Four Essays on Inventory and Supply Chain Management

Abstract

Inventory and supply chain management are key research areas in operations management. In the first chapter, we generalize classic maximin and minimax regret models (Scarf 1958, Perakis and Roels 2008) of the distributionally robust Newsvendor problem, creating data driven models for censored demand (i.e., sales). In particular, we focus on a single-period single-item distributionally robust Newsvendor context, where only observations of sales (censored demand) data are available. We first calculate confidence intervals for the first ℓ = 2 sales moments and then derive necessary and sufficient conditions to ensure that a valid demand distribution exists for any combination of sales moments contained in the union of the confidence intervals, which lead to guidance on appropriate confidence levels. Once the confidence intervals are well-posed, their union forms the data-driven ambiguity set in our new distributionally robust Newsvendor models. Focusing on the case where confidence intervals for only the first two moments are utilized, we derive a closed-form solution for the optimal order quantity for the maximin model and an equation whose unique solution is the optimal order quantity for the minimax regret model. We extend our models by incorporating information about the probability of demand censoring as well as allowing the sales data to be censored by multiple inventory levels. For the general case where demands are censored by multiple capacities, we show that both the maximin and minimax regret models can be solved via semidefinite programming. We also describe an implementation framework for practice, based on dynamic programming, that allows some learning effects. Extensive experiments, based on real data, explore the impact of various parameters and complement our theoretical contributions. Our study provides the first robust Newsvendor models that can accommodate censored demand using only data, whose solutions may be implemented easily via either closed-form solutions or tractable semidefinite programs. In the second chapter, we study an auto-delivery inventory system which is a subscription model widely employed in supply chain, whereby a supplier delivers products to a buyer (or multiple buyers) according to the buyer’s choice of a constant shipping quantity to be delivered at prescheduled dates. The buyer enjoys a discount for the auto-delivery ordersand other benefits, including free subscription and cancellation. Because these benefits seem to all accrue to the buyer at the supplier’s expense, the rationale for the supplier’s decision to offer auto-delivery and its impact on the profitability of both parties is an intriguing concern. We first develop a model that consists of a supplier and a single buyer, whereby the supplier offers a discount for the auto-delivery orders and the buyer chooses the auto delivery quantity with the flexibility of cancelling the subscription. We derive the two parties’ operating characteristics of their inventory systems and examine their optimal decisions. Our analysis shows that buyers benefit from the auto-delivery discount, the supplier benefits from the demand-expansion effect and the inventory-reduction effect, a potential discount on the cost of the auto-delivery units, and the supply chain benefits from reducing the bullwhip effect. We also find that channel coordination requires the supplier to pass the inventory related savings to the buyer through the auto-delivery discount, which depends on the ratio of the two parties’ holding cost rates. Moreover, we examine a model extension whereby the supplier announces a discount that is available for multiple buyers, we show that the supplier’s optimal auto-delivery discount under exponential demand can be determined based on the aggregate-level demand information from all buyers. Finally, we discuss another model extension whereby the lead time of the supplier’s recurring orders for auto-delivery is longer than that of the regular orders and present a full analysis of the case when the lead time differential is one time period. In the third chapter, we study a two-stage supply chain, where the supplier procures a key component to manufacture a product and the buyer orders from the supplier to meet a price-sensitive demand. As the input price is volatile, the two parties enter into either a standard contract, where the buyer orders just before the supplier starts production, or a time-flexible contract, where the buyer can lock a wholesale price in advance. Moreover, we consider three selling-price schemes: Market-Driven, Cost-Plus, and Profit-Max. This problem is motivated by real practices in the cloud industry. Our model and optimization approach can address similar problems in other industries as well. We assume that the inputprice follows a Geometric Brownian motion. To determine the optimal ordering time, we propose an optimization approach that is different from the classic approach by Dixit et al. (1994) and Li and Kouvelis (1999). Our approach leads to deeper analytical results and more transparent ordering policy. Through a numerical experimentation, we compare profitability of different parties under different contracts, pricing schemes, and market conditions. Our results show: The buyer’s ordering policy is determined by a threshold policy based on the current time and input price; The optimal threshold depends on not only the drift and volatility of the input price, but also their relative magnitude. The supplier’s optimal procurement time should be determined by analyzing a trade-off between the holding cost of storing the components and the future input price movement. We summarize the following managerial implications. (1) Under the Profit-Max and the Cost-Plus pricing schemes, the time-flexible contract is a Pareto improvement compared to the standard contract, whereas, under the Market-Driven pricing scheme, the supplier may be better off under the standard contract. (2) Moreover, although the most favorable scenario for the buyer is under the Profit-Max pricing scheme, the most favorable scenario for the supplier oftentimes is under the Cost-Plus pricing scheme. (3) Furthermore, this study provides valuable insights into impacts of various characteristics of the component market, such as the trend and volatility of the input price, on the expected profit of the supply chain and its split between the two parties. Finally, we apply theories of inventory and supply chain management to solve a practical operations problem in the cloud computing industry. Over the last decade, the adoption of cloud computing has been accelerating, while firms are struggling to manage their growing cloud expenditures in the face of intermittent demand surges caused by planned or random events, including marketing campaigns, new product introductions, and natural disasters. To deal with such challenges, a firm can employ base contracts (“reserved instances” with standard length terms) to meet the base demand, complemented by supplementary contracts (additional “reserved instances” with short length terms) and on-demand instances to cope with the demand surges. We first analyze a model whereby the surge and inter-surge durationsof demands are deterministic, but demand magnitude is random, and cancellation of the reservation contracts is allowed. We characterize the capacity management policy for a cloud user (the “firm”), including the capacity levels and the policy for managing the purchase, renewal, cancellation, and expiration of the supplementary contracts. We also construct an effective heuristic policy by excluding the renewal of supplementary contracts, which can also be applied to a more general setting where the surge and inter-surge durations are random. Moreover, we examine two model extensions: (1) When trades of reserved instances are allowed in the presence of a secondary marketplace; (2) when the firm does not have exact information about the distribution parameters of the surge demand magnitude and duration. For the first extension, we devise a heuristic for determining the length of the supplementary contracts to be purchased from the marketplace combined with a policy for determining the timing of selling the excess capacity. For the second extension, we propose a plausible policy for adjusting capacity levels and managing the supplementary contracts as data unveils and estimates are updated according to Bayesian updating rules. Our results show that the optimal management of the supplementary contracts depends on the relative magnitude of the surge and inter-surge durations in relationship to the cancellation fee rate. In particular, it is optimal for the firm to cancel the supplementary contracts after enduring the first (last) surge duration if the cancellation fee rate is low (high, respectively). Moreover, cloud platforms that offer a secondary marketplace are more attractive to firms from a cost standpoint than those that offer cancellation only. However, the latter, without the secondary marketplace, can achieve parity with the former by offering a deeper discount rate for the reserved instances, thereby bypassing the cost of administering the secondary marketplace.