Walid W. Nasr

Transshipment and safety stock under stochastic supply interruption in a production system

We consider a two-echelon system with one source supplying two locations with the same product. The random occurrence of interruptions at the source where downtime is also stochastic can result in stockouts at the two receiving locations. Our model studies the benefit of allowing each location to carry a safety stock where holding costs can be different at each location. The objective is to reduce overall cost at both locations. In some cases it is optimal to allow for a transshipment of inventory from the safety stock of one location to the other. We jointly solve for the optimal safety stock at each location and the optimal amount to be transshipped from a location to the other. We show that by conditioning on the transshipment direction the total cost becomes convex as a function of the safety stock levels at the receiving locations and the amount to be transshipped from a location to the other. Numerical examples are presented for different system cost parameters and probability distributions.

Continuous (s, S) policy with MMPP correlated demand

This work considers a continuous inventory replenishment system where demand is stochastic and dependent on the state of the environment. A Markov Modulated Poisson Process (MMPP) is utilized to model the demand process where the corresponding embedded Markov Chain represents the state of the environment. The equations to calculate the system inventory measures and the number of orders per unit time are obtained for a continuous, infinite horizon and dynamically changing (s, S) policy. An efficient optimization heuristic is presented and compared to the commonly used approach of approximating the demand-count process over the lead time with a Normal distribution. An investigation of the MMPP demand process is considered where we quantify the impact of variability in the demand-count process which is due to auto-correlation. Our findings indicate that when demand correlation is high, a dynamic control, where the (s, S) policy changes with state of the environment governing the MMPP, is highly superior to the commonly used “static” heuristics. We propose two dynamic policies of varying computational complexity, and cost efficiency, depending on the class of the product (one for class A, and one for classes B and C), to handle such high-correlation situations.

Fitting the Pht/Mt/s/c Time-Dependent Departure Process for Use in Tandem Queueing Networks

This paper considers time-dependent Pht/Mt/s/c queueing nodes and small tandem networks of such nodes. We examine characteristics of the departure processes from a multiserver queueing node; in particular, we focus on solving for the first two time-dependent moments of the departure-count process. A finite set of partial moment differential equations is developed to numerically solve for the departure-count moments over specified intervals of time [ti, ti + τi). We also present a distribution fitting algorithm to match these key characteristics with a

Economic production quantity with maintenance interruptions under random and correlated yields

\widetilde{Ph_t}

A multi-station system for reducing congestion in high-variability queues

process serving as the approximate departure process. A distribution fitting algorithm is presented for time-dependent point processes where a two-level balanced mixture of Erlang distribution is used to serve as the approximating process. We then use the

Integrating the economic production model with deteriorating raw material over multi-production cycles

\widetilde{Ph_t}

Continuous inventory control with stochastic and non-stationary Markovian demand

approximating departure process as the approximate composite arrival process to downstream nodes in a network of tandem queues.

MAP fitting by count and inter-arrival moment matching

Abstract This paper considers an economic production quantity with imperfect items where the quality of items produced within the same production run is correlated. Production and scheduled maintenance policies for a correlated binomial production system are investigated. We study the impact of correlation on the system performance measures and draw insights in terms of the effect of correlation on the production and maintenance policies. We also illustrate that the popular and commonly used interrupted geometric production systems can be analysed by an equivalent correlated binomial production model.

Effect of deterioration on the instantaneous replenishment model with imperfect quality items

We consider the problem of allocating processing times in a multi-station series system characterized by high variability. Servers are arranged into multiple stations in series with the objective of minimizing the waiting time through a truncation scheme. Every station has a threshold on the amount of time spent servicing a job. A job being served at Station i that has a processing time exceeding this station’s threshold is forwarded to Station i+1. Otherwise, the job completes its service at Station i and leaves the system. We develop an analytical model to determine the optimal system configuration, in terms of the number of stations, the corresponding thresholds, and the number of servers at each station, for a given number of servers facing Poisson demand. In order to simplify the computation of the thresholds, we assume that the load is balanced among different stations. We justify this assumption with numerical and analytical evidence. Our analytical and numerical results indicate that, under high traffic intensity, our series system performs better than the standard M/G/c and other variants having two stations only, when the shape of the service time distribution allows reducing variability by multiple truncations. Our results also indicate that having a moderate number of stations is beneficial as this offers a good trade-off between variance reduction and idle time downstream. Two by-products of our work are (i) comparing the accuracy of several M/G/c waiting time approximations via simulation, with service times following a family of balanced hyperexponential distributions, and (ii) testing the appropriate M/G/c simulation length. We find that approximations by Whitt (1989, 1993) to be adequate.

An instantaneous replenishment model under the effect of a sampling policy for defective items

This paper considers an Economic Production Quantity (EPQ) model with deteriorating raw material and investigates the impact of deterioration on the production process. The EPQ base case with no deterioration is presented where raw material is ordered for multiple production cycles. We present the differential equations to calculate the on-hand inventory of raw material and present closed-forms expressions for the required order of raw material to result in a desired amount of effective raw material per order cycle. Closed-form expression for the total profit per unit time is obtained and we solve for the optimal production quantity of finished product per production cycle and the order quantity of raw material. We present numerical examples where we compare our model to a system which ignores the impact of deterioration and results in shorter production cycles due to an insufficient amount of effective raw material.