Experimental Results Indicating Lattice‐Dependent Policies May Be Optimal for General Assemble‐To‐Order Systems

We consider an assemble‐to‐order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite‐horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice‐dependent base‐stock and lattice‐dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M‐system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state‐dependent base‐stock and state‐dependent rationing (SBSR) policy, and a fixed base‐stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.     

Managing Perishables with Time and Temperature History

We address the use and value of time and temperature information to manage perishables in the context of a retailer that sells a random lifetime product subject to stochastic demand and lost sales. The product's lifetime is largely determined by the temperature history and the flow time through the supply chain. We compare the case in which information on flow time and temperature history is available and used for inventory management to a base case in which such information is not available. We formulate the two cases as Markov Decision Processes and evaluate the value of information through an extensive simulation using representative, real world supply chain parameters.     

A Newsvendor Who Chooses Informational Effort

We study a newsvendor who can acquire the services of a forecaster, or, more generally, an information gatherer (IG) to improve his information about demand. When the IG's effort increases, does the average ex ante order quantity rise or fall? Do average ex post sales rise or fall? Improvements in information technology and in the services offered by forecasters provide motivation for the study of these questions. Much depends on our model of the IG and his efforts. We study an IG who sends a signal to a classic single‐period newsvendor. The signal defines the newsvendor's posterior probability distribution on the possible demands and the newsvendor uses that posterior to calculate the optimal order. Each of the possible posteriors is a scale/location transform of the same base distribution. When the IG works harder, the average scale parameter drops. Higher IG effort is always useful to the newsvendor. We show that there is a critical value of order cost. For costs on one side of this value more IG effort leads to a higher average ex ante order and for costs on the other side to a lower average order. But for all costs, more IG effort leads to higher average ex post sales. We obtain analogous results for a “regret‐averse” newsvendor who suffers a penalty that is a nonlinear function of the discrepancy between quantity ordered and true demand.     

Optimal Expediting Policies for a Serial Inventory System with Stochastic Lead Time

In recent supply chains, often operating multiple delivery modes such as standard freight shipping and air is an effective way of addressing both delivery lead time uncertainties and service rates. We propose a model on how to optimally operate multiple delivery modes. We consider a serial supply chain and an expediting option from intermediate installations to the downstream of the chain. The goods move stochastically among the installations and the system faces a stochastic demand. We identify systems that yield simple optimal policies, in which both regular ordering and expediting follow a variant of the base stock policy. Expediting allows the system to be leaner due to the reduced regular order amount. In addition, we provide managerial insights linking expediting, base stock levels, and expediting costs based on analytical and numerical results.     

The Failure of Practical Intuition: How Forward‐Coverage Inventory Targets Cause the Landslide Effect

Seasonal demand for products is common at many companies including Kraft Foods, Case New Holland, and Elmer's Products. This study documents how these, and many other companies, experience bloated inventories as they transition from a low season to a high season and a severe drop in service levels as they transition from a high season to a low season. Kraft has termed this latter phenomenon the “landslide effect.” In this study, we present real examples of the landslide effect and attribute its root cause to a common industry practice employing forward days of coverage when setting inventory targets. While inventory textbooks and academic articles prescribe correct ways to set inventory targets, forward coverage is the dominant method employed in practice. We investigate the magnitude and drivers of the landslide effect through both an analytical model and a case study. We find that the effect increases with seasonality, lead time, and demand uncertainty and can lower service by an average of ten points at a representative company. While the logic is initially counterintuitive to many practitioners, companies can avoid the landslide effect by using demand forecasts over the preceding lead time to calculate safety stock targets.     

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent (s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.     

Coordinated Logistics: Joint Replenishment with Capacitated Transportation for a Supply Chain

In this study, we consider the integrated inventory replenishment and transportation operations in a supply chain where the orders placed by the downstream retailer are dispatched by the upstream warehouse via an in‐house fleet of limited size. We first consider the single‐item single‐echelon case where the retailer operates with a quantity based replenishment policy, (r,Q), and the warehouse is an ample supplier. We model the transportation operations as a queueing system and derive the operating characteristics of the system in exact terms. We extend this basic model to a two‐echelon supply chain where the warehouse employs a base‐stock policy. The departure process of the warehouse is characterized in distribution, which is then approximated by an Erlang arrival process by matching the first two moments for the analysis of the transportation queueing system. The operating characteristics and the expected cost rate are derived. An extension of this system to multiple retailers is also discussed. Numerical results are presented to illustrate the performance and the sensitivity of the models and the value of coordinating inventory and transportation operations.     

Differences in Retail Inventory Investment Behavior During Macroeconomic Shocks: Role of Service Level

In this article, we analyze how retailers change their inventory investment behavior in response to macroeconomic shocks. We examine if service level, as measured by the ratio of stockout to inventory holding costs, can explain the differences in observed behavior across retailers. We use data on macroeconomic indicators and quarterly filings of US public retailers from 1985 to 2009 to estimate a dynamic model of short‐ and long‐term impact of macroeconomic shocks on inventory investment. Our results show that retailers with a high service level increase their inventory investment significantly more than those with a low service level during expansion shocks. Conversely, retailers with a low service level curtail their inventory investment significantly more than those with a high service level during periods of economic contractions. Thus, we show that the aggregate change in inventory investment documented in prior macroeconomics research is driven by different sets of retailers, as predicted by newsvendor logic. We draw implications of our findings to retailers as well as their suppliers.     

Lead Time Management through Expediting in a Continuous Review Inventory System

We consider a continuous review inventory system where delivery lead times can be managed by expediting in‐transit orders shipped from the supplier. First, we propose an ordering/expediting policy and derive expressions for evaluating the operating characteristics of such systems. Second, using extensive numerical experiments, we quantify the benefits of such an expediting policy. Third, we investigate a number of managerial issues. Specifically, we analyze the impact of the number of expediting hubs and their locations along the shipment network on the performance of such systems and offer insights into the design of the shipment network. We show (i) a single expediting hub that is optimally located in a shipment network can capture the majority of cost savings achieved by a multi‐hub system, especially when expediting cost is not low or demand variability is not high; (ii) when expediting time is proportional to the time to destination, for small‐enough or large‐enough demand variations, a single expediting hub located in the middle of the shipment network can capture the majority of cost savings of an optimally located hub; and (iii) in general, hubs close to the retailer significantly drive down costs, whereas hubs close to the supplier may not offer much cost savings.