SUFFICIENT CONDITIONS FOR A GEOMETRIC TAIL IN A QBD PROCESS WITH MANY COUNTABLE LEVELS AND PHASES

Abstract

In this paper, we present sufficient conditions, under which the stationary probability vector of a QBD process with both infinite levels and phases decays geometrically, characterized by the convergence norm η and the 1/η-left-invariant vector x of the rate matrix R. We also present a method to compute η and x based on spectral properties of the censored matrix of a matrix function constructed with the repeating blocks of the transition matrix of the QBD process. What makes this method attractive is its simplicity; finding η reduces to determining the zeros of a polynomial. We demonstrate the application of our method through a few interesting examples.     

Economic Production Lot Sizing with Periodic Costs and Overtime*

Traditional approaches for modeling economic production lot‐sizing problems assume that a single, fixed equipment setup cost is incurred each time a product is run, regardless of the quantity manufactured. This permits multiple days of production from one production setup. In this paper, we extend the model to consider additional fixed charges, such as cleanup or inspection costs, that are associated with each time period's production. This manufacturing cost structure is common in the food, chemical, and pharmaceutical industries, where process equipment must be sanitized between item changeovers and at the end of each day's production. We propose two mathematical problem formulations and optimization algorithms. The models' unique features include regular time production constraints, a fixed charge for each time period's production, and the availability of overtime production capacity. Experimental results indicate the conditions under which our algorithms' performance is superior to traditional approaches. We also test the procedures on a set of lot‐sizing problems facing a national food processor and document their potential economic benefit.     

Flow Coordination and Information Sharing in Supply Chains: Review,Implications, and Directions for Future Research

Advances in information technology, particularly in the e‐business arena, are enabling firms to rethink their supply chain strategies and explore new avenues for inter‐organizational cooperation. However, an incomplete understanding of the value of information sharing and physical flow coordination hinder these efforts. This research attempts to help fill these gaps by surveying prior research in the area, categorized in terms of information sharing and flow coordination. We conclude by highlighting gaps in the current body of knowledge and identifying promising areas for future research.     

Information-Processing Alternatives for Coping with Manufacturing Environment Complexity

Investment in information systems and technology is often justified as a necessary strategy for coping with the increased complexity and information needs of today/s manufacturing environments. However, the world class manufacturing paradigm suggests that increased complexity is not always necessary to meet the needs of markets and customers. Galbraith/s (1973, 1977) seminal information-processing model is applied to a manufacturing environment, supported by the world class manufacturing paradigm, to test the role of various information-processing alternatives for coping with increased environmental complexity. Moderated regression and multiple discriminant analysis are used to test hypotheses in a sample of 164 manufacturing plants. Environmental complexity was found to be related to manufacturing performance for each of the five dependent variables. This relationship was moderated by at least one information-processing alternative for each dependent variable, including self-contained tasks, lateral relations, and environmental management strategies for reducing manufacturing, supplier, and goal diversity. Investments in information systems and reduction of labor and customer diversity did not moderate this relationship. Practices that were found to be particularly effective in moderating this relationship included the use of multifunctional employees, communication of manufacturing strategy, coordination of decision making, product design simplicity, reduction of parts counts, supervisory interaction facilitation, recruiting and selection for flexible employees, JIT practices, blanket purchase orders, and strong customer relationships.     

Optimal Policy for a Reseller When the Supplier Offers a Temporary Reduction in Price*

A common practice in product distribution is the case in which the supplier offers a temporary reduction in price. It is suggested in the literature that in such situations, the reseller may engage in forward buying (i.e., purchasing additional stock at the reduced price offered by the supplier for later sale at the regular selling price). In this paper, a model is formulated of the reseller's response when the supplier offers a temporary reduction in price. It is assumed that the market demand for the product is elastic with respect to the selling price the reseller sets. A procedure for determining the optimal response of the reseller is developed. The model presented in this paper can easily be adapted to the case in which the reseller faces a permanent increase in the price charged by the supplier.     

The deterministic EPQ with partial backordering: A new approach

Several authors have developed models for the EOQ when only a percentage of stockouts will be backordered. Most of these models are complicated, with equations unlike those for the EOQ with full backordering. In this paper we extend work by Pentico and Drake [The deterministic EOQ with partial backordering: a new approach. European Journal of Operational Research 2008; in press] that developed equations for the EOQ with partial backordering that are more like those for the EOQ with full backordering to develop a comparable model for the EPQ with partial backordering.     

Inventory management with variable lead-time dependent procurement cost

A reduction in the inventory replenishment lead-time allows reducing safety stock requirements and improving customer service. However, it might be accompanied by increased procurement costs because of premium charges imposed by suppliers, or higher transportation costs. This paper studies a single-stage variable lead-time inventory system with lead-time dependent procurement cost. Selection of the lead-time value represents finding the trade-off between benefits of lead-time reduction and increase in the procurement cost. A model for joint optimization of inventory and procurement costs is developed. Numerical studies are conducted to identify conditions under which lead-time reduction is favorable compared to procuring at the lowest cost.     

Stockouts and Restocking: Monitoring the Retailer from the Supplier’s Perspective

Suppliers and retailers typically do not have identical incentives to avoid stockouts (lost sales due to the lack of product availability on the shelf). Thus, the supplier needs to monitor the retailer’s restocking efforts with the available data. We empirically assess stockout levels using only shipment and sales data that is readily available to the supplier. The model distinguishes between store stockouts (zero inventory in the store) and shelf stockouts (an empty shelf but some inventory in other parts of the store), thereby identifying the cause of the stockout to be either a supply chain or a restocking issue. We find that, as suspected by the supplier, the average stockout rate is much higher than published averages. In addition, stockout rates vary widely between stores. Moreover, almost all stockouts are shelf stockouts. The model identifies stores that may have restocking issues.     

A note on the random yield from the perspective of the supply chain

Keren [The single-period inventory problem: extension to random yield from the perspective of the supply chain. Omega 2009;37:801-10] considers a supply chain in which the distributor faces a known demand and orders from the producer subject to a random production yield, and shows that the distributor may find it optimal to order more than what is needed due to supply uncertainty under a uniform distribution. However, Keren (2009) does not address the questions whether it is always optimal for the distributor to order more, or when to order more. In this note, we point out that ordering more is not always an optimal strategy and specify the condition under which this strategy becomes optimal. We also examine the profit losses of the supply chain members resulting from the random yield supply, which is another question not considered in Keren (2009). The producer is found to possibly benefit from this production yield uncertainty, although the performances of the distributor and of the entire supply chain are always undermined. Our results are obtained under a more generalized yield distribution, and can thus be applied to wider industrial domains.