ALAIN BENSOUSSAN, University of Texas at Dallas - School of Management
Email: alain.bensoussan@utdallas.edu
METIN CAKANYILDIRIM, University of Texas at Dallas - School of Management
Email: metin@utdallas.edu
QI FENG, University of Texas at Austin - Red McCombs School of Business
Email: Annabelle.Feng@mccombs.utexas.edu
SURESH SETHI, University of Texas at Dallas - School of Management
Email: sethi@utdallas.edu

Under many circumstances, demand observations are often censored due to the lack of tracking lost sales caused by stockouts. To understand the impact of the lost sales information on the ordering decisions, a periodic-review inventory model is formulated in which only the sales information is obtained immediately upon the realization of the demand. This is equivalent to observing the demand when the sales are less than the available stock and to inferring that the demand is higher than the stock when there is a stockout. Subsequently, the lost sales information is obtained after a delay. In the resulting model, an optimal policy, if exists, reveals a very complex structure. By decomposing the derivative of the value function, we demonstrate two different roles of inventory in our model: satisfying the demand and extracting the demand information. We show that the optimal inventory levels under the delayed observation of the lost sales are always higher than those for which the demands are fully observed. Moreover, as illustrated in numerical examples, the optimal policy possesses a counterintuitive behavior with respect to the problem parameters. To understand the key drivers of the optimal decisions, we further compare the costs under different demand observations. Two important observations are made. First, a lower cost is obtained when the realized demand is observed than when the demand is only observed to be higher than the inventory level, and, furthermore, the cost difference represents the value of demand information. Second, while a higher inventory level induces a more accurate demand forecast, the value of exact demand observation is not monotone in the procurement cost. Consequently, the optimal ordering quantity is not always decreasing in the procurement cost.

HAOYA CHEN, affiliation not provided to SSRN
FRANK CHEN, Chinese University of Hong Kong - Department of Systems Engineering & Engineering Management
Email: yhchen@se.cuhk.edu.hk
TSAN-MING CHOI, affiliation not provided to SSRN
Email: tcjason@inet.polyu.edu.hk
SURESH SETHI, University of Texas at Dallas - School of Management
Email: sethi@utdallas.edu

We study a coordination contract for a supplier-retailer channel producing and selling a fashionable product exhibiting a stochastic price-dependent demand. The product's selling season is short, and the supply chain faces great demand uncertainty. We consider a scenario where the supplier reserves production capacity for the retailer in advance, and permits the retailer to place an order not exceeding the reserved capacity after a demand information update during a leadtime. We formulate a two-stage optimization problem in which the supplier decides the amount of capacity reservation in the first stage, and the retailer determines the order quantity and the retail price after observing the demand information in the second stage. We propose a three-parameter risk and profit sharing contract that coordinates the supply chain. The proposed contract is robust which permits any agreed-upon division of the supply chain profit between the channel members.

VISHAL GAUR, Johnson Graduate School of Management, Cornell University
Email: vg77@cornell.edu
NIKOLAY OSADCHIY, New York University - Leonard N. Stern School of Business
Email: nosadchiy@yahoo.com
SRIDHAR SESHADRI, University of Texas at Austin - McCombs School of Business
Email: sseshadr@stern.nyu.edu

The volume of retail sales is commonly understood to be correlated with the state of the economy. This information can potentially be employed in demand forecasting, operations decisions, and risk management. We propose a model in which the total sales of a retailer is a function of sales forecasts generated by equity analysts, the term of the forecast, and the return on an aggregate financial market index over the term of the forecast. We test this model on a panel of 4,698 observations of annual firm-level sales forecasts for 97 retailers over 10 years, each year containing multiple forecasts of varying terms. We show that the correlation coefficient of sales forecast error with the financial market return is significant, and varies across firms depending on the retail segment, the gross margin, and the term of the forecast. Our model provides results on other parameters for forecasting as well, and a method for forecast updating. We show that forecast updates from our model provide new information not contained in the forecast updates by equity analysts, so that a combined forecast leads to improved forecast accuracy. These results have applications in forecast updating, decision postponement, production planning, and risk management.