Uday S. Rao

Multi-product inventory planning with downward substitution, stochastic demand and setup costs

In this paper we consider a single period multi-product inventory problem with stochastic demand, setup cost for production, and one-way product substitution in the downward direction. We model the problem as a two-stage integer stochastic program with recourse where the first stage variables determine which products to produce and how much to produce, and the second stage variables determine how the products are allocated to satisfy the realized demand. We exploit structural properties of the model and utilize a combination of optimization techniques including network flow, dynamic programming, and simulation-based optimization to develop effective heuristics. Through a computational study, we evaluate the performance of our heuristics by comparison with the corresponding optimal solution obtained from a large scale mixed integer linear program. The computational study indicates that our solution methodology can be very effective (98.8% on average) and can handle industrial-sized problems efficiently. We also provide several new qualitative insights on issues such as the effect of demand variance and cost parameters on the optimal number of products setup, the amount produced or inventoried, and the benefits of allowing substitution.

Managing two-stage serial inventory systems under demand and supply uncertainty and customer service level requirements

We consider a two-echelon serial inventory system with demand and supply uncertainty, non-zero lead times for component procurement and end-product assembly, and a minimum customer service level requirement. We present two supply models which incorporate both quantity and timing uncertainty; these models correspond to current and proposed supply environments. Assuming that installation base-stock ordering policies are followed and that the demand distribution is quasi-concave, we show that the chance-constrained problem of determining optimal base-stock levels which minimize the total inventory investment (cost-weighted stock levels) subject to a service constraint is a convex programming problem. We characterize the relation between the optimal base-stock levels of the component and the end-product. We also illustrate how an optimal internal (component) service level can be computed, which permits decomposition of the two-stage serial system into two coordinated single-echelon systems. Computational experiments illustrate insights on the effects of supply uncertainty and other problem parameters on stock-positioning in a two-echelon serial system. In particular, we evaluate the benefits of switching from one supply environment to another.

Reconfiguring a Remanufacturing Line at Visteon, Mexico

Visteons remanufacturing facility in Lamosa, Mexico was plagued with heavy fluctuations of supply and demand, leading to periods of severe capacity shortage. Management asked us to assess options for improving capacity. We developed a simulation-based line-configuration model that simultaneously considers line balancing and line length (number of production stations) to maximize the remanufacturing systems effective throughput. We computationally analyzed the effect of processing-time variability on line-reconfiguration decisions, the effect of correlated task-processing times on throughput, and the marginal benefits of using dynamic line balancing. Based on the data we collected, we made recommendations for reconfiguring Visteons remanufacturing line. Management successfully implemented these changes, increased asset utilization, and reduced its planned new investments in capital equipment.

Building Cyclic Schedules for Emergency Department Physicians

Physicians at a branch of the emergency department at Cincinnati Childrens Hospital Medical Center complained that their schedules were too erratic because of the multitude of operating requirements, regulatory constraints, physician preferences, and holiday requests. We addressed this issue by using integer programming to build cyclic schedules that can be repeated throughout the year. These schedules are flexible enough to handle incorporating holidays, work assignments, and vacation requests ex post. After we rolled out the calendar-year-based cyclic schedule, we captured statistics to assess the viability and the quality of the yearly schedule generated. Surveys of the physicians and the scheduler after implementation showed that the new schedule provides predictability and well-balanced work patterns.

Comparing two operating-room-allocation policies for elective and emergency surgeries

When organizing the operating theatre and scheduling surgeries, hospitals face a trade-off between the need to be responsive to emergency cases and to conduct scheduled elective surgeries efficiently. We develop a simulation model to compare a flexible and a focused resource-allocation policy. We evaluate these two policies on patient and provider outcome measures, including patient wait time and physician overtime. We find that the focused policy results in lower elective wait time and lower overtime, which leads to the conclusion that electives benefit more from the elimination of emergency disruptions than what they lose from the reduced access to operating rooms. Emergency patient wait time, however, increases significantly as we shift from the flexible to the focused policy. The sensitivity analysis showed that average emergency wait time can decrease as the processing time variability increases. The trade-off between efficiency and responsiveness calls for additional research on other operating-room-allocation policies.

The 2Bin system for controlling medical supplies at point-of-use

The increase in cost of supplies and services is outpacing the increase in revenues at many hospitals. To address this cost increase hospitals are seeking more efficient ways to store and manage vast inventories of medical supplies. A parsimonious and efficient inventory system which we call 2Bin is becoming increasingly popular in North American hospitals. Under the 2Bin system inventory is stored in two equal-sized bins. 2Bin systems are reviewed periodically and empty bins are replenished. In recent years the adoption of RFID technology for 2Bin systems is allowing continuous-time tracking of empty bins, increasing inventory visibility. In this paper we model the 2Bin inventory system under periodic and continuous review. For periodic review we show that the long-run average cost per unit time is quasi-convex, enabling a simple search for the optimal review cycle. For continuous review, we present a semi-Markov decision model, characterize the optimal replenishment policy, and provide a solution approach to obtain the long-run average cost per unit time. Using data obtained from hospitals currently using RFID-enabled 2Bin systems, we estimate the economic benefits of using the best periodic review length (i.e., parameter optimization), and of using a continuous review inventory policy (i.e., policy improvement). We characterize system conditions such as the number of medical supplies used, replenishment costs, stock-out costs, etc. that favor each option, and provide insights to hospital management on system design considerations that favor the use of periodic or continuous review.

Managing operating room efficiency and responsiveness for emergency and elective surgeries—A literature survey

This paper provides a review and classification of the state of research on the question of how a hospital can best utilize its operating rooms (ORs) to balance efficiency and responsiveness when performing surgeries on scheduled electives and high-priority emergencies. We first provide an overview of the specific research questions and conclusions in the literature, as well as a synthesis of the different types of approaches. Then we classify these approaches by methodology and performance measures considered. We also extend the review to other application domains that face a similar question, and highlight similarities and differences to identify potential learning points that apply to the surgery setting. We anticipate this survey highlights the need for future quantitative research that improves the balance of efficiency and responsiveness in the OR.

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.

Partially Flexible Operating Rooms for Elective and Emergency Surgeries

In hospitals, the management of operating rooms faces a trade-off between the need to be responsive to emergency surgeries and to conduct scheduled elective surgeries efficiently. Operating rooms can be configured as flexible and handle both electives and emergencies, or as dedicated to focus on either electives or emergencies. With flexible rooms, the prioritization of emergencies over scheduled electives can lead to schedule disruptions. Focused rooms can lead to imbalances between capacity and surgery workload. Whereas hospital administrators typically handle this trade-off by employing either flexible rooms (complete flexibility) or dedicated rooms (complete focus), we investigate whether a combination of flexible and dedicated rooms (partial flexibility) could be a preferable alternative. The ensuing question is what is the right combination of flexible and dedicated rooms? A versatile simulation model is developed to evaluate different resource allocation policies under various environmental parameters and performance metrics, including patient wait time, staff overtime, and operating room utilization. The main result is that partial flexibility configurations outperform both complete flexibility and complete focus policies by providing solutions with improved values of expected wait time for both emergency and elective patients.

Retailer Transshipment versus Central Depot Allocation for Supply Network Design

We consider a supply chain structure with shipments from an external warehouse directly to retailers and compare two enhancement options: costly transshipment among retailers after demand has been realized vs. cost-free allocation to the retailers from the development of a centralized depot. Stochastic programming models are developed for both the transshipment and allocation structures. We study the impact of cost parameters and demand coefficient of variation on both system structures. Our results show an increasing convex relationship between average costs and demand coefficient of variation, and furthermore that this increase is more pronounced for the allocation structure. We employ simulation and nonlinear search techniques to computationally compare the cost performance of allocation and transshipment structures under a wide range of system parameters such as demand uncertainty and correlation; lead times from the external warehouse to retailers, from warehouse to central depot, and from depot to retailers; and transshipment, holding, and penalty costs. The transshipment approach is found to outperform allocation for a broad range of parameter inputs including many situations for which transshipment is not an economically sound decision for a single period. The insights provided enable the manager to choose whether to invest in reducing lead times or demand uncertainty and assist in the selection of investments across identical and nonidentical retailers.