Uniform fractional part: a simple fast method for generating continuous random variates

A known theorem in probability is adopted and through a probabilistic approach, it is generalized to develop a method for generating random deviates from the distribution of any continuous random variable. This method, which may be considered as an approximate version of the Inverse Transform algorithm, takes two random numbers to generate a random deviate, while maintaining all the other advantages of the Inverse Transform method, such as the possibility of generating ordered as well as correlated deviates and being applicable to all density functions, regardless of their parameter value

Service Rate Control in Mn/Gn/1 Queue

Part 5: Smart Production for Mass CustomizationInternational audienceService rate control in queues is an important problem in practice. For example, when the number of customers waiting for finished products is small production has a normal speed, but if it is greater, the production speed should be faster to meet the demand. For an exponential service time distribution, the optimality of the threshold type policy has been proved in literature. On the other hand, in production systems, production time follows a general distribution in general. In this paper, service control of speed depending on the number of customers is discussed. The analytical results of an M/G/1 queue with arrival and service rates depending on the number of customers in the system, which is called an Mn/Gn/1 queue, are utilized for computing performance measure of service rate control. Constant, uniform and exponential distributions on the service time are considered through numerical experiments. The results show that the optimal threshold depends on the type of the distributions even when the mean of service time is the same

Competitive analysis of online inventory problem with interrelated prices

This is a pre-print of an article published in Applied Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11766-017-3360-4This paper investigates the online inventory problem with interrelated prices in which a decision of when and how much to replenish must be made in an online fashion even without concrete knowledge of future prices. Four new online models with different price correlations are proposed in this paper, which are the linear-decrease model, the log-decrease model, the logarithmic model and the exponential model. For the first two models, the online algorithms are developed, and as the performance measure of online algorithm, the upper and lower bounds of competitive ratios of the algorithms are derived respectively. For the exponential and logarithmic models, the online algorithms are proposed by the solution of linear programming and the corresponding competitive ratios are analyzed, respectively. Additionally, the algorithm designed for the exponential model is optimal, and the algorithm for the logarithmic model is optimal only under some certain conditions. Moreover, some numerical examples illustrate that the algorithms based on the dprice-conservative strategy are more suitable when the purchase price fluctuates relatively flat

Multilevel rationing policy for spare parts when demand is state dependent

The multilevel rationing (MR) policy is the optimal inventory control policy for single-item M / M / 1 make-to-stock queues serving different priority classes when demand rate is constant and backlogging is allowed. Make-to-repair queues serving different fleets differ from make-to-stock queues because in the setting of the former, each fleet comprises finitely many machines. This renders the characterization of the optimal control policy of the spare part inventory system difficult. In this paper, we implement the MR policy for such a repair shop/spare part inventory system. The state-dependent arrival rates of broken components at the repair shop necessitate a different queueing-based solution for applying the MR policy from that used for make-to-stock queues. We find the optimal control parameters and the cost of the MR policy; we, then compare its performance to that of the hybrid FCFS and hybrid priority policies described in the literature. We find that the MR policy performs close to the optimal policy and outperforms the hybrid policies