manufacturing systems, when demand is random and capacity is finite. Considering a network flow type model as the basis of the analysis, general structural properties of flexibility design pertaining to the marginal values of flexibility and capacity are identified.     

Performance evaluation for general queueing networks in manufacturing systems: Characterizing the trade-off between queue time and utilization

Performance evaluation plays a key role in manufacturing system design and productivity improvement. Characterizing performance objectively is the first step. Inspired by the underlying structure of tandem queues, we have derived an approximate model to characterize the system performance. The model decomposes system queue time and variability into bottleneck and non-bottleneck parts while capturing the dependence among workstations. Compared the new model with prior approaches, the new model not only is more accurate but also requires less information. The property of manufacturing system performance is given based on the insight from the model.     

On the control of queueing systems with failures and repairs

Several classes of problems can be modelled as queueing systems with failures where preventative maintenance has to be optimized: relevant examples are computer systems, databases and production lines. This paper studies a simple case of such a situation based on the M/M/1 queue where the state of the server can take two values (on, off); the transition on–off happens either when there is a failure or when one decides to maintain. The characterization and an approximation of an optimal policy are given. Extensions to more general models, including general Markov processes, are examined.     

Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems

In this paper we classify the centers, the cyclicity of their Hopf bifurcation and the isochronicity of the polynomial differential systems in R² of degree d that in complex notation z=x+iy can be written as

     

On the optimal control of a single-server queueing system: Comment

In a recent paper by Scott and Jefferson, the optimal control of the service rate for a single-server queue with limited waiting space is treated by the maximum principle. We show that their control policies are necessarily suboptimal. Characterizations for optimal control are derived and used to obtain corresponding optimal trajectories in both nonsingular and singular regions.     

A bi-level programming model and solution algorithm for the location of logistics distribution centers

In this paper, by considering benefits of customers and logistics planning departments, a bi-level programming model is presented to seek the optimal location for logistics distribution centers. The upper-level model is to determine the optimal location by minimizing the planners’ cost, and the lower gives an equilibrium demand distribution by minimizing the customers’ cost. Based on the special form of constraints, a simple heuristic algorithm is proposed. Finally, a numerical example is used to illustrate the application of the method, which shows that the algorithm is feasible and advantageous.     

On the validity and utility of queueing models of human service systems

Based on observations made during an extensive study of police patrol operations in New York City, we examine the issues of the validity and utility of queueing models of service systems in which adaptive behavior by the (human) customers or servers is likely. We find that in addition to depending on the technical accuracy of its assumptions, the accuracy of such a model will also depend upon the level of managerial control of the system and adequacy of resources. We recommend that queueing models of human service systems be used in a normative fashion and incorporated in the management feedback loop.     

Global convergence and rate of convergence of a method of centers

We consider a method of centers for solving constrained optimization problems. We establish its global convergence and that it converges with a linear rate when the starting point of the algorithm is feasible as well as when the starting point is infeasible. We demonstrate the effect of the scaling on the rate of convergence. We extend afterwards, the stability result of [5] to the infeasible case anf finally, we give an application to semi-infinite optimization problems.