In the “faster, better, and cheaper” information age, rapid technological breakthroughs create significant risks of obsolescence at the product level or the component level. Consequently, enormous challenges in jointly coordinating inventory replenishment and technology selection arise. The purpose of this dissertation is to develop analytical models to study technology selection and inventory replenishment joint optimization in inventory systems that face frequent technology innovations.
Chapter 1 describes rapid technological obsolescence in the high-tech industry and documents the incredible turn-around in eMachines to demonstrate the importance of jointly optimizing technology selection and inventory control. Several research questions related to jointly optimizing technology selection and inventory control are raised.
Chapter 2 reviews the related literatures. The major differences between the models in this dissertation and those in the existing literatures are also discussed. Chapter 3 to Chapter 6 study the technology selection and inventory replenishment joint optimization in three different production systems.
First, Chapter 3 considers a Make-to-Stock (MTS) system that markets a single product in each time period and investigates optimal timing for technology upgrading. Over the infinite planning horizon, the firm introduces the new and improved product depending on the availability of new generation products. The arrival time of next generation product follows an exogenous discrete-time, phase-type (PH) distribution. The cost parameters and demand distributions are phase- and technology-dependent. In each period, the firm needs to decide which generation product to offer and how much inventory to order. A dynamic programming problem is formulated to determine the technology and inventory joint control policy that maximizes the total expected discounted profit over the infinite horizon. In a special case, where the firm is under the ”inventory return” protection, the optimal policy is explicitly derived. However, when the “inventory return” condition is not satisfied and there is only one period remaining, the optimal policy operates as follows: if and only if the initial inventory is old generation and its inventory level is strictly below a state-dependent threshold, upgrading is optimal; meanwhile the optimal inventory policy follows a two-limit policy with control limits independent of initial inventory (i.e., when the initial technology is kept and its inventory level is below the first limit, order up-to the first limit; if the inventory is above the second limit, salvage inventory down to the second limit; otherwise, neither order nor salvage).
However, when the analysis is extended to the multi-period model, the optimal policy is unclear because the objective function could be neither concave nor quasi-concave.
A sufficient condition that guarantees the objective function to be concave is discussed.
When the objective function is concave, the structure of the optimal joint technology and inventory policy resembles to the counterparts for the single-period problem. Based on the structural property of the special case, a sequential optimization heuristic is proposed, in which the product is upgraded as soon as the development phase reaches a threshold. Under this technology plan, the optimal inventory policy is a two-limit policy.
Second, Chapter 4 extends the model in Chapter 3 to allow the firm to offer an assortment of products in each time period. At the beginning of each period, the firm learns the cost parameters and phases associated with each available technology and makes the assortment and inventory decisions. If the firm decides to remove a product from the initial assortment, the initial inventory of that product will be salvaged immediately
and will not be re-introduced. On the other hand, after knowing what assortment the firm offers, customers make their choice decision following a multinomial logit (MNL) model. As a result, the actual demand for each product included in the assortment is dependent on the firm’s assortment decision as well as the phase and generation of the product. The unmet demand is assumed to be lost and the replenishment lead time is assumed to be negligible. For the final (single) period, the optimal ordering policy follows a two-limit control policy and the optimal assortment policy is a switch-over policy. That is, there exist two increasing functions that partition the plane into (at most) three non-overlapping regions, where each region corresponds to one dominating assortment. When the analysis is extended to the infinite-period model, once again, the objective function could be neither quasi-concave nor concave. If concavity is preserved, then the optimal ordering and assortment policies resemble to their counterparts in the singleperiod model. To gain more insights into the structural properties of the optimal policy, I analyze a special case where the firm is under the protection of “inventory return”. I show that the optimal inventory policy is myopic and always adjusts the inventory level to the newsvender solution. With an additional assumption that the assortment decision does not change the coefficient of variation of product demand, I derive the optimal policy for the unconstrained problem. In addition, I devise a comprehensive measure, the profit per unit, which takes into account the profit margin, overage cost, and demand uncertainty, to conveniently determine which assortment to use. Under some conditions on cost parameters, the optimal policy for the unconstrained problem is also optimal vi
for the constrained problem and indeed the optimal assortment evolves in a phase-based pattern. Several heuristics are proposed. Among them, the sequential optimization heuristic (SH) outperforms others. Under the SH heuristic, when the development state is below the first threshold, the firm offers the old generation product only; when the
development state is between the first and the second thresholds, the firm offers both generation products; when the development state exceeds the second threshold, the firm discontinues the older product and offers the new generation product only. In the meantime,
the inventory ordering policy follows a state-dependent two-limit policy according to the assortment plan. Numerical examples (based on 800 random samples) show that the SH heuristic outperforms the other heuristics, although the computation time for SH heuristic is more intensive. Numerical experiments also suggest that it is more important for the firm with a low profit margin to jointly optimize assortment and inventory control than for a firm with a high profit margin. In particular, the joint optimization becomes more important when demand variability is high or technology innovation is fast.
In practice, the final product is usually assembled from multiple components. As such, technology innovations occur at the component level and impact the system at the product level. The firm needs to effectively coordinate the technology configurations as well as the inventory decisions across different components. Chapter 5 analyzes an Assemble-to-Order (ATO) system that faces frequent component-based innovations. The innovation process of various components is governed by an exogenous discrete-time, multivariate, phase-type renewal process. I first consider centralized decision making, in which the firm jointly determines the technologies to be used and the inventories to be ordered across different components. Under the ”inventory return” condition, the joint optimal technology and inventory policy is myopic and can be solved efficiently by the Interval Partitioning Algorithm (IPA). I then study the dynamic behavior of the optimal myopic policy to gain insights on how the innovation processes affect the firm’s technology selection and inventory replenishment decisions. Using the insights from the structural analysis, a heuristic method that makes the decentralized technology selection decision and the centralized inventory replenishment decision is proposed in Chapter 6. A numerical study using randomly generated data shows that the heuristic is efficient, robust, and yields near-optimal solutions.
Finally, Chapter 7 concludes the dissertation by summarizing the analytical and managerial insights. Several directions for future research are outlined. The appendix contains the definitions of several key terminologies that have been used in the dissertation.
In addition the proofs of several important lemmas and theorems are also relegated into the appendix.
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