Studying the Effects of the Skewness of Inter-Arrival and Service Times on the Probability Distribution of Waiting Times

Previous studies have shown that the mean queue length of a GI/G/1 system is significantly influenced by the skewness of inter-arrival times, but not by the skewness of service times. These results are limited because all the distributions considered in previous studies were positively skewed. To address this limitation, this paper investigates the effects of the skewness of inter-arrival and service times on the probability distribution of waiting times, when a negatively skewed distribution is used to model inter-arrival and service times. Subsequent to a series of experiments on a GI/G/1 queue using discrete-event simulation, results have shown that the lowest mean waiting time and the lowest variance of waiting times can be attained with a combination of positive inter-arrival skewness and negative service skewness. Results also show an interesting effect of the skewness of service times in the probability of no-delay in environments with a higher utilization factor

Studying the effects of skewness of inter-arrival and service times on the probability distribution of waiting times

Previous studies have shown that the mean queue length of a GI/G/1 system is significantly influenced by the skewness of inter-arrival times, but not by the skewness of service times. These results are limited because all the distributions considered in previous studies were positively skewed. To address this limitation, this paper investigates the effects of the skewness of inter-arrival and service times on the probability distribution of waiting times, when a negatively skewed distribution is used to model inter-arrival and service times. Subsequent to a series of experiments on a GI/G/1 queue using discrete-event simulation, results have shown that the lowest mean waiting time and the lowest variance of waiting times can be attained with a combination of positive inter-arrival skewness and negative service skewness. Results also show an interesting effect of the skewness of service times in the probability of no-delay in environments with a higher utilization factor

Inventory Control for Remanufacturing with Batch Processing, Seed Stock Planning, and Coordination Considerations

In recent years, the general area of remanufacturing has received significant attention both in academia and practice. While there is a growing body of literature in production planning models for remanufacturing, there is still a need for analytical decision-making tools considering general cost/revenue structures, stochastic demands, stochastic returns, and multiple agents/decision makers. Of particular interest in this dissertation are inventory control models with batch processing, seed stock planning, and coordination considerations for efficient inventory control practices. More specifically we investigate three distinct, yet related, inventory control problems: (1) a fundamental inventory and production planning problem arising in a batch processing environment for a third party remanufacturer, which is characterized by a stochastic used-item return process along with a stochastic remanufactured item demand process; (2) a seed stock planning problem in a batch processing environment with two agents including an original equipment manufacturer (OEM) and a remanufacturing supplier (RS), for which three game-theoretic scenarios and two types of controls are investigated; (3) a channel coordination problem in the reverse supply chain, which generalizes the above two problems in the sense that the stochastic nature of returns is modeled in a batch processing environment for channel coordination purposes. Our analytical decision-making models contribute to the existing literature in the following ways: (1) we investigate the impact of more general cost structures (including both fixed operational costs and inventory-related costs) and disposal options in a batch processing environment with stochastic demand and return; (2) we systematically study seed stock planning issues in a batch processing environment for remanufacturing using the game-theoretic framework; and (3) we build an analytical framework for channel coordination mechanism design for the reverse supply chain in a stochastic environment