On the first come–first served rule in multi‐echelon inventory control

A two‐echelon distribution inventory system with a central warehouse and a number of retailers is considered. The retailers face stochastic demand and replenish from the warehouse, which, in turn, replenishes from an outside supplier. The system is reviewed continuously and demands that cannot be met directly are backordered. Standard holding and backorder costs are considered. In the literature on multi‐echelon inventory control it is standard to assume that backorders at the warehouse are served according to a first come–first served policy (FCFS). This allocation rule simplifies the analysis but is normally not optimal. It is shown that the FCFS rule can, in the worst case, lead to an asymptotically unbounded relative cost increase as the number of retailers approaches infinity. We also provide a new heuristic that will always give a reduction of the expected costs. A numerical study indicates that the average cost reduction when using the heuristic is about two percent. The suggested heuristic is also compared with two existing heuristics. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A produce‐to‐stock system with advance demand information and secondary customers

We consider a manufacturer (i.e., a capacitated supplier) that produces to stock and has two classes of customers. The primary customer places orders at regular intervals of time for a random quantity, while the secondary customers request a single item at random times. At a predetermined time the manufacturer receives advance demand information regarding the order size of the primary customer. If the manufacturer is not able to fill the primary customer's demand, there is a penalty. On the other hand, serving the secondary customers results in additional profit; however, the manufacturer can refuse to serve the secondary customers in order to reserve inventory for the primary customer. We characterize the manufacturer's optimal production and stock reservation policies that maximize the manufacturer's discounted profit and the average profit per unit time. We show that these policies are threshold‐type policies, and these thresholds are monotone with respect to the primary customer's order size. Using a numerical study we provide insights into how the value of information is affected by the relative demand size of the primary and secondary customers. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Joint pricing,assortment, and inventory decisions for a retailer's product line

Consider a set of product variants that are differentiated by some secondary attributes such as flavor, color, or size. The retailer's problem is to jointly determine the set of variants to include in her product line (“assortment”), together with their prices and inventory levels, so as to maximize her expected profit. We model the consumer choice process using a multinomial logit choice model and consider a newsvendor type inventory setting. We derive the structure of the optimal assortment for some important special cases, including the case of horizontally differentiated items, and propose a dominance relationship for the general case that simplifies the search for an optimal assortment. We also discuss structural properties of the optimal prices. Finally, motivated by our analytical results, we propose a heuristic solution procedure, which is shown to be quite effective through a numerical study. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

On the effectiveness of top‐down strategy for forecasting autoregressive demands

We investigate the relative effectiveness of top‐down versus bottom‐up strategies for forecasting the demand of an item that belongs to a product family. The demand for each item in the family is assumed to follow a first‐order univariate autoregressive process. Under the top‐down strategy, the aggregate demand is forecasted by using the historical data of the family demand. The demand forecast for the items is then derived by proportional allocation of the aggregate forecast. Under the bottom‐up strategy, the demand forecast for each item is directly obtained by using the historical demand data of the particular item. In both strategies, the forecasting technique used is exponential smoothing. We analytically evaluate the condition under which one forecasting strategy is preferred over the other when the lag‐1 autocorrelation of the demand time series for all the items is identical. We show that when the lag‐1 autocorrelation is smaller than or equal to 1/3, the maximum difference in the performance of the two forecasting strategies is only 1%. However, if the lag‐1 autocorrelation of the demand for at least one of the items is greater than 1/3, then the bottom‐up strategy consistently outperforms the top‐down strategy, irrespective of the items' proportion in the family and the coefficient of correlation between the item demands. A simulation study reveals that the analytical findings hold even when the lag‐1 autocorrelation of the demand processes is not identical. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.