OPTIMAL BUFFER ALLOCATION IN ASYNCHRONOUS CYCLIC MIXED-MODEL ASSEMBLY LINES

This paper considers a problem of optimal buffer allocation in cyclic asynchronous mixedmodel assembly lines with deterministic processing times. An analytical model is used to provide new insights into properties of optimal buffer allocation, that is, a buffer configuration that guarantees the highest possible throughput rate on the assembly line with a minimum number of buffers. Optimal buffer configuration is characterized, and an efficient algorithm to find such a configuration is developed. The approach proposed in this paper also provides insights on how to allocate a given number of buffers to workstations on the assembly line to maximize the throughput rate.     

Optimal Workforce Mix in Service Systems with Two Types of Customers

We consider a service system with two types of customers. In such an environment, the servers can either be specialists (or dedicated) who serve a specific customer type, or generalists (or flexible) who serve either type of customers. Cross‐trained workers are more flexible and help reduce system delay, but also contribute to increased service costs and reduced service efficiency. Our objective is to provide insights into the choice of an optimal workforce mix of flexible and dedicated servers. We assume Poisson arrivals and exponential service times, and use matrix‐analytic methods to investigate the impact of various system parameters such as the number of servers, server utilization, and server efficiency on the choice of server mix. We develop guidelines for managers that would help them to decide whether they should be either at one of the extremes, i.e., total flexibility or total specialization, or some combination. If it is the latter, we offer an analytical tool to optimize the server mix.     

Dynamic Assignment of Flexible Service Resources

Resource flexibility is an important tool for firms to better match capacity with demand so as to increase revenues and improve service levels. However, in service contexts that require dynamically deciding whether to accept incoming jobs and what resource to assign to each accepted job, harnessing the benefits of flexibility requires using effective methods for making these operational decisions. Motivated by the resource deployment decisions facing a professional service firm in the workplace training industry, we address the dynamic job acceptance and resource assignment problem for systems with general resource flexibility structure, i.e., with multiple resource types that can each perform different overlapping subsets of job types. We first show that, for systems containing specialized resources for individual job types and a versatile resource type that can perform all job types, the exact policy uses a threshold rule. With more general flexibility structures, since the associated stochastic dynamic program is intractable, we develop and test three optimization‐based approximate policies. Our extensive computational tests show that one of the methods, which we call the Bottleneck Capacity Reservation policy, is remarkably effective in generating near‐optimal solutions over a wide range of problem scenarios. We also consider a model variant that requires dynamic job acceptance decisions but permits deferring resource assignment decisions until the end of the horizon. For this model, we discuss an adaptation of our approximate policy, establish the effectiveness of this policy, and assess the value of postponing assignment decisions.     

Fairness Among Servers When Capacity Decisions Are Endogenous

We look at a simple service system with two servers serving arriving jobs (single class). Our interest is in examining the effect of routing policies on servers when they care about fairness among themselves, and when they can endogenously choose capacities in response to the routing policy. Therefore, we study the two‐server game where the servers’ objective functions have a term explicitly modeling fairness. Moreover, we focus on four commonly seen policies that are from one general class. Theoretical results concerning the existence and uniqueness of the Nash equilibrium are proved for some policies. Further managerial insights are given based on simulation studies on servers’ equilibrium/off‐equilibrium behaviors and the resulting system efficiency performance under different policies.     

Social Optimal Location of Facilities with Fixed Servers,Stochastic Demand,and Congestion

We consider two capacity choice scenarios for the optimal location of facilities with fixed servers, stochastic demand, and congestion. Motivating applications include virtual call centers, consisting of geographically dispersed centers, walk‐in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems. The choice of locations for such facilities influences both the travel cost and waiting times of users. In contrast to most previous research, we explicitly embed both customer travel/connection and delay costs in the objective function and solve the location–allocation problem and choose facility capacities simultaneously. The choice of capacity for a facility that is viewed as a queueing system with Poisson arrivals and exponential service times could mean choosing a service rate for the servers (Scenario 1) or choosing the number of servers (Scenario 2). We express the optimal service rate in closed form in Scenario 1 and the (asymptotically) optimal number of servers in closed form in Scenario 2. This allows us to eliminate both the number of servers and the service rates from the optimization problems, leading to tractable mixed‐integer nonlinear programs. Our computational results show that both problems can be solved efficiently using a Lagrangian relaxation optimization procedure.     

Design Principles for Flexible Systems

A fundamental aspect of designing systems with dedicated servers is identifying and improving the system bottlenecks. We extend the concept of a bottleneck to networks with heterogeneous, flexible servers. In contrast with a network with dedicated servers, the bottlenecks are not a priori obvious, but can be determined by solving a number of linear programming problems. Unlike the dedicated server case, we find that a bottleneck may span several nodes in the network. We then identify some characteristics of desirable flexibility structures. In particular, the chosen flexibility structure should not only achieve the maximal possible capacity (corresponding to full server flexibility), but should also have the feature that the entire network is the (unique) system bottleneck. The reason is that it is then possible to shift capacity between arbitrary nodes in the network, allowing the network to cope with demand fluctuations. Finally, we specify when certain flexibility structures (in particular chaining, targeted flexibility, and the “N” and “W” structures from the call center literature) possess these desirable characteristics.     

Cross‐training Decisions in Field Services with Three Job Types and Server–Job Mismatch*

To be cost‐effective, field service managers must balance the high cost of machine downtime with the high cost of cross‐training technicians in multiple skills. We study a field service system with three job types requiring three different skills. Each server has a primary skill, the cost of which is considered sunk, and up to two secondary skills, which is a managerial decision. We model two important characteristics that distinguish field services: server–job mismatch and the ratio of travel time to service time. We use a queueing framework and simulation to study three cross‐training decisions: the number of servers cross‐trained in secondary skills, the number of secondary skills each server should have, and the efficiency in each secondary skill. We find that complete cross‐training is cost‐effective in some field service situations. Typically, efficiency in secondary skills must be close to 100%, but when the probability of mismatch is high and the ratio of travel time to service time is high, efficiency in secondary skills must be less than 100%.     

Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System

We review queueing‐theory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the long‐run steady‐state behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that time‐dependent performance is captured and staffing requirements can be set. Relatively little modification of straightforward stationary analysis applies in systems where service times are short and the targeted quality of service is high. When service times are moderate and the targeted quality of service is still high, time‐lag refinements can improve traditional stationary independent period‐by‐period and peak‐hour approximations. Time‐varying infinite‐server models help develop refinements, because closed‐form expressions exist for their time‐dependent behavior. More difficult cases with very long service times and other complicated features, such as end‐of‐day effects, can often be treated by a modified‐offered‐load approximation, which is based on an associated infinite‐server model. Numerical algorithms and deterministic fluid models are useful when the system is overloaded for an extensive period of time. Our discussion focuses on telephone call centers, but applications to police patrol, banking, and hospital emergency rooms are also mentioned.     

Cellular Bucket Brigades on U‐Lines with Discrete Work Stations

It is challenging to maximize and maintain productivity of a U‐line with discrete stations under the impact of variability. This is because maximizing productivity requires assigning workers to suitable tasks and maintaining productivity requires sufficient flexibility in task assignment to absorb the impact of variability. To achieve this goal, we propose an operating protocol to coordinate workers on the U‐line. Under the protocol the system can be configured such that its productivity is maximized. Workers are allowed to dynamically share work so that the system can effectively absorb the impact of variability. Analysis based on a deterministic model shows that the system always converges to a fixed point or a period‐2 orbit. We identify a sufficient condition for the system to converge to the fixed point. Increasing the number of stations improves productivity only under certain circumstances. The improvement is most significant when the number of stations in each stage increases from one to two, but further dividing the U‐line into more stations has diminishing return. Simulations based on random work velocities suggest that our approach significantly outperforms an optimized, static work allocation policy if variability in velocity is large.     

Scheduling of Multi‐skilled Staff Across Multiple Locations

We address the problem of assigning airline customer service agents (CSAs) to tasks related to departing flights, such as selling tickets and collecting boarding cards, at an international terminal of a large airport. The airline specifies minimum and target levels of staff and required (or desired) types and levels of skills for each location in each time period. The assignment problem is complicated by staff heterogeneity, time required for moves between locations, and lunch and rest‐break requirements. We present a mixed‐integer formulation that considers both staffing shortages and skills mismatches and show that the problem is NP‐hard. We derive valid inequalities that tighten the bounds within a branch‐and‐cut procedure, enabling us to obtain near‐optimal solutions for problems of realistic size very quickly. We also present a generalization to simultaneously optimize shift starting times and task assignments, which can aid in longer term workforce planning. Finally, we utilize our procedure to obtain managerial insights regarding the benefits of flexibility derived from more highly skilled staff, allowing more frequent moves, and choices of shift starting times. We also demonstrate the benefits of our procedure vs. a heuristic that mimics what an experienced scheduler might choose.     

Dynamic Policies for Optimal LEO Satellite Launches

Low‐earth orbit satellite (LEO) systems continue to provide mobile communication services. The issue of cost containment in system maintenance is a critical factor for continued operation. Satellite finite life‐times follow a stochastic process, and since satellite replenishment cost is the most significant on‐going cost of operation, finding optimal launch policies is of paramount importance. This paper formulates the satellite launch problem as a Markovian decision model that can be solved using dynamic programming. The policy space of the system is enormous and traditional action space dominance rules do not apply. In order to solve the dynamic program for realistic problem sizes, a novel procedure for limiting the state space considered in the dynamic program is developed. The viability of the proposed solution procedure is demonstrated in example problems using realistic system data. The policies derived by the proposed solution procedure are superior to those currently considered by LEO system operators, and result in substantial annual cost savings.     

Maximizing Throughput of Bucket Brigades on Discrete Work Stations

One way to coordinate workers along an assembly line that has fewer workers than work stations is to form a bucket brigade. The throughput of a bucket brigade on discrete work stations may be compromised due to blocking even if workers are sequenced from slowest to fastest. For a given work distribution on the stations we find policies that maximize the throughput of the line. When workers have very different production rates, fully cross‐training the workers and sequencing them from slowest to fastest is almost always the best policy. This policy outperforms other policies for most work distributions except for some cases in which limiting the work zones of workers produces higher throughput. In environments where the work can be adjusted across stations, we identify conditions for a line to prevent blocking.     

APPROXIMATE QUEUEING NETWORK MODELS FOR CLOSED FABRICATION/ASSEMBLY SYSTEMS. PART I: SINGLE LEVEL SYSTEMS

We address the issue of performance analysis of fabrication/assembly (F/A) systems, which are systems that first fabricate components and then join the components and subassemblies into a product. Here we consider an F/A system consisting of a single assembly station with input from K fabrication stations. We assume that the system uses a Kanban control mechanism with a fixed number of kanbans circulating between each input station and the assembly station. Even with Markovian assumptions, computing an exact solution for the performance evaluation of such systems becomes intractable due to an explosion in the state-space. We develop computationally efficient algorithms to approximate the throughput and mean queue lengths. The accuracy of the approximations is studied by comparison to exact results (K = 2) and to simulations (K > 2). Part II of this paper demonstrates how these models can be used as building blocks to evaluate more complex F/A systems with multiple levels of assembly stations.     

Point‐of‐Use Hybrid Inventory Policy for Hospitals

Modern point‐of‐use technology at hospitals has enabled new replenishment policies for medical supplies. One of these new policies, which we call the hybrid policy, is currently in use at a large U.S. Midwest hospital. The hybrid policy combines a low‐cost periodic replenishment epoch with a high‐cost continuous replenishment option to avoid costly stockouts. We study this new hybrid policy under deterministic and stochastic demand. We develop a parameter search engine using simulation to optimize the long‐run average cost per unit time and, via a computational study, we provide insights on the benefits (reduction in cost, inventory, and number of replenishments) that hospitals may obtain by using the hybrid policy instead of the commonly used periodic policies. We also use the optimal hybrid policy parameters from the deterministic analysis to propose approximate expressions for the stochastic hybrid policy parameters that can be easily used by hospital management.      

Hedging strategic flexibility in the distribution optimization problem

Motivated by the increasing prevalence of flexibility hedging in corporate-level risk management programs, this paper focuses on the treatment of hedging operational risks in the coordinated replenishment and shipment for distribution systems. The forward option pricing model with the generalized autoregressive conditional heteroskedasticity (GARCH) model for stochastic demand forecasting is adopted for constructing inventory volume flexibility. We therefore propose a hedge-based coordinated inventory replenishment and shipment (HCIRS) methodology for flexibly making inventory hedging and optimal routing assignment decisions as well as coordinating replenishment and shipment policies. The HCIRS methodology provides insight into strategic flexibility adopted for a real-life inventory–distribution problem faced by one of the major East Asia food supply networks and turns out to be very efficient. The proposed HCIRS methodology has provided evidence of better results than the traditional operational techniques for the presented case in this paper.     

Lot‐sizing Decisions Under Limited‐time Price Reduction*

We consider the optimal lot‐sizing policy for an inventoried item when the vendor offers a limited‐time price reduction. We use the discounted cash flow (DCF) approach in our analysis, thereby eliminating the sources of approximation found in most of the earlier studies that use an average annual cost approach. We first characterize the optimal lot‐sizing policies and their properties, then develop an algorithm for determining the optimal lot sizes. We analytically demonstrate that the lot sizes derived using an average annual cost approach for the different variants of the problem are, in general, larger than the DCF optimum. While DCF analysis is more rigorous and yields precise lot sizes, we recognize that the associated mathematical models and the solution procedure are rather complex. Since simple and easy‐to‐understand policies have a strong practical appeal to decision makers, we propose a DCF version of a simple and easy‐to‐implement heuristic called the “Early Purchase” (EP) strategy and discuss its performance. We supplement our analytical developments with a detailed computational analysis and discuss the implications of our findings for decision making.     

Inventory Rationing for Multiple Class Demand under Continuous Review

We consider how a firm should ration inventory to multiple classes in a stochastic demand environment with partial, class‐dependent backlogging where the firm incurs a fixed setup cost when ordering from its supplier. We present an infinite‐horizon, average cost criterion Markov decision problem formulation for the case with zero lead times. We provide an algorithm that determines the optimal rationing policy, and show how to find the optimal base‐stock reorder policy. Numerical studies indicate that the optimal policy is similar to that given by the equivalent deterministic problem and relies on tracking both the current inventory and the rate that backorder costs are accumulating. Our study of the case of non‐zero lead time shows that a heuristic combining the optimal, zero lead time policy with an allocation policy based on a single‐period profit management problem is effective.     

Redundant configuration of automated flow lines based on “Industry 4.0”-technologies

Over the past decades, robots have been heavily used for flow lines to increase productivity and product quality and to relieve workers of repetitive and dangerous tasks. However, despite continuous improvement of robots, the occurrence of failures remains a significant challenge in the operation of automated flow lines. Due to the connection of the stations in a flow line via a material handling system, failures at one station can quickly lead to throughput losses due to blocking and starving of upstream and downstream stations, respectively. To some extent, these throughput losses can be reduced by installing buffers between the stations. However, the installation of buffers requires considerable investments and scarce factory space. Therefore, the minimization of the total number of buffers is one of the primary objectives in flow line planning. Due to the advances of manufacturing technologies that form the foundation of “Industry 4.0”, new solutions to reduce throughput losses caused by equipment failures open up. One solution is a redundant configuration, in which downstream stations automatically take over the operations of failed stations in the event of failure. The throughput loss in these situations mainly depends on the level of redundancy designed into the system. Based on existing methods for the design of automated flow lines, we present two line balancing formulations for the configuration of automated flow lines under consideration of redundancies. The first formulation aims at maximizing the lines’ level of redundancy. The second formulation aims at a balanced allocation of redundancies along the line. To evaluate the presented formulations, we compare the performance with an existing line balancing approach for automated lines. With respect to this approach, improvements of the throughput rate between 3 % and 7 % are achieved.     

The Critical Few Minutes in Scheduling Time‐Varying Queuing Systems

For nonstationary queuing systems where demand varies over time, an important practical issue is scheduling the number of servers to be available at various times of the day. Widely used scheduling procedures typically involve adding servers at natural time points (e.g., on the hour or at half past the hour) during peak demand periods. Scheduling is often complicated by restrictions on the minimum amount of time (human) servers must work, the earliest (or latest) time a server is available, and limits on the maximum number of servers that can be used at any one time. This paper was motivated by experience with actual queuing systems that embodied such complications. For these systems common scheduling methods that used “natural” starting times for servers resulted in needlessly long customer waits. This research demonstrates that changing the starting times of servers by only a few minutes can have dramatic impacts on customer waiting times for extended periods. In addition, the results highlight the importance of server punctuality.     

Schedule Recovery: Unplanned Absences in Service Operations*

The U.S. service sector loses 2.3% of all scheduled labor hours to unplanned absences, but in some industries, the total cost of unplanned absences approaches 20% of payroll expense. The principal reasons for unscheduled absences (personal illness and family issues) are unlikely to abate anytime soon. Despite this, most labor scheduling systems continue to assume perfect attendance. This oversight masks an important but rarely addressed issue in services management: how to recover from short‐notice, short‐term reductions in planned capacity. In this article, we model optimal responses to unplanned employee absences in multi‐server queueing systems that provide discrete, pay‐per‐use services for impatient customers. Our goal is to assess the performance of alternate absence recovery strategies under various staffing and scheduling regimes. We accomplish this by first developing optimal labor schedules for hypothetical service environments with unreliable workers. We then simulate unplanned employee absences, apply an absence recovery model, and compute system profits. Our absence recovery model utilizes recovery strategies such as holdover overtime, call‐ins, and temporary workers. We find that holdover overtime is an effective absence recovery strategy provided sufficient reserve capacity (maximum allowable work hours minus scheduled hours) exists. Otherwise, less precise and more costly absence recovery methods such as call‐ins and temporary help service workers may be needed. We also find that choices for initial staffing and scheduling policies, such as planned overtime and absence anticipation, significantly influence the likelihood of successful absence recovery. To predict the effectiveness of absence recovery policies under alternate staffing/scheduling strategies and operating environments, we propose an index based on initial capacity reserves.