**A Framework for Improving Access and Customer Service Times in Healthcare: Application and Analysis at the UCLA Medical Center. C. Duda, K. Rajaram, C. Barz, T. Rosenthal. The Health Care Manager. July-September 2013.**

There has been an increasing emphasis on health care efficiency, costs and improving quality in health care settings such as hospitals or clinics. However, there has not been sufficient work on methods to improve access and customer service times in health care settings. The study develops a framework to improve access and customer service time for health care settings. In the framework, the operational concept of the bottleneck is synthesized with queuing theory to improve access and reduce customer service times without reduction in clinical quality. The framework is applied at the Ronald Reagan UCLA Medical Center to determine the drivers for access and customer service times and then provides guidelines on how to improve these drivers. Validation using simulation techniques shows significant potential to reduce customer service times and increase access at this institution. Finally, the study provides several practice implications that could be used to improve access and customer service times without reduction in clinical quality across a range of health care settings from large hospitals to small community clinics.

**The Retail Planning Problem under Demand Uncertainty.** G. Georgiadis, K. Rajaram. *Production and Operations Management*. Forthcoming.

We consider the Retail Planning Problem in which the retailer chooses suppliers, and determines the production, distribution and inventory planning for products with uncertain demand in order to minimize total expected costs. This problem is often faced by large retail chains that carry private label products. We formulate this problem as a convex mixed integer program and show that it is strongly NP-hard. We determine a lower bound by applying a Lagrangean relaxation and show that this bound out- performs the standard convex programming relaxation, while being computationally efficient. We also establish a worst-case error bound for the Lagrangean relaxation. We then develop heuristics to generate feasible solutions. Our computational results indicate that our convex programming heuristic yields feasible solutions that are close to optimal with an average suboptimality gap at 3.4%. We also develop managerial insights for practitioners who choose suppliers, and make production, distribution and inventory decisions in the supply chain.

**Buffer Sizing in Multi-Product Multi-Reactor Batch Processes: Impact of Allocation and Campaign Sizing Policies.** I.V. Nieuwenhuyse, N. Vandaele, K. Rajaram, U.S. Karmarkar. *European Journal of Operational Research*. 179(2): 424-443. June 2007.

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.

**Buffer Location and Sizing to Optimize Cost and Quality in Semi-Continuous Manufacturing Processes: Methodology and Application.** [Best Application Paper 2011]. K. Rajaram, Z. Tian. *IIE Transactions*. 41(12): 1035-1048. December 2009.

The problem of optimizing the location and size of buffers in semi-continuous manufacturing processes is considered. This problem is formulated as a non-linear integer program that determines the optimal buffer size for individual stages and allocates tanks to those stages in order to minimize total tank inclusion, holding, quality, process overshoot and undershoot costs. Heuristics are developed to solve the problem and bounds are derived to evaluate the quality of the heuristics. This method has been implemented at three glucose and three sorbitol production processes at a leading food processing company. This has resulted in total annual cost savings of around 6.4% or $9,000,000. In addition, this work has had a significant impact on several strategic operational decisions at this company.

**Distribution Planning to Optimize Profits in the Motion Picture Industry.** B. Somlo, K. Rajaram, R. Ahmadi. *Production and Operations Management*. 20(4): 618–636. July-August 2011.

We consider the distribution planning problem in the motion picture industry. This problem involves forecasting theater-level box office revenues for a given movie and using these forecasts to choose the best locations to screen a movie. We first develop a method that predicts theater-level box office revenues over time for a given movie as a function of movie attributes and theater characteristics. These estimates are then used by the distributor to choose where to screen the movie. The distributor’s location selection problem is modeled as an integer programming based optimization model that chooses the location of theaters in order to optimize profits. We tested our methods on realistic box office data and show that it has the potential to significantly improve the distributor’s profits. We also develop some insights into why our methods outperform existing practice, which are crucial to their successful practical implementation.

**Joint Pricing And Inventory Control With A Markovian Demand Model.** R. Yin, K. Rajaram. *European Journal of Operational Research*. 182(1): 113-126. October 2007.

We consider the joint pricing and inventory control problem for a single product over a finite horizon and with periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show the existence of an optimal (s,S,p)-type feedback policy for the additive demand model. We extend the model to the case of emergency orders. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing through numerical examples. The results indicate that it is more beneficial to implement dynamic pricing in a Markovian demand environment with a high fixed ordering cost or with high demand variability.

**A Generalization of the Inventory Pooling Effect to Non-Normal Dependent Demand.** C.J.Corbett, K. Rajaram. *Manufacturing and Service Operations Management*. 8(4): 351-358. Fall 2006.

Eppen (1979) showed that inventory costs in a centralized system increase with the correlation between multivariate normal product demands. Using multivariate stochastic orders, we generalize this statement to arbitrary distributions. We then describe methods to construct models with arbitrary dependence structure, using the copula of a multivariate distribution to capture the dependence between the components of a random vector. For broad classes of distributions with arbitrary marginals, we confirm that centralization or pooling of inventories is more valuable when demands are less positively dependent.

**Bundling Retail Products: Models and Analysis.** K.F. McCardle, K. Rajaram, C.S. Tang. *European Journal of Operational Research*. 177(2): 1197-1217. 2007.

We consider the impact of bundling products on retail merchandising. We consider two broad classes of retail products: basic and fashion. For these product classes, we develop models to calculate the optimal bundle prices, order quantities, and profits under bundling. We use this analysis to establish conditions and insights under which bundling is profitable. Our analysis confirms that bundling profitability depends on individual product demands, bundling costs, and the nature of the relationship between the demands of the products to be bundled. We also provide detailed numerical examples.

**Analyzing Variability In Continuous Processes.** K. Rajaram, A. Robotis. *European Journal of Operational Research.*156(2): 312-325. 2004.

We analyze the impact of variability on a continuous flow production process. To perform this analysis, we consider a n-stage serial continuous process in which variability is introduced at each stage. We develop a continuous time model to capture the propagation of variability through the system and use this model to calculate the mean and the variance of the distribution of the output from this process. These results are then used to determine the optimal decisions for variability reduction when designing and operating these processes.

**Campaign Planning And Scheduling For Multi-Product Batch Operations With Applications To The Food Processing Industry.** U.S. Karmarkar, K. Rajaram. *Manufacturing and Service Operations Management*. 6(3): 253-269. 2004.

We analyze planning and scheduling of multi-product batch operations in the food processing industry. Such operations are encountered in many applications including manufacturing of sorbitol, modified starches and specialty sugars. Unlike discrete manufacturing, batch sizes in these operations cannot be set arbitrarily, but are often determined by equipment sizes. Multiple batches of the same product are often run sequentially in “campaigns” to minimize set up and quality costs. We consider the problem of determining the timing and duration of product campaigns in order to minimize average setup, quality and inventory holding costs over a horizon. We formulate the deterministic static version of this problem over an infinite horizon. We show that in general a feasible finite cyclic solution may not exist. We provide sufficient conditions for the existence of a finite cycle, use single-product problems to provide lower bounds on the costs for the multi-product problem and use them to test heuristics developed for this problem. Next we modify this formulation to incorporate fixed cycles that may be necessary due to factors such as product obsolescence, perishability or contracts with customers. We do this by allowing for disposal of excess stock so that finite cycles are always feasible, though they may not be optimal. We also develop bounds and heuristic solution procedures for this case. These methods are applied to data from a leading food processing company. Our results suggest that our methods could potentially reduce total annual costs by about 7.7%, translating to an annual savings of around $7 million.

**Advance Booking Discounts Under Retail Competition.** K.F. McCardle, K. Rajaram, C.S. Tang. *Management Science*. 50(5): 701-708. 2004.

As product demand uncertainty increases and life cycles shorten, retailers respond by developing mechanisms for more accurate demand forecasting and supply planning to avoid over-stocking or under-stocking a product. We consider a situation in which two retailers consider launching one such mechanism, known as the 'Advance Booking Discount' (ABD) program. In this program customers are enticed to pre-commit their orders at a discount selling season. While the ABD program enables the retailers to lock in a portion of the customer demand and use this demand information to develop more accurate forecasts and supply plans, the advance booking discount price reduces profit margin. We analyze the four possible scenarios wherein each of the two firms offer an ABD program or not, and establish conditions under which the unique equilibrium calls for launching the ABD program at both retailers. We also provide a detailed numerical example to illustrate how these conditions are affected by the level of demand uncertainty, demand correlation, market share, and fixed costs for instituting an ABD program.

**The Benefits Of Advance Booking Discount Programs: Models And Analysis.** K. Rajaram, C.S. Tang, A. Alptekinoglu, J. Ou. *Management Science*. 50(4): 465-478. 2004.

Consider a retailer who sells perishable seasonal products with uncertain demand. Due to the short sales season and the long replenishment lead times associated with such products, the retailer is unable to update demand forecasts by using actual sales data generated from the early part of the season and to respond by replenishing stocks during the season. To overcome this limitation, we examine the case in which the retailer develops a program called the 'Advance Booking Discount’ (ABD) program that entices customers to commit to their orders at a discount price prior to the selling season. The time between placement and fulfillment of these pre-committed orders provides an opportunity for the retailer to update demand forecasts by utilizing information generated from the pre-committed orders and to respond by placing a cost-effective order at the beginning of the selling season. In this paper, we evaluate the benefits of the ABD program and characterize the optimal discount price that maximizes the retailers expected profit.

**Flow Management To Optimize Retail Profits At Theme Parks.** K. Rajaram, R. Ahmadi. *Operations Research*. 51(2): 175-184. 2003.

In many theme parks, stores are located within major attractions to sell related merchandise. Sales at such stores form a significant portion of theme park profits. Typically, store sales depend upon visitor flows through the attraction, customer satisfaction with the attraction and the merchandise at the store. In addition, such stores constitute a unique retail environment, as visitor flows to attractions can be managed and stores are not competitors, but belong to the same parent company. This provides the opportunity to increase store sales by interfacing park operations, which manages visitor flows by setting schedules and capacity of attractions, with the store-level merchandising process, which determines which and how much product to order. Motivated by a study at Universal Studios Hollywood (USH), we develop a flow management model to link park operations with store-level merchandising. This model sets the capacities and schedules of the major attractions to increase visitor flows to high profit retail areas subject to visitor satisfaction, capacity, scheduling and flow balance constraints. In addition, this model serves as an important tool to generate and evaluate various strategies aimed at increasing theme park profitability at USH.

**Achieving Environmental And Productivity Improvements Through Model Based Process Redesign.** K. Rajaram, C.J. Corbett. *Operations Research*. 50(5): 751-763. 2002.

Large-scale industrial production processes face increasingly tight environmental constraints, which can be addressed through costly but relatively simple end-of-pipe solutions, or through cheaper but more subtle pollution prevention approaches. Achieving the process improvements necessary for pollution prevention is challenging due to the inherent complexity and the unpredictability of several types of processes found in the food processing, pharmaceuticals, biotechnology and specialty chemical industries. We propose and iterative procedure to achieve process improvements through model-bases process redesign. This process is based on successive convex approximations of the process performance model, where product flows and process settings are optimized for a given configuration and the solution and dual variables of this optimization problem are used to update the process configuration following a greedy capacity reallocation procedure. We implemented over a five-year period at a large wheat-starch extraction process at Cerestar, a major European producer of wheat and starch based products. This procedure led to a dramatic simplification in process configuration. Reduced energy and water consumption led to an estimated $3 million annual cost savings. Moreover, the reduction in environmental impacts allowed Cerestar to maintain current production levels without investing $100 million in additional wastewater treatment capacity to comply with new environmental constraints.

**Product Cycling With Uncertain Yields: Analysis And Application To The Process Industry.** U.S. Karmarkar, K. Rajaram. *Operations Research*. 50(4): 680-691. 2002.

We formulate the dynamic product cycling problem with yield uncertainty and buffer limits to determine which product to produce at which times to minimize total expected switching, production, inventory storage and backorder costs. A "restricted" Lagrangian technique is used to develop a lower bound and a model-based Lagrangian heuristic. We also develop an operational heuristic and a greedy heuristic. The operational heuristic has been implemented at seven refineries at Cerestar, Europe's leading manufacturer of wheat and starch-based products in the food processing industry. This has already reduced costs by around 5% or $3 million annually at these sites. Tests of the Lagrangian heuristic on data from these refineries during this period has shown the potential to further reduce total costs by at least 2% or about $1 million. In addition, the Lagrangian heuristic has provided an objective basis to evaluate the economic impact of several strategic decisions involving issues such as buffer expansion, variability reduction and product selection.

**An Interactive Decision Support System For On-Line Process Control.** K. Rajaram, R. Jaikumar. *European Journal of Operational Research*. 138(3): 554-568. 2002.

We develop a technique for operational decision-making at a starch refinery. The dynamic set of input control decisions required at process stages is computed based on overall production objectives. This technique, implemented as an interactive decision support system for online process control, has already contributed to significantly reducing the duration of transients, which, in turn, has directly increased daily refinery production by more than 18%.

**The Impact Of Product Substitution On Retail Merchandising.** K. Rajaram, C.S. Tang. *European Journal of Operational Research*. 135(3): 582-601. 2001.

The impact of product substitution on two key aspects of retail merchandising, order quantities, and expected profits, is analyzed. To perform this analysis, the basic newsvendor model is extended to include the possibility that a product with surplus inventory can be used as a substitute for out of stock products. This extension requires a definition and an approximation for the resulting effective demand under substitution. A service rate heuristic is developed to solve the extended problem. The performance of this heuristic is evaluated using an upper bound generated by solving the associated Lagrangian dual problem. Analysis suggests that this heuristic provides a tractable and accurate method to determine order quantities and expected profits under substitution. This heuristic is applied to examine how the level of demand uncertainty and correlation, and the degree of substitution between products, affect order quantities and expected profits under substitutable demand. In addition, the heuristic is used to better understand the mechanism by which substitution improves expected profits.

**Optimizing Inventory Replenishment Of Retail Fashion Products.** M.L. Fisher, K. Rajaram, A. Raman. *Manufacturing and Service Operations Management*. 3(3): 230-241. 2001.

We consider the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory. We model this problem as a two-stage stochastic dynamic program, propose a heuristic, establish conditions under which the heuristic finds an optimal solution, and report results of the application of our procedure at a catalog retailer. Our procedure improves on the existing method by enough to double profits. In addition, our method can be used to choose the optimal reorder time, to quantify the benefit of lead time reduction, and to choose the best replenishment contract.

**Grade Selection And Blending To Optimize Cost And Quality.** U.S. Karmarkar, K. Rajaram. *Operations Research*. 49(2): 271-280. 2001.

In many chemical process applications, a large mix of products is produced by blending them from a much smaller set of basic grades. The basic grades themselves are typically produced on the same process equipment and inventoried in batches. Decisions that arise in this process include selecting the set of basic grades, determining how much of each basic grade to produce, and how to blend basic grades to meet final product demand. We model this problem as a nonlinear mixed-integer program, which minimizes total grade inclusion, batching, blending, and quality costs subject to meeting quality and demand constraints for these products. Heuristics and lower bounds are developed and tested. The methods are applied to data from Europe's leading manufacturer of wheat- and starch-based products. Our results suggest that this model could potentially reduce annual costs by a minimum of 7%, translates to annual savings of around $5 million.

**Assortment Planning In Fashion Retailing: Methodology, Application And Analysis.** K. Rajaram. *European Journal of Operational Research*. 129(1): 186-208. 2001.

Assortment planning is the process conducted by the retailer to determine the number and types of products in the line. Key questions that arise in this process include choosing the inventory depth and variety breadth, and the mix between basic and fashion merchandise of the assortment to maximize expected profits. A method is described for resolving these questions. Using demand forecasts derived from historical sales patterns, a nonlinear integer programming model is used to make the assortment choice. Efficient heuristics are developed to solve this problem. The method is applied at a large catalog retailer specializing in women's apparel. The method is then compared to the existing rules used by this retailer and it is found that it could choose the assortment in a manner that reduces markdowns due to excessive inventory and lost margins due to stock outs by enough to increase profits by at least 40%.

**Accurate Retail Testing Of Fashion Merchandise: Methodology And Application.** M.L. Fisher, K. Rajaram. *Marketing Science*. 19(3): 266-278. 2000.

In a merchandise depth test, a retail chain introduces new products at a small sample of selected stores for a short period prior to the primary selling season and uses the observed sales to forecast demand for the entire chain. Described is a method for resolving 2 key questions in merchandise testing: 1. which stores to use for the test and 2. how to extrapolate from test sales to create a forecast of total season demand for each product for the chain. The method uses sales history of products sold in a prior season, similar to those to be tested, to devise a testing program that would have been optimal if it had been applied to this historical sample.

**Incorporating Operator-Process Interactions In Process Control: A Framework And Application To Glucose Refining.** K. Rajaram, R. Jaikumar. *International Journal of Production Economics*. 63(1): 19-31. 2000.

The challenge for process control in dynamic manufacturing environments is to develop systems that reduce variation in key process parameters without compromising the responsiveness of the process. Contemporary engineering control paradigms, because they do not explicitly include the effects of the operator-process interactions that are inevitable in even the most sophisticated processes, trade off high variation for process responsiveness. Consideration of these interactions and their effects are termed operational intelligence and this concept is used to develop a generalized framework for operationally intelligent control systems. This framework is used to develop analytical models to control the operations of a glucose refinery. Application of this methodology reduced throughput variation by more than 50% while increasing the refinery's daily glucose production by roughly 12%.

**Robust Process Control At Cerestar's Refineries.** K. Rajaram, R. Jaikumar, F. Behlau, C. Heynen, F. van Esch, R. Kaiser, A. Kuttner, I. Van Dewege. *Interfaces*. Special Issue: Edelman Award Papers. 29(1): 30-48. 1999.

With annual sales of over $2 billion, Cerestar is Europe's leading manufacturer of made-to-order wheat- and corn-based starch products. Cerestar relies on refineries that are highly automated and require large fixed investments. Starting in 1993, robust process control (RPC) was developed to increase average throughput and reduce throughput variation by combining engineering principles with operations research/management science techniques. RPC includes a mathematical-programming model to reduce downtimes due to product switchovers, models for process optimization, and dynamic control models for process-flow synchronization. Cerestar implemented the resulting decision support system at 8 refineries in 6 countries. It has increased average daily throughputs by 20% and reduced average throughput variation by 50%. Concomitantly, the refineries have reduced their consumption of supplies and utilities. In addition to over $11 million in annual benefits, RPC has had major strategic and organizational impact.

**Costing For Manufacturing Decisions: An Analytical Framework.** R. Giglio, K. Rajaram. *Engineering Valuation and Cost Analysis*. 2: 45-54. 1998.

We develop a mathematical framework for activity based costing (ABC) and examine two characteristics inherent in ABC: the exclusion of most capacity-related costs, and the assumption that processes can meaningfully be divided into discrete elements. These characteristics can limit ABC’s usefulness in providing cost estimates suitable for making sound economic decisions. A framework is developed for identifying manufacturing environments in which such limitations could lead to distortions, and analytical models are developed to properly account for capacity costs and the special characteristics of continuous processes.