Retailers are introducing new store brands at a rapid pace, and annual sales of store brands in the U.S. now exceeds $108 billion. In the literature on store brand decisions, it is commonly assumed that (1) the retailer is a downstream monopolist; (2) either the store brand quality level is fixed, or, the marginal cost of production is constant and independent of the quality level of the store brand; and (3) the retailer either produces the store brand in-house, or sources it from a non-strategic manufacturer. Although these assumptions significantly simplify the analysis, they do not capture what is commonly seen in practice. As a consequence, the insights from these studies may not apply more broadly. Assumption (1) needs to be relaxed in order to study retailers' product assortment decisions (in terms of store and national brands) and related pricing decisions at two competing retailers, along with pricing decisions of a leading national brand manufacturer. Assumption (1) and (2) need to be simultaneously relaxed in order to investigate a retailer's store brand quality-positioning decision when facing competition from another retailer that already carries a store brand. Assumptions (2) and (3) need to be relaxed simultaneously in order to study how a retailer's optimal quality-positioning strategy changes across various sourcing arrangements and various pricing power relationships among retailers and manufacturers. This dissertation contributes to the store brand literature by analyzing models based on more realistic assumptions than those in the literature.

This dissertation consists of three stand-alone papers. The first paper (in Chapter 2) investigates a retailer's product assortment and pricing problem when she has the option to carry a store brand, a national brand, or both. I compare her decision when she is a downstream monopolist and when she faces competition from another retailer who may also oer the same national brand and a competing store brand. Specifically, I assume the quality levels of the products are exogenous and analyze a manufacturer-Stackelberg game involving a national brand manufacturer and two competing retailers. The national brand manufacturer sets a wholesale price for the national brand product (the same for both retailers; I assume they are similar in size and can therefore secure the same wholesale price). Then, observing the wholesale price, the retailers engage in a Nash game in which they set the retail prices for the product(s) they choose to carry. Finally, customers decide whether and what to purchase. Customers are heterogeneous in two dimensions: location, which can be interpreted as the degree of loyalty to one retailer or the other, and willingness to pay per unit of quality. Each customer visits the retailer where he can obtain the maximum surplus (willingness to pay less purchasing and transportation costs) among the offered products. After the customer arrives at the selected retailer, the transportation cost is now sunk, so he buys the offered product with the larger difference between his willingness to pay for the product and its price, if it is non-negative.

The second paper (in Chapter 3) addresses store brand quality positioning decisions for retailers facing retail competition. Specifically, I assume one of the two retailers (Retailer 2) already carries a store brand product whose quality level is fixed, and both retailers may offer the national brand product with a fixed quality level. The representation of customer preferences and the resultant demands are the same as in the first paper. I model the dynamics via a two-stage game. In the first stage, Retailer 1 decides whether to introduce a store brand product, and if so, its quality level. Then the three parties engage in a manufacturer-Stackelberg pricing game. Finally, customers decide whether and what to purchase. In the first stage, Retailer 1 anticipates the outcome of the second-stage game. I analyzed the second stage game in the first paper; it is a subproblem in the second paper. I also analyze a setting in which both retailers may choose the quality levels of their store brand products simultaneously.

The third paper (in Chapter 4) studies a retailer's equilibrium quality-positioning strategy under three sourcing structures, and for each sourcing structure, I consider three types of channel price leadership. Specifically, I study games between (among) a retailer, a national brand manufacturer and a strategic third-party manufacturer, where applicable. The retailer carries a product (with a fixed quality) offered by the national brand manufacturer, and is considering introducing a store brand whose quality can be decided. Customers are heterogeneous in their willingness-to-pay (WTP) per unit of quality. The utility a customer derives from either product equals her WTP per unit of quality times the product quality. Each customer chooses the product that gives her the greatest surplus (utility less price), provided that it is non-negative. The unit production cost of both products is strictly convex and increasing in the quality level of the product. I derive the retailer's equilibrium store-brand quality decision under three sourcing arrangements and three pricing power scenarios. The three sourcing arrangements are in-house (IH), a leading national brand manufacturer (NM) (whose product the retailer also carries), and a strategic third-party manufacturer (SM). The three power scenarios are the ones most commonly seen in the literature: Manufacturer-Stackelberg (MS), Retailer-Stackelberg (RS), and Vertical Nash (VN). In sum, I examine nine (i.e., three times three) combinations of sourcing and pricing power (or game) scenarios, and compare the retailer's optimal quality positioning decision and other equilibrium results (including prices) across the nine scenarios. In all nine combinations of sourcing and pricing power scenarios, the retailer moves rst in setting the quality of her store-brand (during the product development phase) before any pricing decisions are made. I derive subgame perfect equilibria for all scenarios. To the best of my knowledge, I am the first to present a comparison of equilibria for these nine realistic combinations of sourcing and pricing power in this context.

This dissertation makes several contributions to the literature on store brand strategies. First, the majority of papers on store brand strategies consider a monopolist retailer. The few papers that consider retail competition are based on restrictive assumptions concerning factors such as product quality (e.g., assuming store brand products have equal quality levels) or product offering (e.g., both retailers must oer the national brand product). My work in papers 1 and 2 takes a first step in presenting a model that is general enough to allow me to study retailers' strategies in a context with store and national brands, and with retail competition. Second, prior research utilizes demand models that are limited in their ability to capture customers' joint selection of a retailer and a product. My work in papers 1 and 2 is based on a model of customer preferences that allows me to incorporate both quality differentiation among the products and the degree of customer loyalty to retailers, both of which are important in my problem context. This model is flexible enough to support a fairly rich representation of demands. Third, in paper 3, I take a first step in studying the interaction between store-brand sourcing and positioning decisions, and the interplay of these decisions with the retailer's pricing power. From a comparison of the retailer's equilibrium store brand quality levels for the nine combinations of sourcing and game structure, I obtain a full characterization of the ordering of store-brand quality, retailer's prot, retail prices and consumer welfare across the nine combinations. To the best of my knowledge, I am the first to present a comparison of equilibria for these nine realistic combinations of sourcing and pricing power in the store brand context. I also show that sourcing of store brands plays a key role in the competitive interaction between a retailer and a national brand manufacturer. Whereas the marketing and economics literatures have emphasized the role of store brands in helping retailers elicit price concessions from national brand manufacturers, I find that having a preferable sourcing arrangement for a store brand product is more valuable than having pricing power.

This dissertation is concerned with pricing issues facing manufacturers when retailers offer periodic discounts and customers stockpile in response. Chapter 1 provides an overview of the dissertation.

In Chapter 2, we study a new Pareto-improving pricing scheme in which the manufacturer subsidizes the retailer's setup (transportation) cost in exchange for a (possibly) higher wholesale price. The retailer responds by choosing regular and discount prices and his order frequency to maximize his revenue less setup, purchasing and inventory holding costs, considering the customers' response.There are two customer segments that differ in their reservation prices and inventory holding costs. Customers make purchasing (including stockpiling) decisions to maximize their utility from consumption less purchasing and inventory holding costs. We characterize the retailer's optimal response to the manufacturer's pricing decisions and the consumers' response to the retailer's pricing schemes. We then show how to solve the manufacturer's decision problem in view of the downstream responses.

In Chapter 3, we investigate the retailer's pass--through of manufacturer trade discounts. The manufacturer offers a fixed wholesale price and periodic trade discounts. The retailer optimizes his ordering plan (including stockpiling when a trade discount is offered) and the pattern of discounts to offer to customers, seeking to maximize revenue less setup, purchasing and inventory holding costs. Customers differ in their reservation prices, and in our model, we account for the adverse effect of retail discounts on consumers' reservation prices. For a given frequency and depth of the manufacturer's trade discount, we characterize the retailer's optimal discounting pattern for a given ordering schedule that spans the time between the manufacturer's trade discount offers. We solve for the retailer's jointly optimal ordering and discounting patterns by enumerating appropriate ordering schedules and optimizing the retailer's discount pattern for each.

For the models in Chapters 2 and 3, we also perform associated numerical studies which, together with our analytical results, provide insight into how both manufacturers and retailers should make decisions in these problem settings, and circumstances in which various policies

are most effective in increasing profit.

Chapter 4 concludes the dissertation with a summary of contributions and key findings.

Many modern consumer electronics firms design their own products but outsource the production to contract manufacturers. Some of these products are also multi-generational, with short product life cycles and updated versions released on a regular schedule. Therefore, firms must eventually make an end-of-production decision for each product generation. We consider a new version of the last time buy problem—traditionally, a procurement quantity problem for the last possible purchase of a product—facing such a consumer electronics firm. In our problem setting, the contract manufacturer requires the firm to make sequential capacity reservations to retain the option to procure new units, a contract feature that commonly arises when the contract manufacturer has a high opportunity cost of capacity. The presence of the sequential capacity reservation requirement also creates the need to decide the timing of the last time buy, prior to which orders can be placed in each period. We formulate the problem as a dynamic program and identify properties of the optimal policy that are different and more complex than under the usual simpler assumption that capacity reservations (or analogously, production setups) do not need to be for sequential periods.

The dynamic program to find the optimal strategy for any problem instance is computationally intensive. From a numerical study, we observed that most optimal strategies have up to two order-up-to levels, a low-to-moderate value---appropriate for satisfying this period's demand---to be used with low starting inventory levels, and a higher order-up-to level---appropriate for serving as the last time buy---to be used with starting inventory levels above a threshold. We developed a heuristic solution procedure based on these insights that performs near optimally (with an average optimality gap of 0.03% for our set of problem instances) and takes very little computing time.

We also consider a variant of our original problem in which the firm must commit to the timing of the last time buy at the beginning of the problem horizon. From a numerical study, we found that the value of the option to dynamically extend the capacity reservation, as in our original problem variant, is quite small due to the effects of the sequential capacity reservation requirement. We also consider an extension with an option to buy back units from the firm's customers after the last time buy has been made, which is especially applicable when all remaining demand is for warranty replacement units and the buy-back units can be refurbished to satisfy warranty claims. We consider both the case in which the customer response to the buy-back offer is deterministic and the case in which it is stochastic. From a numerical study, we find that the introduction of the buy-back offer has the potential to greatly reduce the firm's expected costs, and this is true whether the customer response to the buy-back offer is deterministic or stochastic. Furthermore, our results suggest that, in a sequential capacity reservation setting, the buy-back option is more valuable than the flexibility afforded by a period-to-period capacity reservation contract.

It is well accepted that uncertainties in supply, production processes, and demand have a major impact on the manufacturers' production and inventory decisions. Manufacturers in capital-intensive industries such as automotive, chemical and food processing face special challenges because they need to maintain high levels of utilization, leaving little flexibility to respond to fluctuations in demands and production yields. Furthermore, many such firms produce multiple products within the same factory, requiring time-consuming or costly changeovers between products, and unanticipated changeovers due to various sources of uncertainty can lead to a reduction in usable capacity and/or an increase in changeover-related costs.

The goal of the dissertation is to develop multi-product production and inventory strategies for manufacturers who use stable production plans due to economies of scale in production and tight capacity, and face various sources of uncertainty. This dissertation consists of two studies. In the first study (Chapters 2 and 3), we investigate a supply chain problem in which a manufacturer needs to maintain a stable production plan while attempting to be responsive to unpredictable orders from distributors. The distributors would like to order in full truckloads as much as possible to spread the high per-truckload cost of transportation across a larger quantity of items. As a consequence, their preferred ordering policy tends to exhibit variability in the time between orders, which makes it difficult for the manufacturer to predict future orders. In such settings, manufacturers are often forced to hold high safety stock levels to limit the number of product shortages and/or to reschedule production to respond to unexpected demands.

Motivated by this context, we propose and analyze a new multi-product (R, T) inventory policy with short-shipping in which an order is placed every T time units and the distributor aims to raise the inventory position of each product i to its respective Ri (produce-up-to) value, but short-shipping (shipping less than the unconstrained optimal order quantities) occurs when the aggregate order would exceed a truckload. By allowing short-shipments, it is possible to maintain both a fixed ordering interval which manufacturers often prefer because it facilitates their production planning, as well as relatively high utilization of truck capacity which distributors prefer due to economies of scale in transportation. We also evaluate how much benefit the manufacturer can obtain from the use of our proposed (R, T) policy which, due to its periodic review form, facilitates balancing of orders from distributors over time. To do so, we quantify the potential benefit to the manufacturer of having all of the distributors switch from their current mode of operation, which we approximate by a continuous-review full-truckload (Q, S) policy, to our proposed (R, T) policy. For both policies, we construct analytical models and develop accurate approximations that enable us to estimate the required base stock levels for the manufacturer to maintain a specified service level for a set of potentially non-identical distributors. Very few articles in the literature have developed systematic analytical models to address this issue for the case of non-identical distributors (or retailers). We conduct a numerical study to compare a system in which all distributors use an (R, T) policy with short-shipments to one in which they all use a (Q, S) policy. From our numerical study, we observe percentage reductions in the manufacturer's base stock level of 2% to 40% and safety stock reductions of 38% to 95% when the distributors switch from a (Q, S) policy to an (R, T) policy with short-shipping, representing substantial savings for the manufacturer.

There are two major contributions from the research presented in Chapters 2 and 3. First, our proposed (R, T) policy with short-shipping contributes to the literature on the stochastic joint replenishment problem (SJRP). Much of the past research on this topic has focused on finding optimal replenishment policies for the buyer (distributor or retailer), but these policies may have an adverse effect on the upstream supplier by increasing uncertainty in the order timing and quantities, thereby exacerbating the bullwhip effect. Our proposed policy, on the other hand, is designed to find a solution that is near-optimal for the distributors and simultaneously has the potential for making production planning easier for the manufacturer, thereby offering the potential for improving supply chain performance. Second, our work contributes to the literature on optimal or near-optimal policies, as well as performance evaluation of specific inventory policies for single-manufacturer (warehouse), multi-retailer (distributor) systems. Although much work has been done in this area, to the best of our knowledge, ours is the first to consider a supply chain in which the upstream stage uses a fixed-cycle (or discrete-time) production schedule and the downstream retailers (distributors) use a continuous-time ordering policy. One reason for the absence of such research in the literature may be that the literature has focused on situations in which the upstream location is a warehouse, which typically has fewer constraints on ordering than a manufacturer faces in planning its production. It is this feature of our problem that makes it distinctive, and is also the main reason why the manufacturer faces a challenge.

In the second study (Chapter 4), we seek to optimize production and inventory decisions of a manufacturer of seasonal products in a capital-intensive industry when demands are uncertain and the production yields of new products are also uncertain. Due to the capital-intensive nature of the industry, the manufacturer sets capacity levels far below peak demand and utilizes slack capacity during off-peak periods to build inventory in anticipation of peak demands. In such a setting, the manufacturer faces the difficult decision of whether to start production of new products well before the selling season (when spare capacity may be available) in order to ``work the bugs out" early, or minimally, to learn about achievable production yields, or to wait until closer to the selling season when capacity may be tight but more accurate demand forecasts may be available.

Motivated by this setting, we construct a parsimonious model to analyze production and inventory decisions for a manufacturer who introduces a new product to be produced in the same facility with existing products, and faces uncertainty in both demands and in the production yield of the new product.

We derive optimal policies for this setting and use these results as the basis for understanding conditions in which the manufacturer should make an early production run to learn the yield of the new product. We also perform comparative static analysis to investigate the effects of demand parameters (mean and range), production capacity, and yield parameters (mean and range) on the manufacturer's optimal decisions. We find not only that the optimal production quantity for the new product may be non-monotonic in the expected demand of the new product, but the decision of whether to learn the yield may also be non-monotonic in the expected demand. Furthermore, we find that, under some conditions, increased aggregate uncertainty about the demand and yield of the new product may deter the manufacturer from learning about the yield, contrary to the common wisdom that early resolution of uncertainty is advantageous.

Our model differs from those in the literature on demand updating in several key respects. First, unlike most papers in the literature, we incorporate capacity constraints and setup times in a context where products share capacity. Although these factors complicate the analysis and lead to a non-convex optimization model, they are critical practical considerations in our motivating context. Second, and perhaps more importantly, we consider yield learning along with demand forecast updating. In our setting, the manufacturer has the option to reduce his uncertainty about the yield of the new product by making an early production run. This gives the manufacturer an incentive to produce the new product early, an incentive which does not exist in models with only demand forecast updating.

In the past two decades, retailers have witnessed rapid changes in markets due to an increase in competition, the rise of e-commerce, and ever-changing consumer behavior. As a result, retailers have become increasingly aware of the need to better coordinate inventory control with pricing in order to maximize their profitability. This dissertation was motivated by two of such problems facing retailers at the interface between pricing and inventory control. One considers inventory control decisions for settings in which planned prices fluctuate over time, and the other considers pricing of multiple substitutable products for settings in which customers hold inventory as a consequence of stockpiling when promotional prices are offered.

In Chapter 1, we provide a brief motivation for each problem. In Chapter 2, we consider optimization of procurement and inventory allocation decisions by a retailer that sells a product with a long production lead time and a short selling season. The retailer orders most products months before the selling season, and places only one order for each product due to short product life cycles and long delivery lead times. Goods are initially stored at the warehouse and then sent to stores over the course of the season. The stores are in high-rent locations, necessitating efficient use of space, so there is no backroom space and it is uneconomical to send goods back to the warehouse; thus, all inventory at each store is available for sale. Due to marketing and logistics considerations, the planned trajectory of prices is determined in advance and may be non-monotonic. Demand is stochastic and price-dependent, and independent across time periods. We begin our analysis with the case of a single store. We first formulate the inventory allocation problem given a fixed initial order quantity with the objective of maximizing expected profit as a dynamic program and explain both technical and computational challenges in identifying the optimal policy. We then present two variants of a heuristic based on the notion of equalizing the marginal value of inventory across the time periods. Results from a numerical study indicate that the more sophisticated variant of the heuristic performs well when compared with both an upper bound and an industry benchmark, and even the simpler variant performs fairly well for realistic settings. We then generalize our approaches to the case of multiple stores, where we allow the stores to have different price trajectories. Our numerical results suggest that the performance of both heuristics is still robust in the multiple store setting, and does not suffer from the same performance deterioration observed for the industry benchmark as the number of stores increases or as price differences increase across stores and time periods. For the pre-season procurement problem, we develop a heuristic based on a generalization of the newsvendor problem that accounts for the two-tiered salvage values in our setting, specifically, a low price during end-of-season markdown periods and a very low or zero salvage value after the season has concluded. Results for numerical examples indicate that our modified newsvendor heuristic provides solutions that are as good as those obtained via grid search.

In Chapter 3, we address a retailer's problem of setting prices, including promotional prices, over a multi-period horizon for multiple substitutable products in the same product category. We consider the problem in a setting in which customers anticipate the retailer's pricing strategy and the retailer anticipates the customers' purchasing decisions. We formulate the problem as a two-stage game in which the profit maximizing retailer chooses prices and the utility maximizing customers respond by making explicit decisions regarding purchasing and consumption, and thus also implicit decisions regarding stockpiling. We incorporate a fairly general reference price formation process that allows for cross-product effects of prices on reference prices. We initially focus on a single customer segment. The representative customer's utility function accounts for the value of consumption of the products, psychological benefit (for deal-seekers) from purchasing at a price below his/her reference price but with diminishing marginal returns, costs of purchases, penalties for both shortages and holding inventory, and disutility for deviating from a consumption target in each period (where applicable). We are the first to develop a model that simultaneously accounts for this combination of realistic factors for the customer, and we also separate the customer's purchasing and consumption decisions. We develop a methodology for solving the customer's problem for arbitrary price trajectories based on a linear quadratic control formulation of an approximation of the customer's utility maximization problem. We derive analytical representations for the customer's optimal decisions as simple linear functions of prices, reference prices, inventory levels (as state variables), and the cumulative aggregate consumption level (as a state variable). We then embed the consumer's optimal policy (in analytic form) in the retailer's profit maximization problem and show that the retailer's problem can be reformulated as a quadratic program that can be solved numerically. Despite the additional generality of our problem context, our solution methodology is computationally tractable. Results for numerical examples indicate that the separation of the customer's two types of decisions turns out to be important in inducing realistic purchasing patterns, including demand spikes like those observed in practice and the associated stockpiling, as well as pre- and post-promotion dips, which are also observed in practice. We discuss how our approach can be extended to multiple customer segments, limitations of our approach, and future research directions.