By committing to long-term supply contracts, buyers seek to lower their purchasing costs, and have products delivered without interruption. When a long-term contract is available, suppliers are less pressured to ®nd new customers, and can aord to charge a price lower than the prevailing spot market price. We examine sourcing decisions of a ®rm in the presence of a capacity reservation contract that this ®rm makes with its long-term supplier in addition to the spot market alternative. This contract entails delivery of any desired portion of a reserved ®xed capacity in exchange for a guaranteed payment by the buyer. We investigate rational actions of the two parties under two dierent types of periodic review inventory control policies used by the buyer: the two-number policy, and the base stock policy. When typical demand probability distributions are considered, inclusion of the spot market source in the buyerÕs procurement plan signi®cantly reduces the capacity commitments from the long-term supplier. Ó

Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by adding constraints associated with in-control and out-of-control average run lengths. The quality related production costs are calculated using Taguchi's quadratic loss function. The optimal values of smoothing constants, sampling interval, sample size, and control chart limits are determined by using a numerical search method. The average run length of the control scheme is computed by using the Markov chain approach. Computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and/or variance increase, and higher values of quality loss coefficient lead to shorter sampling intervals. The sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an EWMA-based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance.

For monitoring the stability of a process, various control charts based on exponentially weighted moving average (EWMA) statistics have been proposed in the literature. We study the economic design of EWMA-based mean and dispersion charts when a linear, quadratic, or exponential loss function is used for computing the costs arising from poor quality. The chart parameters (sample size, sampling interval, control limits and smoothing constant) minimizing the overall cost of the control scheme are determined via computational methods. Using numerical examples, we compare the performances of the EWMA charts with Shewhart over(X, -) and S charts, and investigate the sensitivity of the chart parameters to changes in process parameters and loss functions. Numerical results imply that rather than sample size or control limits, the users need to adjust the sampling interval in response to changes in the cost of poor quality. © 2008 Elsevier Ltd. All rights reserved

a b s t r a c tQuick response systems enable retailers to estimate customer demand more accurately, and improve stocking decisions for perishable products with uncertain demand. Retailers place separate orders for a product at two different times before the selling season. Following the initial order, additional market information is obtained, and the second-order amount is decided based on an improved demand forecast. In some cases, purchase cost associated with the second order is uncertain, and demand for the product during the season depends on the selling price. We present a solution procedure for finding the optimal order quantity and selling price in this setting. We also study the case where any desired portion of the initial order can be cancelled after updating the demand forecast. In the numerical study, the optimal price is observed to be relatively insensitive to changes in demand variability.

a b s t r a c tWe explore an extension of the single-period (newsboy) inventory problem when supply is uncertain. We look into the negotiations between a newsvendor (retailer) and a manufacturer when there is competition from a second supplier. There is a chance that the second supplier will not be able to deliver the product. The retailer can maximize his expected profit by optimally allocating his order between the two suppliers. The retailer's ordering problem is analyzed in conjunction with the manufacturer's related pricing problem. The effects of demand and supply uncertainties on the optimal decisions of the parties are explored using numerical examples. We also explore extension of the retailer's problem to the cases of order cancellation, price-dependent demand, and demand-dependent supply availability.

The reduction of variability in product performance characteristics is an important focus of quality improvement programs. Learning is intrinsically linked to process improvement and can assume two forms: (i) autonomous learning; and (ii) induced learning. The former is experientially-based, while the latter is a result of deliberate managerial action. Our involvement in quality and capacity planning with several major corporations in different industries suggested that it would be instructive to devise a model that would prescribe an optimal combination of autonomous and induced learning over time to maximize process improvement. We thus propose such a model to investigate the optimal quality improvement path for a company given that quality costs depend on both autonomous and induced types of learning experienced on a number of quality characteristics. Several properties of an optimal investment path are developed for this problem. For example, it is shown that decisions maximizing short-term gains may actually lead to suboptimal resource utilization decisions when total costs associated with a longer planning horizon are taken into account. Numerical examples are used to assess the sensitivity of the optimal investment plan with respect to changes in several model parameters.

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