Assessing the Accuracy of Self-Reported Data: an Evaluation of the Toxics Release Inventory

Self-reported regulatory data are hard to verify. This article compares air emissions reported by plants in the Toxics Release Inventory with chemical concentration levels measured by EPA pollution monitors. We find that the large drops in air emissions reported by firms in the TRI are not always matched by similar reductions in measured concentrations from EPA monitors. When the first digits of the monitored chemical concentrations follow a monotonically decreasing distribution, we expect (via Benford's Law) a similar distribution of first digits for the TRI data. For lead and nitric acid the self-reported data do not follow the expected first digit pattern. This suggests that for these two heavily regulated chemicals plants are not reporting accurate estimates of their air emissions. JEL Classification K32, Q53     

Cash‐Flow Based Dynamic Inventory Management

Small‐to‐medium‐sized enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this study, we model a firm that can finance its inventory (ordered or manufactured) with loans in order to meet random demand which in general may not be time stationary. The firm earns interest on its cash on hand and pays interest on its debt. The objective is to maximize the expected value of the firm's capital at the end of a finite planning horizon. The firm's state at the beginning of each period is characterized by the inventory level and the capital level measured in units of the product, whose sum represents the “net worth” of the firm. Our study shows that the optimal ordering policy is characterized by a pair of threshold parameters as follows. (i) If the net worth is less than the lower threshold, then the firm employs a base stock order up to the lower threshold. (ii) If the net worth is between the two thresholds, then the firm orders exactly as many units as it can afford, without borrowing. (iii) If the net worth is above the upper threshold, then the firm employs a base stock order up to the upper threshold. Further, upper and lower bounds for the threshold values are developed using two simple‐to‐compute myopic ordering policies which yield lower bounds for the value function. We also derive an upper bound for the value function by considering a sell‐back policy. Subsequently, it is shown that policies of similar structure are optimal when the loan and deposit interest rates are piecewise linear functions, when there is a maximal loan limit and when unsatisfied demand is backordered. Finally, further managerial insights are provided with extensive numerical studies.     

Exploring Framing Effects in Inventory Control Decisions: Violations of Procedure Invariance

Recent research on decision framing has shown that (i) there are multiple types of framing effects and (ii) the context of the decision can influence framing effects. This research examines decision framing effects in inventory control contexts by questioning the assumption of procedure invariance, that preference should not be impacted by how options are presented to a supply chain manager making an inventory control decision. Study 1 uses three single‐shot decision experiments to establish that all three types of framing effects identified by Levin et al. ( 1998 ) apply in basic inventory control contexts. Results were consistent with theory in all three cases. Given this evidence that framing effects have potential to impact inventory control decisions, two laboratory experiments in Study 2 utilize multi‐period decision tasks to demonstrate that framing effects can impact performance in a dynamic inventory decision setting similar to practice. One of the experiments in Study 2 was conducted with student subjects, while the other with inventory managers from a large retail firm. Results from both experiments provide evidence that even when initial framing effects on order quantities fade, there can be longer term effects on inventory levels and performance. Furthermore, these effects are robust to education and professional experience. The findings suggest that although a manager might select appropriate inventory control metrics, prudence must be exercised in the presentation of these metrics, and that mere presentation can be used to alleviate known human biases in inventory control decisions.     

Managing Inventory with Cash Register Information: Sales Recorded but Not Demands

Inventory inaccuracy is common in many businesses. While retailers employ cash registers to enter incoming orders and outgoing sales, inaccuracy arises because they do not record invisible demand such as spoilage, damage, pilferage, or returns. This setting results in incomplete inventory and demand information. An important inventory control problem therefore is to maximize the total expected discounted profit under this setting. Allowing for dependence between demand and invisible demand, we obtain the associated dynamic programming equation with an infinite‐dimensional state space, and reduce it to a simpler form by employing the concept of unnormalized probability. We develop an analytical upper bound on the optimal profit as well as an iterative algorithm for an approximate solution of the problem. We compare profits of the iterative solution and the myopic solution, and then to the upper bound. We see that the iterative solution performs better than the myopic solution, and significantly so in many cases. Furthermore, it gives a profit not far from the upper bound, and is therefore close to optimal. Using our results, we also discuss meeting inventory service levels.     

Multi‐Echelon Inventory Management under Short‐Term Take‐or‐Pay Contracts

We extend the Clark–Scarf serial multi‐echelon inventory model to include procuring production inputs under short‐term take‐or‐pay contracts at one or more stages. In each period, each such stage has the option to order/process at two different cost rates; the cheaper rate applies to units up to the contract quantity selected in the previous period. We prove that in each period and at each such stage, there are three base‐stock levels that characterize an optimal policy, two for the inventory policy and one for the contract quantity selection policy. The optimal cost function is additively separable in its state variables, leading to conquering the curse of dimensionality and the opportunity to manage the supply chain using independently acting managers. We develop conditions under which myopic policies are optimal and illustrate the results using numerical examples. We establish and use a generic one‐period result, which generalizes an important such result in the literature. Extensions to cover variants of take‐or‐pay contracts are included. Limitations are discussed.     

Knowing What Your Customer Wants: Improving Inventory Allocation Decisions in Online Movie Rental Systems

In Online Movie Rental Systems, customer desire to rent can often be observed before the actual consumption occurs. Desire represents uncensored (or true) demand information. Hence, the impact of inventory decisions (numbers of physical copies of different movies) can be accurately traced to the creation of desire (via Word‐of‐mouth), and then to rental. Word‐of‐Mouth (WOM) has been recognized as one of the most influential sources of information transmission, especially for experience goods. Poor inventory decisions may result in lost rentals in two ways: One is the loss of rentals because of low inventory (direct effect), and the other is the loss of the possible demand (rentals) that could have been created through WOM (indirect effect). We use data from an online DVD‐by‐mail firm to estimate the direct and indirect effects of inventory decisions, considering the circular relationship: Rental generates WOM, WOM creates Desire, and Desire turns into Rental. We find that the magnitude of indirect effects is significant, comparable to and sometimes even exceeding direct effects. The value of the empirical findings to facilitate better inventory allocation decisions is examined.     

A hybrid inventory management system responding to regular demand and surge demand

This paper proposes a hybrid policy for a stochastic inventory system facing regular demand and surge demand. The combination of two different demand patterns can be observed in many areas, such as healthcare inventory and humanitarian supply chain management. The surge demand has a lower arrival rate but higher demand volume per arrival. The solution approach proposed in this paper incorporates the level crossing method and mixed integer programming technique to optimize the hybrid inventory policy with both regular orders and emergency orders. The level crossing method is applied to obtain the equilibrium distributions of inventory levels under a given policy. The model is further transformed into a mixed integer program to identify an optimal hybrid policy. A sensitivity analysis is conducted to investigate the impact of parameters on the optimal inventory policy and minimum cost. Numerical results clearly show the benefit of using the proposed hybrid inventory model. The model and solution approach could help healthcare providers or humanitarian logistics providers in managing their emergency supplies in responding to surge demands.     

Updating Inventories of Substitutable Resources in Response to Forecast Updates

We show simple yet optimal results to update the inventory/capacity levels, expected profit, fill rates, and service levels of substitutable resources in response to an updating of the mean demand forecasts for the resources. We find that a change in the mean demand of one resource does not affect the optimal inventory level of any other resource. The results are obtained for demands with location‐scale distribution, and for a revenue structure satisfying a triangle property such that the manager will always use the inventory of a resource to meet her own demand first before using it for substitution. The results for updating the performance measures also extend to managers who maintain non‐optimal inventory/capacity levels. Implications for procurement, sales and operational planning, and multi‐store operations are discussed.     

A Capacitated Multi‐echelon Inventory Placement Model under Lead Time Constraints

We develop an inventory placement model in the context of general multi‐echelon supply chains where the delivery lead time promised to the customer must be respected. The delivery lead time is calculated based on the available stocks of the different input and output products in the different facilities and takes into account the purchasing lead times, the manufacturing lead times, and the transportation lead times. We assume finite manufacturing capacities and consider the interactions of manufacturing orders between time periods. Each facility manages the stocks of its input and output products. The size of customer orders and their arrival dates and due dates are assumed to be known as in many B2B situations. We perform extensive computational experiments to derive managerial insights. We also derive analytical insights regarding the manufacturing capacities to be installed and the impacts of the frequency of orders on the system cost.     

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

We consider a periodic‐review inventory system with regular and expedited supply modes. The expedited supply is faster than the regular supply but incurs a higher cost. Demand for the product in each period is random and sensitive to its selling price. The firm determines its order quantity from each supply in each period as well as its selling price to maximize the expected total discounted profit over a finite or an infinite planning horizon. We show that, in each period if it is optimal to order from both supplies, the optimal inventory policy is determined by two state‐independent thresholds, one for each supply mode, and a list price is set for the product; if only the regular supply is used, the optimal policy is a state‐dependent base‐stock policy, that is, the optimal base‐stock level depends on the starting inventory level, and the optimal selling price is a markdown price that decreases with the starting inventory level. We further study the operational impact of such supply diversification and show that it increases the firm's expected profit, reduces the optimal safety‐stock levels, and lowers the optimal selling price. Thus that diversification is beneficial to both the firm and its customers. Building upon these results, we conduct a numerical study to assess and compare the respective benefit of dynamic pricing and supply diversification.