Jing-Sheng Song

Inventory control in a fluctuating demand environment

We present an inventory model, where the demand rate varies with an underlying state-of-the-world variable. This variable can represent economic fluctuations, or stages in the product life-cycle, for example. We derive some basic characteristics of optimal policies and develop algorithms for computing them. In addition, we show that certain monotonicity patterns in the problem data are reflected in the optimal policies.

Price, delivery time guarantees and capacity selection

This paper studies the impact of using delivery time guarantees as a competitive strategy in service industries where demands are sensitive to both price and delivery time. We assume that delivery reliability is crucial, and investment in capacity expansion is plausible in order to maintain a high probability of delivering the time guarantee. A mathematical framework is proposed to understand the interrelations among pricing, delivery time guarantee and capacity expansion decisions. Specifically, an optimization model is developed to determine the joint optimal selection of these three important decision variables, with an objective of maximizing the average net profit. We characterize the optimal decisions and study their qualitative behaviors as various parameters change. We further present a numerical example to illustrate how the results of our model can be used to provide useful managerial insights for selecting the best competing strategies for firms with different operating characteristics. Our model and results are also applicable to a make-to-order manufacturing environment.

Supply Chain Operations: Assemble-to-Order Systems

Publisher Summary An assemble-to-order (or ATO) system includes several components and several products. The time to acquire or produce a component is substantial. A product is assembled only in response to demand. This chapter reviews the research on ATO systems. It discusses the modeling issues and analytical methods, and summarizes the managerial insights gained from the research. An assembly system has just one product, and a distribution system has just one component. The key issue in an assembly system is the coordination of the components, while the key issue in a distribution system is the allocation of the component among the products. An ATO system combines the elements of assembly and distribution, and resolves both coordination and allocation issues. This makes the ATO systems difficult to analyze, design, and manage. The chapter also discusses one-period models, multi-period models, discrete-time models, and continuous-time models.

Order-Fulfillment Performance Measures in An Assemble-To-Order System with Stochastic Leadtimes

We study a multicomponent, multiproduct production and inventory system in which individual components are made to stock but final products are assembled to customer orders. Each component is produced by an independent production facility with finite capacity, and the component inventory is controlled by an independent base-stock policy. For any given base-stock policy, we derive the key performance measures, including the probability of fulfilling a customer order within any specified time window. Computational procedures and numerical examples are also presented. A similar approach applies to the generic multi-item make-to-stock inventory systems in which a typical customer order consists of a kit of items.

Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand

This paper considers a multistage serial inventory system with Markov-modulated demand. Random demand arises at Stage 1, Stage 1 orders from Stage 2, etc., and Stage N orders from an outside supplier with unlimited stock. The demand distribution in each period is determined by the current state of an exogenous Markov chain. Excess demand is backlogged. Linear holding costs are incurred at every stage, and linear backorder costs are incurred at Stage 1. The ordering costs are also linear. The objective is to minimize the long-run average costs in the system. The paper shows that the optimal policy is an echelon base-stock policy with state-dependent order-up-to levels. An efficient algorithm is also provided for determining the optimal base-stock levels. The results can be extended to serial systems in which there is a fixed ordering cost at stage N and to assembly systems with linear ordering costs.

On the Order Fill Rate in a Multi-Item, Base-Stock Inventory System

A customer order to a multi-item inventory system typically consists of several different items in different amounts. The probability of satisfying an arbitrary demand within a prespecified time window, termed the order fill rate, is an important measure of customer satisfaction in industry. This measure, however, has received little attention in the inventory literature, partly because its evaluation is considered a hard problem. In this paper, we study this performance measure for a base-stock system in which the demand process forms a multivariate compound Poisson process and the replenishment leadtimes are constant. We show that the order fill rate can be computed through a series of convolutions of one-dimensional compound Poisson distributions and the batch-size distributions. This procedure makes the exact calculation faster and much more tractable. We also develop simpler bounds to estimate the order fill rate. These bounds require only partial order-based information or merely the item-based information. Finally, we investigate the impact of the standard independent demand assumption when the demand is actually correlated across items.

Performance Analysis and Optimization of Assemble-to-Order Systems with Random Lead Times

We study a single-product assembly system in which the final product is assembled to order whereas the components (subassemblies) are built to stock. Customer demand follows a Poisson process, and replenishment lead times for each component are independent and identically distributed random variables. For any given base-stock policy, the exact performance analysis reduces to the evaluation of a set ofM/ G/8 queues with a common arrival stream. We show that unlike the standardM/ G/8 queueing system, lead time (service time) variability degrades performance in this assembly system. We also show that it is desirable to keep higher base-stock levels for components with longer mean lead times (and lower unit costs). We derive easy-to-compute performance bounds and use them as surrogates for the performance measures in several optimization problems that seek the best trade-off between inventory and customer service. Greedy-type algorithms are developed to solve the surrogate problems. Numerical examples indicate that these algorithms provide efficient solutions and valuable insights to the optimal inventory/service trade-off in the original problems.

Order Fill Rate, Leadtime Variability, and Advance Demand Information in an Assemble-to-Order System

We study an assemble-to-order system with stochastic leadtimes for component replenishment. There are multiple product types, of which orders arrive at the system following batch Poisson processes. Base-stock policies are used to control component inventories. We analyze the system as a set of queues driven by a common, multiclass batch Poisson input, and derive the joint queue-length distribution. The result leads to simple, closed-form expressions of the first two moments, in particular the covariances, which capture the dependence structure of the system. Based on the joint distribution and the moments, we derive easy-to-compute approximations and bounds for the order fulfillment performance measures. We also examine the impact of demand and leadtime variability, and investigate the value of advance demand information.

Newsvendor Bounds and Heuristic for Optimal Policies in Serial Supply Chains

We consider the classicN-stage serial supply systems with linear costs and stationary random demands. There are deterministic transportation leadtimes between stages, and unsatisfied demands are backlogged. The optimal inventory policy for this system is known to be an echelon base-stock policy, which can be computed through minimizingN nested convex functions recursively. To identify the key determinants of the optimal policy, we develop a simple and surprisingly good heuristic. This method minimizes 2 N separate newsvendor-type cost functions, each of which uses the original problem data only. These functions are lower and upper bounds for the echelon cost functions; their minimizers form bounds for the optimal echelon base-stock levels. The heuristic is the simple average of the solution bounds. In extensive numerical experiments, the average relative error of the heuristic is 0.24%, with the maximum error less than 1.5%. The bounds and the heuristic, which can be easily obtained by simple spreadsheet calculations, enhance the accessibility and implementability of the multiechelon inventory theory. More importantly, the closed-form expressions provide an analytical tool for us to gain insights into issues such as system bottlenecks, effects of system parameters, and coordination mechanisms in decentralized systems.

Bricks-and-mortar vs. "clicks-and-mortar": An equilibrium analysis

Abstract The Internet has provided traditional retailers a new means with which to serve customers. Consequently, many “bricks-and-mortar” retailers have transformed to “clicks-and-mortar” by incorporating Internet sales. Examples of companies making such a transition include Best Buy, Wal-Mart, Barnes & Noble, etc. Despite the increasing prevalence of this practice, several fundamental questions remain: (1) Does it pay off to go online? (2) Which is the equilibrium industry structure? (3) What is the implication of this business model for consumers? We study these issues in an oligopoly setting and show that clicks-and-mortar arises as the equilibrium channel structure. However, we find that this equilibrium does not necessarily imply higher profits for the firms: in some cases, rather, it emerges as a strategic necessity. Consumers are generally better off with clicks-and-mortar retailers. If firms align with pure e-tailers to reach the online market, we show that a prisoner’s dilemma-type equilibrium may arise.