Xiting Gong

Optimal Production Planning with Emissions Trading

Emissions trading is a market-based mechanism for curbing emissions, and it has been implemented in Europe, North America, and several other parts of the world. To study its impact on production planning, we develop a dynamic production model, where a manufacturer produces a single product to satisfy random market demands. The manufacturer has access to both a green and a regular production technology, of which the former is more costly but yields fewer emissions. To comply with the emissions regulations, the manufacturer can buy or sell the allowances in each period via forward contracts in an outside market with stochastic trading prices while needing to keep a nonnegative allowance account balance at the end of the planning horizon. We first derive several important structural properties of the model, and based upon them, we characterize the optimal emissions trading and production policies that minimize the manufacturers expected total discounted cost. In particular, the optimal emissions trading policy is a target interval policy with two thresholds that decrease with the starting inventory level. The optimal production policy is established by first determining the optimal technology choice and then showing the optimality of a base-stock type of production policy. We show that the optimal base-stock level is independent of the starting inventory level and the allowance level when the manufacturer trades the allowance or uses both technologies simultaneously. A numerical study using representative data from the cement industry is conducted to illustrate the analytical results and to examine the value of green technology for the manufacturer.

Approximation Algorithms for Perishable Inventory Systems

We develop the first approximation algorithms with worst-case performance guarantees for periodic-review perishable inventory systems with general product lifetime, for both backlogging and lost-sales models. The demand process can be nonstationary and correlated over time, capturing such features as demand seasonality and forecast updates. The optimal control policy for such systems is notoriously complicated, thus finding effective heuristic policies is of practical importance. In this paper, we construct a computationally efficient inventory control policy, called the proportional-balancing policy, for systems with an arbitrarily correlated demand process and show that it has a worst-case performance guarantee less than 3. In addition, when the demands are independent and stochastically nondecreasing over time, we propose another policy, called the dual-balancing policy, which admits a worst-case performance guarantee of 2. We demonstrate through an extensive numerical study that both policies perform consistently close to optimal.

Technical Note—Optimal Control Policy for Capacitated Inventory Systems with Remanufacturing

This paper studies the optimal control policy for capacitated periodic-review inventory systems with remanufacturing. The serviceable products can be either manufactured from raw materials or remanufactured from returned products; but the system has finite capacities in manufacturing, remanufacturing, and/or total manufacturing/remanufacturing operations in each period. Using L -natural convexity and lattice analysis, we show that, for systems with a remanufacturing capacity and a manufacturing/total capacity, the optimal remanufacturing policy is a modified remanufacture-down-to policy and the optimal manufacturing policy is a modified total-up-to policy. Our study reveals that the optimal policies always give production priority to remanufacturing for systems with a remanufacturing capacity and/or a total capacity; but this priority fails to hold for systems with a manufacturing capacity.

Optimal pricing and inventory policies with reliable and random-yield suppliers: characterization and comparison

In this paper, we study the joint pricing and inventory replenishment problem for a periodic-review inventory system with random demand and dual suppliers, one of the suppliers is reliable but more expensive, the other supplier is less expensive but is unreliable with random yield. We characterize the firm’s optimal policies that simultaneously determine the optimal ordering and pricing decisions in each period over a finite planning horizon, and investigate the impacts of supply source diversification and supplier reliability on the firm and on its customers. We show that having source diversification or higher reliability of suppliers not only increases the firm’s expected profit, but also results in a lower optimal selling price, thus they benefit both the firm and its customers.

Approximation Algorithms for Capacitated Perishable Inventory Systems with Positive Lead Times

Managing perishable inventory systems with positive lead times and finite ordering capacities is important but notoriously difficult in both theory and computation. The optimal control policy is extremely complicated, and no effective heuristic policy has been proposed in the literature. In this paper, we develop an easy-to-compute approximation algorithm for this class of problems and prove that it admits a theoretical worst-case performance guarantee under independent and many commonly used positively correlated demand processes. Our worst-case analysis departs significantly from those in the previous studies, requiring several novel ideas. In particular, we introduce a transient unit-matching rule to dynamically match the supply and demand units, and the notion of associated demand processes that provides the right future demand information to establish the desired results. Our numerical study demonstrates the effectiveness of the proposed algorithm. This paper was accepted by Yinyu Ye, optimization.

Design of online auctions: Proxy versus non-proxy settings

Recent years have witnessed the rapid development of online auctions. Currently, some online auctions, such as eBay, introduce a proxy bidding policy, under which bidders submit their maximum bids and delegate to a proxy agent to automatically outbid other competitors for the top bidder, whereas other online auctions do not. This paper compares these two widely used auction mechanisms (proxy setting and non-proxy setting) and characterizes the equilibrium bidding behavior and the sellers expected revenue. We find the proxy auction outperforms the non-proxy auction in terms of the sellers expected revenue. This dominance result is not prone to the specific bid announcement policy, the bidders knowledge regarding the number of bidders, the impact of traffic congestion along the bidding process, the number of items sold through the auction, and the existence of a reserve price. We further find that the proxy setting usually fails to sustain the truthful bidding as a dominant strategy equilibrium even if no minimum bid increments are adopted, and the possibility of a low-valuation-bidder dilemma where the low-valuation bidders could be better off if all bidders collude to bid at the last minute. We also discuss the dramatically different equilibrium bidding behaviors under the two auction mechanisms.

The Use of Switching Point and Protection Levels to Improve Revenue Performance in Order-Driven Production Systems

In a multiproduct order-driven production system, an organization has to decide how to selectively accept orders and allocate capacity to these orders so as to maximize total profit (TP). In this article, we incorporate the novel concept of switching point in developing three capacity-allocation with switching point heuristics (CASPa-c). Our analysis indicates that all three CASP heuristics outperform the first-come-first-served model and Barut and Sridharans dynamic capacity-allocation process (DCAP) model. The best model, CASPb, has an 8% and 6% average TP improvement over DCAP using the split lot and whole lot policies, respectively. In addition, CASPb performs particularly well under operating conditions of tight capacity and large price differences between product classes. The introduction of a switching point, which has not been found in previous capacity-allocation heuristics, provides for a better balance between forward and backward allocation of available capacity and plays a significant role in improving TP.

Constant-Order Policies for Lost-Sales Inventory Models with Random Supply Functions: Asymptotics and Heuristic

We consider an infinite-horizon lost-sales inventory model where the supply takes positive lead times and is a random function of the order quantity (e.g., random yield/capacity). The optimal policy for this model is computationally intractable; and no heuristic has been proposed in the literature. In this paper, we focus on a simple class of constant-order policies (COP) that place the same order in every period, regardless of the system state. Under some assumptions on the random supply function, we prove that the best COP is asymptotically optimal with large lead times and the optimality gap converges to zero exponentially fast in the lead time. We also prove that, if the mean supply capacity is less than the mean demand, then the best COP is also asymptotically optimal with large penalty costs; otherwise, the long-run average cost of the best COP asymptotically increases at the rate of square-root of the penalty cost. Further, we construct a simple heuristic COP and show that it performs very close to the best COP. Finally, we provide a numerical study to derive further insights into the performance of the best COP.

Dynamic Inventory Management with Total Minimum Order Commitments and Two Supply Options

We study optimal policies for dual-supply inventory systems where a firm commits to buying a total minimum quantity from both supplies or two separate total minimum quantities from each supply over a finite planning horizon. The two supply options differ in their costs and lead times. For the system under the joint commitment, the optimal policy has a simple structure and can be fully characterized by three critical numbers in each period. For the system under the separate commitments, we show that the optimal order quantities in each period are monotonic in the starting inventory and the remaining commitments with bounded sensitivity. Moreover, we establish convergence results on the optimal order quantities when the committed quantity from either supply approaches infinity. These findings highlight the effects of order commitments on the optimal inventory policies. On the basis of these results, we develop a simple heuristic for the system under separate commitments and show numerically that it performs...