Inventory consideration and management in two supply chain problems

Ph.DDOCTOR OF PHILOSOPH

An Optimization of (

Addressing the problems of a health care center which produces tailor-made clothes for specific people, the paper proposes a single product continuous review model and establishes an optimal policy for the center based on (Q,r) control policy to minimize expected average cost on an order cycle. A generic mathematical model to compute cost on real-time inventory level is developed to generate optimal order quantity under stochastic stock variation. The customer demands are described as compound Poisson process. Comparisons on cost between optimization method and experience-based decision on Q are made through numerical studies conducted for the inventory system of the center

Lost sales inventory models with batch ordering and handling costs

In this paper, we integrate inventory and handling into a single model for analysis and optimization of inventory replenishment decisions for a grocery retail store. We consider a retailer who periodically manages his inventory of a single item facing stochastic demand. The retailer may only order in multiples of a xed batch size, the lead time is less than the review period length and all unmet demand is lost, which is a realistic situation for a large part of the assortment of grocery retailers. The replenishment cost includes both xed and variable components, dependent on the number of batches and units in the order. This structure captures the shelf-stacking costs in retail stores. We investigate the optimal policy structure under the long-run average cost criterion. Our results show that it is worthwhile to explicitly take handling costs into account when making inventory decisions. We use parameter values typical for rocery retail environments. For an important subset of the retail assortment, we show that signicant cost reductions exist by explicitly considering handling in the inventory policy. Keywords: Retail inventory control, Handling, Lost sales, Periodic review, Fixed batch size

Convexity Properties and Comparative Statics for M/M/S Queues with Balking and Reneging

We use sample path arguments to derive convexity properties of an M/M/S queue with impatient customers that balk and renege. First, assuming that the balking probability and reneging rate are increasing and concave in the total number of customers in the system (head-count), we prove that the expected head-count is convex decreasing in the capacity (service rate). Second, with linear reneging and balking, we show that the expected lost sales rate is convex decreasing in the capacity. Finally, we employ a sample-path sub-modularity approach to comparative statics. That is, we employ sample path arguments to show how the optimal capacity changes as we vary the parameters of customer demand and impatience. We find that the optimal capacity increases in the demand rate and decreases with the balking probability, but is not monotone in the reneging rate. This means, surprisingly, that failure to account for customersâ reneging may result in over-investment in capacity. Finally, we show that a seemingly minor change in system structure, customer commitment during service, produces qualitatively different convexity properties and comparative statics.Operations Management Working Papers Serie

Collaborative Policy of the Supply-Hub for Assemble-to-Order Systems with Delivery Uncertainty

This paper considers the collaborative mechanisms of the Supply-Hub in the Assemble-to-Order system (ATO system hereafter) with upstream delivery uncertainty. We first propose a collaborative replenishment mechanism in the ATO system, and construct a replenishment model with delivery uncertainty in use of the Supply-Hub. After transforming the original model into a one-dimensional optimization problem, we derive the optimal assembly quantity and reorder point of each component. In order to enable the Supply-Hub to conduct collaborative replenishment with each supplier, the punishment and reward mechanisms are proposed. The numerical analysis illustrates that service level of the Supply-Hub is an increasing function of both punishment and reward factors. Therefore, by adjusting the two factors, suppliers’ incentives of collaborative replenishment can be significantly enhanced, and then the service level of whole ATO system can be improved

Convexity Properties and Comparative Statics for M/M/S Queues with Balking and Reneging

We use sample path arguments to derive convexity properties of an M/M/S queue with impatient customers that balk and renege. First, assuming that the balking probability and reneging rate are increasing and concave in the total number of customers in the system (head-count), we prove that the expected head-count is convex decreasing in the capacity (service rate). Second, with linear reneging and balking, we show that the expected lost sales rate is convex decreasing in the capacity. Finally, we employ a sample-path sub-modularity approach to comparative statics. That is, we employ sample path arguments to show how the optimal capacity changes as we vary the parameters of customer demand and impatience. We find that the optimal capacity increases in the demand rate and decreases with the balking probability, but is not monotone in the reneging rate. This means, surprisingly, that failure to account for customersâ reneging may result in over-investment in capacity. Finally, we show that a seemingly minor change in system structure, customer commitment during service, produces qualitatively different convexity properties and comparative statics.Operations Management Working Papers Serie