Sean X. Zhou

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.

Exclusive Channels and Revenue Sharing in a Complementary Goods Market

This paper evaluates the joint impact of exclusive channels and revenue sharing on suppliers and retailers in a hybrid duopoly common retailer and exclusive channel model. The model bridges the gap in the literature on hybrid multichannel supply chains with bilateral complementary products and services with or without revenue sharing. The analysis indicates that, without revenue sharing, the suppliers are reluctant to form exclusive deals with the retailers; thus, no equilibrium results. With revenue sharing from the retailers to the suppliers, it can be an equilibrium strategy for the suppliers and retailers to form exclusive deals. Bargaining solutions are provided to determine the revenue sharing rates. Our additional results suggest forming exclusive deals becomes less desirable for the suppliers if revenue sharing is also in place under nonexclusivity. In our extended discussion, we also study the impact of channel asymmetry, an alternative model with fencing, composite package competition, and enhanced price-dependent revenue sharing.

TECHNICAL NOTE---Optimal Product Acquisition, Pricing, and Inventory Management for Systems with Remanufacturing

Acquisition of used products (cores) is central to the success of remanufacturing programs for companies. At the same time, dynamic pricing strategies have been adopted in various industries to better balance supply and customer demand. In this paper, we study the integration of these two aspects of operations together with inventory management for a production/remanufacturing firm. We develop a periodic-review single-product inventory system with price-dependent customer demand. The product return in each period is random but can be actively controlled by the firms acquisition effort. The firm aims to maximize its total discounted profit over a finite planning horizon by implementing optimal production, remanufacturing, product acquisition, and pricing strategies. We first show that with an exogenous selling price, the optimal production-remanufacturing-disposal policy is simple and characterized by three state-independent parameters. The optimal acquisition effort is decreasing in the aggregate inventory level of serviceable product and cores. Nevertheless, when pricing is an endogenous decision, we find that the optimal policy becomes much more complicated, and its control parameters are state dependent. The optimal selling price is decreasing, whereas the optimal acquisition effort is increasing in the serviceable product inventory level, and both decisions decrease with the aggregate inventory level.

Optimal Control of Inventory Systems with Multiple Types of Remanufacturable Products

Product returns have become a significant feature of many manufacturing systems. Because products are returned under different operational conditions, they usually require different remanufacturing effort/costs. Motivated by a project with a major energy company that manages its inventory through options of ordering and remanufacturing returned products (cores) in various condition, in this paper, we study a single-product, periodic-review inventory system with multiple types of cores. The serviceable products used to fulfill stochastic customer demand can be either manufactured from new parts or remanufactured from the cores, and the objective is to minimize the expected total discounted cost over a finite planning horizon. We show that the optimal manufacturing--remanufacturing--disposal policy has a simple structure and can be completely characterized by a sequence of constant control parameters when manufacturing and remanufacturing leadtimes are the same. To demonstrate the value of the optimal policy, we conduct a numerical study that compares its performance with two simple heuristics, namely, pull policy without and with sorting. The results show that the reduction in system cost by using the optimal policy can be significant. When manufacturing and remanufacturing leadtimes are different, we develop a heuristic method for computing the near-optimal control policy that performs quite well as demonstrated numerically.

Joint inventory-and-pricing strategy for a stochastic continuous-review system

We analyze an infinite-horizon continuous-review stochastic inventory system in which the selling price and inventory replenishment are determined simultaneously. The demand process is Poisson with a price-dependent arrival rate. The ordering cost includes a fixed setup cost and a variable cost proportional to the order quantity. We obtain closed-form solutions for the optimal inventory control strategy and optimal pricing strategy, which provide managerial insights as well as quantitative and qualitative relationships between decision rules and system parameters. We show that the optimal price is a unimodal function of the inventory level. We also develop efficient algorithms to compute the optimal strategies and present numerical examples.

Integration of Inventory and Pricing Decisions with Costly Price Adjustments

Motivated by the widespread adoption of dynamic pricing in industry and the empirical evidence of costly price adjustments, in this paper we consider a periodic-review inventory model with price adjustment costs that consist of both fixed and variable components. In each period, demand is stochastic and price-dependent. The firm needs to coordinate the pricing and inventory replenishment decisions in each period to maximize its total discounted profit over a finite planning horizon. We develop the general model and characterize the optimal policies for two special scenarios, namely, a model with inventory carryover and no fixed price-change costs and a model with fixed price-change costs and no inventory carryover. Finally, we propose an intuitive heuristic policy to tackle the general system whose optimal policy is expected to be very complicated. Our numerical studies show that this heuristic policy performs well.

Improving Supply Chain Performance: Real-Time Demand Information and Flexible Deliveries

In some supply chains, materials are ordered periodically according to local information. This paper investigates how to improve the performance of such a supply chain. Specifically, we consider a serial inventory system in which each stage implements a local reorder interval policy; i.e., each stage orders up to a local base-stock level according to a fixed-interval schedule. A fixed cost is incurred for placing an order. Two improvement strategies are considered: (1) expanding the information flow by acquiring real-time demand information and (2) accelerating the material flow via flexible deliveries. The first strategy leads to a reorder interval policy with full information; the second strategy leads to a reorder point policy with local information. Both policies have been studied in the literature. Thus, to assess the benefit of these strategies, we analyze the local reorder interval policy. We develop a bottom-up recursion to evaluate the system cost and provide a method to obtain the optimal policy. A numerical study shows the following: Increasing the flexibility of deliveries lowers costs more than does expanding information flow; the fixed order costs and the system lead times are key drivers that determine the effectiveness of these improvement strategies. In addition, we find that using optimal batch sizes in the reorder point policy and demand rate to infer reorder intervals may lead to significant cost inefficiency.

Technical Note---Preservation of Quasi-K-Concavity and Its Applications

In this paper, we establish a new preservation property of quasi-K-concavity under certain optimization operations. One important application of the result is to analyze joint inventory-pricing models for single-product periodic-review inventory systems with concave ordering costs. At each period, an ordering quantity and a selling price of the product are determined simultaneously. Demand is random but sensitive to the price. The objective is to maximize the total expected discounted profit over a finite planning horizon. Assuming that demand is a deterministic function of the selling price plus a random perturbation with a positive Polya or uniform distribution, we show that a generalized (s, S, p) policy is optimal.

Approximation Balancing Policies for Inventory Systems with Remanufacturing

We consider a single-product, periodic-review inventory system with remanufacturable returned products, in which the serviceable product used to fulfill stochastic customer demand can be either manufactured from new parts or remanufactured from returned products. Demand and returns follow general stochastic processes and may be correlated, nonstationary, and evolving across different periods. The system costs include remanufacturing and manufacturing costs as well as inventory holding and demand backlogging costs. The objective is to minimize the expected total discounted cost over a finite planning horizon. The optimal policy for this model has a simple structure but its computation can be practically intractable because of the large and high-dimensional state space. Henceforth, we propose an efficient approximation algorithm based on cost balancing techniques to compute manufacturing and remanufacturing quantities in each period and show that the expected cost under this remanufacturing balancing policy...

A simple heuristic for echelon (r,nQ, T) policies in serial supply chains

This paper proposes a simple heuristic that generates a solution for echelon (r,nQ,T) policies by sequentially solving a deterministic demand problem, a subproblem with fixed reorder intervals, and a subproblem with fixed batch sizes. For each of these problems, we further simplify the computation by solving a series of single-stage systems whose parameters are obtained directly from the original problem data. In a numerical study, we find that this heuristic outperforms an existing one in the literature.