Lotfi Tadj

Model predictive production planning in a three-stock reverse-logistics system with deteriorating items

A model predictive control approach is applied to a closed-loop supply chain where remanufactured items are as-good-as-old. Three stocks are considered, one for newly produced items, one for returned items, and one for remanufactured items. New and remanufactured items target different market segments, as they are subject to different dynamic demands. Further, new and remanufactured items are subject to different deterioration rates. Returned items that cannot be remanufactured for excessive spoilage are discarded. The goal of the firm is to determine the optimal manufacturing rate, the optimal remanufacturing rate, and the optimal disposal rate, under a quadratic cost structure. Using the Trapezoid formula and Taylor expansion, an optimal solution is obtained explicitly when no constraints are imposed on the state and control variables. A numerical example shows the effect of the constraints on the optimal solution.

Model Predictive Control of a Forecasting Production System with Deteriorating Items

The authors consider in this paper an integrated forecasting production system of the tracking type. The demand rate during a certain period depends on the demand rate of the previous period. Also, the demand rate depends on the inventory level. Items on the shelves are subject to deterioration. Using a model predictive control approach, the authors obtain the optimal production rate, the optimal inventory level, the optimal demand rate, and the optimal objective function value, explicitly in terms of the system parameters. A numerical example is presented.

An Unreliable Server Retrial Queue with Two Phases of Service and General Retrial Times Under Bernoulli Vacation Schedule

Abstract This paper deals with the steady state behavior of an M/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with the FCFS (first come, first served) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability p or serves the next unit, if any, with probability (1 – p). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property. We also provide a reliability analysis of this model, which is one of the chief objectives of the paper. Finally, numerical illustrations show how the performance measures obtained are used to manage the system.

Binomial Schedule for an M/G/1 Type Queueing System with an Unreliable Server under N-Policy

We consider in this paper an M/G/1 type queueing system with the following extensions. First, the server is unreliable and is subject to random breakdowns. Second, the server also implements the well-known -policy. Third, instead of a Bernoulli vacation schedule, the more general notion of binomial schedule with vacations is applied. A cost function with two decision variables is developed. A numerical example shows the effect of the system parameters on the optimal management policy.

Optimal Production Planning Strategy for Deteriorating Items in Terms of Emission Tax, Pollution, and R&D Investment

Firms are faced with the question of what policies to implement to ensure efficient abatement behavior? In this paper, we aim to determine the optimal production rate and the optimal investment rate in pollution abatement technology. The situation is modeled as an optimal control problem with two state variables and two control variables. The optimal trajectories, the optimal control, and the optimal objective function value are obtained explicitly in both cases where the firm adopts either a continuous-review policy or a periodic-review policy. A numerical example is presented.