Yao Zhao

Safety Stock Positioning in Supply Chains with Stochastic Lead Times

We study the safety stock positioning problem in single-product multistage supply chains with tree network structures, where each stage controls its inventory using an installation continuous-time base-stock policy. External demands follow independent Poisson processes, and unsatisfied demands at each stage are fully backordered. The processing (e.g., production) cycle times and transportation lead times are assumed to be stochastic, sequential, and exogenously determined. We derive recursive equations for the backorder delays (because of stockout) at all stages in the supply chain. Based on the recursive equations, we characterize the dependencies of the backorder delays across different stages in the network, and develop insights into the impact of safety stock positioning in various supply chain topologies. We present approximations and algorithms to coordinate the base-stock levels in these supply chains, so as to minimize systemwide inventory cost subject to meeting certain service-level requirements of the external customers.

A Multiproduct Risk-Averse Newsvendor with Law-Invariant Coherent Measures of Risk

We consider a multiproduct risk-averse newsvendor under the law-invariant coherent measures of risk. We first establish several fundamental properties of the model regarding the convexity of the problem, the symmetry of the solution, and the impact of risk aversion. Specifically, we show that for identical products with independent demands, increased risk aversion leads to decreased orders. For a large but finite number of heterogeneous products with independent demands, we derive closed-form approximations for the optimal order quantities. The approximations are as simple to compute as the classical risk-neutral solutions. We also show that the risk-neutral solution is asymptotically optimal as the number of products tends to be infinity, and thus risk aversion has no impact in the limit. For a risk-averse newsvendor with dependent demands, we show that positively (negatively) dependent demands lead to lower (higher) optimal order quantities than independent demands. Using a numerical study, we examine the convergence rates of the approximations and develop additional insights into the interplay between dependent demands and risk aversion.

Performance Analysis and Evaluation of Assemble-to-Order Systems with Stochastic Sequential Lead Times

We consider the multiproduct and multicomponent assemble-to-order (ATO) systems where the replenishment lead times of the components are stochastic, sequential, and independent of the system state. The component inventories are either controlled by the continuous-time base-stock policies, namely, a base-stock ATO system, or by the continuous-time batch-ordering policies, namely, a batch-ordering ATO system. This paper develops the following results: First, for a base-stock ATO system with a single end product and renewal demand arrivals, we characterize the probability distribution of the delivery lead time, i.e., the time it takes to satisfy a demand. The exact analysis allows us to provide simple proofs for the important system properties. Second, for a base-stock ATO system with multiple end products and demand following independent Poisson processes, we characterize the dependence among the stockout delays of the components. We show that a multiproduct ATO system can be decomposed into multiple single-product subsystems with each subsystem corresponding to one product. The analysis allows us to develop two numerical methods to evaluate the performance of the base-stock ATO systems of medium to large sizes. A hypothetical example inspired by a real-world problem is presented. Third, for a batch-ordering ATO system, we develop efficient numerical methods for performance evaluation based on Monte Carlo simulation. Given the sample size, the number of products, and the reorder points, the computational complexity of the methods is no more than that of sorting a set of real numbers, where the set size equals to the sum of the batch sizes of all components. Finally, we characterize the impact of the dependence among the components on various ATO systems, and discuss the limits of the approach.

No-Holdback Allocation Rules for Continuous-Time Assemble-to-Order Systems

This paper analyzes a class of common-component allocation rules, termed no-holdback (NHB) rules, in continuous-review assemble-to-order (ATO) systems with positive lead times. The inventory of each component is replenished following an independent base-stock policy. In contrast to the usually assumed first-come-first-served (FCFS) component allocation rule in the literature, an NHB rule allocates a component to a product demand only if it will yield immediate fulfillment of that demand. We identify metrics as well as cost and product structures under which NHB rules outperform all other component allocation rules. For systems with certain product structures, we obtain key performance expressions and compare them to those under FCFS. For general product structures, we present performance bounds and approximations. Finally, we discuss the applicability of these results to more general ATO systems.

The Value of Component Commonality in a Dynamic Inventory System with Lead Times

Component commonality has been widely recognized as a key factor in achieving product variety at low cost. Yet the theory on the value of component commonality is rather limited in the inventory literature. The existing results were built primarily on single-period models or periodic-review models with zero lead times. In this paper, we consider a continuous-review system with positive lead times. We find that although component commonality is in general beneficial, its value depends strongly on component costs, lead times, and dynamic allocation rules. Under certain conditions, several previous findings based on static models do not hold. In particular, component commonality does not always generate inventory benefits under certain commonly used allocation rules. We provide insight on when component commonality generates inventory benefits and when it may not. We further establish some asymptotic properties that connect component lead times and costs to the impact of component commonality. Through numerical studies, we demonstrate the value of commonality and its sensitivity to various system parameters in between the asymptotic limits. In addition, we show how to evaluate the system under a new allocation rule, a modified version of the standard first-in-first-out rule.

On The Structure Of Optimal Ordering Policies For Stochastic Inventory Systems With Minimum Order Quantity

We study a single-product periodic-review inventory model in which the ordering quantity is either zero or at least a minimum order size. The ordering cost is a linear function of the ordering quantity, and the demand in different time periods are independent random variables. The objective is to characterize the inventory policies that minimize the total discounted ordering, holding, and backorder penalty costs over a finite time horizon. We introduce the concept of an M-increasing function. These functions allow us to characterize the optimal inventory policies everywhere in the state space outside of an interval for each time period. Furthermore, we identify easily computable upper bounds and asymptotic lower bounds for these intervals. Finally, examples are given to demonstrate the complex structure of the optimal inventory policies.

Analysis and evaluation of an Assemble-to-Order system with batch ordering policy and compound Poisson demand

We consider a multi-product and multi-component Assemble-to-Order (ATO) system where the external demand follows compound Poisson processes and component inventories are controlled by continuous-time batch ordering policies. The replenishment lead-times of components are stochastic, sequential and exogenous. Each element of the bill of material (BOM) matrix can be any non-negative integer. Components are committed to demand on a first-come-first-serve basis. We derive exact expressions for key performance metrics under either the assumption that each demand must be satisfied in full (non-split orders), or the assumption that each unit of demand can be satisfied separately (split orders). We also develop an efficient sampling method to estimate these metrics, e.g., the expected delivery lead-times and the order-based fill-rates. Based on the analysis and a numerical study of an example motivated by a real world application, we characterize the impact of the component interaction on system performance, demonstrate the efficiency of the numerical method and quantify the impact of order splitting.

Managing stochastic inventory systems with free shipping option

In many industries, customers are offered free shipping whenever an order placed exceeds a minimum quantity specified by suppliers. This allows the suppliers to achieve economies of scale in terms of production and distribution by encouraging customers to place large orders. In this paper, we consider the optimal policy of a retailer who operates a single-product inventory system under periodic review. The ordering cost of the retailer is a linear function of the ordering quantity, and the shipping cost is a fixed constant K whenever the order size is less than a given quantity - the free shipping quantity (FSQ), and it is zero whenever the order size is at least as much as the FSQ. Demands in different time periods are i.i.d. random variables. We provide the optimal inventory control policy and characterize its structural properties for the single-period model. For multi-period inventory systems, we propose and analyze a heuristic policy that has a simple structure, the (s, t, S) policy. Optimal parameters of the proposed heuristic policy are then computed. Through an extensive numerical study, we demonstrate that the heuristic policy is sufficiently accurate and close to optimal.

Performance Evaluation of Stochastic Multi-Echelon Inventory Systems: A Survey

Globalization, product proliferation, and fast product innovation have significantly increased the complexities of supply chains in many industries. One of the most important advancements of supply chain management in recent years is the development of models and methodologies for controlling inventory in general supply networks under uncertainty and their widefspread applications to industry. These developments are based on three generic methods: the queueing-inventory method, the lead-time demand method and the flow-unit method. In this paper, we compare and contrast these methods by discussing their strengths and weaknesses, their differences and connections, and showing how to apply them systematically to characterize and evaluate various supply networks with different supply processes, inventory policies, and demand processes. Our objective is to forge links among research strands on different methods and various network topologies so as to develop unified methodologies.

THE VALUE OF INFORMATION SHARING IN A TWO-STAGE SUPPLY CHAIN WITH PRODUCTION CAPACITY CONSTRAINTS: THE INFINITE HORIZON CASE

We study the value of information sharing in a two-stage supply chain with a single manufacturer and a single retailer in an infinite time horizon, where the manufacturer has finite production capacity and the retailer faces independent demand. The manufacturer receives demand information even during periods of time in which the retailer does not order. Allowing for time-varying cost functions, our objective is to characterize the impact of information sharing on the manufacturers cost and service level. We develop a new approach to characterize the induced Markov chains under cyclic order-up-to policy and provide a simple proof for the optimality of cyclic order-up-to policy for the manufacturer under the average cost criterion. Using extensive computational analysis, we quantify the impact of information sharing on the manufacturers performance in an infinite time horizon under both i.i.d. demand and independent but nonstationary demand.