Kumar Rajaram

The impact of product substitution on retail merchandising

Abstract We analyze the impact of product substitution on two key aspects of retail merchandising: order quantities and expected profits. To perform this analysis, we extend the basic news-vendor model 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. Our analysis suggests that this heuristic provides a tractable and accurate method to determine order quantities and expected profits under substitution. We apply this heuristic 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, we use the heuristic to better understand the mechanism by which substitution improves expected profits.

Optimizing Inventory Replenishment of Retail Fashion Products

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 leadtime reduction, and to choose the best replenishment contract.

Bundling retail products: Models and analysis

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.

A Generalization of the Inventory Pooling Effect to Nonnormal Dependent Demand

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.

Assortment planning in fashion retailing: methodology, application and analysis

Abstract Assortment planning is the process conducted by the retailer to determine the number and types of products in a 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. We describe a method for resolving these questions. Using demand forecasts derived from historical sales patterns, we use a nonlinear integer programming model to make the assortment choice. Efficient heuristics are developed to solve this problem. We applied our method at a large catalog retailer specializing in women’s apparel. We compared our method to the existing rules used by this retailer and found that it could choose the assortment in a manner that reduces markdowns due to excessive inventory and lost margins due to stockouts by enough to increase profits by at least 40%. Insights are developed to better understand why products are included in an assortment and the implications of this choice on the realized profit. We extend our model to include shelf space constraints and the effect of assortment choice on product demand.

Joint pricing and inventory control with a Markovian demand model

We consider the joint pricing and inventory control problem for a single product with a finite horizon and 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 and also incorporate capacity and service level constraints. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing strategies through numerical examples. The results indicate that it is more beneficial to implement the dynamic pricing strategy in a Markovian demand environment with a high fixed ordering cost or with high demand uncertainty.

Product Cycling With Uncertain Yields: Analysis and Application to the Process Industry

We formulate the dynamic product-cycling problem with yield uncertainty and buffer limits to determine how much product to produce at what time 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, Europes leading manufacturer of wheat-and corn-based starch products in the food-processing industry. This has already reduced total costs by around 5 percent or

Grade Selection and Blending to Optimize Cost and Quality

3 million annually at these sites. Tests of the Lagrangian heuristic on data from these refineries during this period have shown the potential to further reduce total costs by at least 2 percent or about

A Decision Analysis Tool for Evaluating Fundraising Tiers

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.

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

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 Europes 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