Mabel C. Chou

Models for Effective Deployment and Redistribution of Bicycles Within Public Bicycle-Sharing Systems

We develop practical operations research models to support decision making in the design and management of public bicycle-sharing systems. We develop a network flow model with proportionality constraints to estimate the flow of bicycles within the network and the number of trips supported, given an initial allocation of bicycles at each station. We also examine the effectiveness of periodic redistribution of bicycles in the network to support greater flow, and the impact on the number of docks needed.We conduct our numerical analysis using transit data from train operators in Singapore. Given that a substantial proportion of passengers in the train system commute a short distance---more than 16% of passengers alight within two stops from the origin---this forms a latent segment of demand for a bicycle-sharing program. We argue that for a bicycle-sharing system to be most effective for this customer segment, the system must deploy the right number of bicycles at the right places, because this affects the utilization rate of the bicycles and how bicycles circulate within the system. We also identify the appropriate operational environments in which periodic redistribution of bicycles will be most effective for improving system performance.

Design for Process Flexibility: Efficiency of the Long Chain and Sparse Structure

The concept of chaining, or in more general terms, sparse process structure, has been extremely influential in the process flexibility area, with many large automakers already making this the cornerstone of their business strategies to remain competitive in the industry. The effectiveness of the process strategy, using chains or other sparse structures, has been validated in numerous empirical studies. However, to the best of our knowledge, there have been relatively few concrete analytical results on the performance of such strategies vis-a-vis the full flexibility system, especially when the system size is large or when the demand and supply are asymmetrical. This paper is an attempt to bridge this gap. We study the problem from two angles: (1) For the symmetrical system where the (mean) demand and plant capacity are balanced and identical, we utilize the concept of a generalized random walk to evaluate the asymptotic performance of the chaining structure in this environment. We show that a simple chaining structure performs surprisingly well for a variety of realistic demand distributions, even when the system size is large. (2) For the more general problem, we identify a class of conditions under which only a sparse flexible structure is needed so that the expected performance is already within e optimality of the full flexibility system. Our approach provides a theoretical justification for the widely held maxim: In many practical situations, adding a small number of links to the process flexibility structure can significantly enhance the ability of the system to match (fixed) production capacity with (random) demand.

Models and Insights for Hospital Inpatient Operations: Time-Dependent ED Boarding Time

One key factor contributing to emergency department (ED) overcrowding is prolonged waiting time for admission to inpatient wards, also known as ED boarding time. To gain insights into reducing this waiting time, we study operations in the inpatient wards and their interface with the ED. We focus on understanding the effect of inpatient discharge policies and other operational policies on the time-of-day waiting time performance, such as the fraction of patients waiting longer than six hours in the ED before being admitted. Based on an empirical study at a Singaporean hospital, we propose a novel stochastic processing network with the following characteristics to model inpatient operations: (1) A patient’s service time in the inpatient wards depends on that patient’s admission and discharge times and length of stay. The service times capture a two-time-scale phenomenon and are not independent and identically distributed. (2) Pre- and post-allocation delays model the extra amount of waiting caused by secondary bottlenecks other than bed unavailability, such as nurse shortage. (3) Patients waiting for a bed can overflow to a nonprimary ward when the waiting time reaches a threshold, where the threshold is time dependent. We show, via simulation studies, that our model is able to capture the inpatient flow dynamics at hourly resolution and can evaluate the impact of operational policies on both the daily and time-of-day waiting time performance. In particular, our model predicts that implementing a hypothetical policy can eliminate excessive waiting for those patients who request beds in mornings. This policy incorporates the following components: a discharge distribution with the first discharge peak between 8 a.m. and 9 a.m. and 26% of patients discharging before noon, and constant-mean allocation delays throughout the day. The insights gained from our model can help hospital managers to choose among different policies to implement depending on the choice of objective, such as to reduce the peak waiting in the morning or to reduce daily waiting time statistics. This paper was accepted by Assaf Zeevi, stochastic models and simulation .

Process Flexibility Revisited: The Graph Expander and Its Applications

We examine how to design a flexible process structure for a production system to match supply with demand more effectively. We argue that good flexible process structures are essentially highly connected graphs, and we use the concept of graph expansion (a measure of graph connectivity) to achieve various insights into this design problem. Whereas existing literature on process flexibility has focused on the expected performance of process structure, we analyze in this paper the worst-case performance of the flexible structure design problem under a more general setting, which encompasses a large class of objective functions. Chou et al. [Chou, M. C., G. Chua, C. P. Teo, H. Zheng. 2010. Design for process flexibility: Efficiency of the long chain and sparse structure. Oper. Res.58(1) 43--58] showed the existence of a sparse process structure that performs nearly as well as the fully flexible system on average, but the approach using random sampling yields few insights into the nature of the process structure. We show that the ψ-expander structure, a variant of the graph expander structure (a highly connected but sparse graph) often used in communication networks, is within e-optimality of the fully flexible system for all demand scenarios. Furthermore, the same expander structure works uniformly well for all objective functions in our class. Based on this insight, we derive design guidelines for general nonsymmetrical systems and develop a simple and easy-to-implement heuristic to design flexible process structures. Numerical results show that this simple heuristic performs well for a variety of numerical examples previously studied in the literature and compares favourably even with the best solutions obtained via extensive simulation and known demand distribution.

On the Asymptotic Optimality of a Simple On-Line Algorithm for the Stochastic Single-Machine Weighted Completion Time Problem and Its Extensions

We consider the stochastic single-machine problem, when the objective is to minimize the expected total weighted completion time of a set of jobs that are released over time. We assume that the existence and the parameters of each job including its release date, weight, and expected processing times are not known until its release date. The actual processing times are not known until processing is completed. We analyze the performance of the on-line nonpreemptive weighted shortest expected processing time among available jobs (WSEPTA) heuristic. When a scheduling decision needs to be made, this heuristic assigns, among the jobs that have arrived but not yet processed, one with the largest ratio of its weight to its expected processing time. We prove that when the job weights and processing times are bounded and job processing times are mutually independent random variables, WSEPTA is asymptotically optimal for the single-machine problem. This implies that WSEPTA generates a solution whose relative error approaches zero as the number of jobs increases. This result can be extended to the stochastic flow shop and open shop problems, as well as models with stochastic job weights.

The asymptotic performance ratio of an on-line algorithm for uniform parallel machine scheduling with release dates

Jobs arriving over time must be non-preemptively processed on one of m parallel machines, each running at its own speed, so as to minimize a weighted sum of the job completion times. In this on-line environment, the processing requirement and weight of a job are not known before the job arrives. The Weighted Shortest Processing Requirement (WSPR) heuristic is a simple extension of the well known WSPT heuristic, which is optimal for the single machine problem without release dates. According to WSPR, whenever a machine completes a job, the next job assigned to it is the one with the least ratio of processing requirement to weight among all jobs available for processing at this point in time. We analyze the performance of this heuristic and prove that its asymptotic competitive ratio is one for all instances with bounded job processing requirements and weights. This implies that the WSPR algorithm generates a solution whose relative error approaches zero as the number of jobs increases. Our proof does not require any probabilistic assumption on the job parameters and relies extensively on properties of optimal solutions to a single machine relaxation of the problem.

On range and response: Dimensions of process flexibility

There are two dimensions to process flexibility: range versus response. Range is the extent to which a system can adapt, while response is the rate at which the system can adapt. Although both dimensions are important, the existing literature does not analytically examine the response dimension vis-a-vis the range dimension. In this paper, we model the response dimension in terms of uniformity of production cost. We distinguish between primary and secondary production where the latter is more expensive. We examine how the range and response dimension interact to affect the performance of the process flexible structure. We provide analytical lower bounds to show that under all scenarios on response flexibility, moderate form of range flexibility (via chaining structure) still manages to accrue non-negligible benefits vis-a-vis the fully flexible structure (the bound is 29.29% when demand is normally distributed). We show further that given limited resources, upgrading system response dimension outperforms upgrading system range dimension in most cases. This confirms what most managers believe in intuitively. We observe also that improving system response can provide even more benefits when coupled with initiatives to reduce demand variability. This is in direct contrast with range flexibility, which is more valuable when the system has higher variability.

Stowage planning for container ships: A heuristic algorithm to reduce the number of shifts

We consider the stowage planning problem of a container ship, where the ship visits a series of ports sequentially and containers can only be accessed from the top of the stacks. At some ports, certain containers will be unloaded temporarily and will be loaded back later for various purposes. Such unproductive movements of containers are called shifts, which are both time and money consuming. Literature shows that binary linear programming formulation for such problems is impracticable for real life problems due to the large number of binary variables and constraints. Therefore, we develop a heuristic algorithm which can generate stowage plans with a reasonable number of shifts for such problems. The algorithm, verified by extensive computational experimentations, performs better than the Suspensory Heuristic Procedure (SH algorithm) proposed in Avriel et al. (1998), which, to the best of our knowledge, is one of the leading heuristic algorithms for such stowage planning problem.

The Implications of Pooled Returns Policies

When selling products with highly uncertain demands and short life cycles, it is common for the manufacturer to offer some form of returns policy to entice the distributors to increase their order quantities. In this paper we consider a multi-item returns policy called pooled (or joint) returns policy in which the distributor can return any combination of the products up to R percent of the total purchases across all products. To our knowledge, multi-item joint returns policy has not been examined in the literature even though it has been commonly used in high-tech product distribution. We analyze the distributors optimal profit and order quantity under the pooled returns policy, and compare these operating characteristics to the case when a single-item non-pooled returns policy is instituted. We show that the distributor can achieve a higher profit under the pooled policy. However, we find a counter-intuitive result that the distributors optimal order quantity can be smaller under the pooled policy. Due to the complexity of the exact analysis for the n-product case, we develop a heuristic for determining near-optimal order quantities. We show that our heuristic performs well when the ratio between the understock cost and the overstock cost is reasonably large.

Analysis of a software focused products and service supply chain

In this paper, we study a software-focused products and service supply chain based on the practice of two leading electronic manufacturing services providers in the world and their major corporate clients. We discuss the common and unique issues that a software-focused supply chain has compared with a traditional supply chain. We also indicate the research challenges and opportunities for a software-focused supply chain