Due to the fast development of electronic devices and e-commerce, firms nowadays are interested in considering an online selling channel along with the offline one and adopting the model of dual-channel supply chains. Proposing services such as warranty and after-sales service are considered essential for sellers to survive in a globalized competition and to expand their market share. This work seeks to explore the efficiency of decision planning in dual-channel supply chains, considering the pricing, warranty, manufacturing, remanufacturing, collection and repair activities. Therefore, a mathematical formulation is developed in a multi-periodic context in order to jointly optimize the several considered activities existing along the studied supply chain. The developed mathematical model is coded in a solver, several numerical results are examined and the sensitivity analyses aim to study the impact of some key parameters on the pricing, remanufacturing and proposed warranty lengths optimal decisions in both distribution channels.

An optimal integrated maintenance to production under carbon emission constraint is developed for a closed-loop system. The closed-loop system is composed by a principal unit producing a single type of product and a second unit for remanufacturing the returned products. The two units are subject to random failures. An economical production policy and a maintenance strategy under carbon emission constraint are proposed to minimize the total cost of production, emission and maintenance. Taking into account the correlation of the manufacturing unit degradation with its production rates and the given maintenance plan of the remanufacturing unit, we determine the economical production plans of both units as well as the emission carbon quantities and the optimal plan of maintenance for the principal manufacturing unit.

This work presents a new method for the synthesis of Petri net controller using the theory of regions. Control specifications are expressed as the conjunction of generalized mutual exclusion constraints (GMEC). The great advantage of the proposed method is to reduce the resolution difficulty of the theory of regions by introducing a concept of minimal cut in the reachability graph with minimal number of nodes. This new concept leads to minimize the total number of equations in the linear system of the theory of regions to synthesize the Petri net controller. To illustrate the present approach, an application is implemented on the Flexible Manufacturing System (FMS) at the ENIM (National School of Engineering of Metz), in FRANCE.

This paper deals with the production control of a manufacturing/remanufacturing system within a closed loop reverse logistics system with machines subject to random failures and repairs. Three types of inventories are involved in this system. The manufactured and remanufactured products are stored respectively in the manufacturing and remanufacturing inventories. The returned products are collected in the recovery inventory and then remanufactured. The customer demands are constant and known. To describe the system, a stochastic fluid model is adopted and which take into account returned products and remanufacturing products. The objective of this paper is to evaluate the optimal inventory levels of the manufacturing and remanufacturing products that allow minimizing the total cost which is the sum of inventory and lost sales costs. Infinitesimal perturbation analysis is used for optimization of the considered system. The trajectories of the inventories levels are studied and the infinitesimal perturbation analysis estimates are evaluated. These estimates are shown to be unbiased and then they are implemented in an optimization algorithm which determines the optimal inventories levels.

In this paper, a discrete flow model is used to study a manufacturing-remanufacturing system composed by two parallel machines, a serviceable inventory, a recovery inventory and customers who demand a constant quantity of product. The goal of this paper is to evaluate the optimal serviceable inventory level which allows minimizing the sum of inventory and lost sales costs. Perturbation analysis is applied to the discrete flow model to optimize the considered system. The trajectories of the serviceable inventory level are studied and the perturbation analysis estimates are evaluated. The unbiasedness of these estimates is proved and then they are implemented in an optimization algorithm which determines the optimal serviceable inventory in the presence of returned products.

This article discusses the issue of spare part return in a production system with a single machine subject to a monotone and stochastic deterioration. It investigates the problem of the spare parts returns and the reusing problem of recovered part, with or without remanufacturing actions. Each recovered spare part is stocked, before being inspected and probably reused. We propose an order/remanufacturing replacement policy with an inventory management of the recovered spare parts. A condition-based maintenance policy is adopted with three decision thresholds for order management, preventive maintenance management and corrective maintenance. A genetic algorithm based approach is proposed and an illustrative example is presented to reveal the application of the proposed policy.

In this paper, a multi-period, multi-product single randomly failing and repairable machine under a combined approach of maintenance management and production control is studied. The production unit aims to satisfy the deterministic market demands with variable production rates for non-homogeneous delivery periodicities without postponement or backlog. We consider production cost depends on the using rate of machine. Also, we consider a production rate dependent failure rate. The aim of this study is to determine the optimal production rate and the production period duration for each product order those minimizing the expected total cost, including holding, shortage, production, setup and maintenance costs. We propose a mathematical model and we develop a genetic algorithm based optimization procedure. We discuss and conduct computational experiments to study the managerial insights for the developed strategy.

In this paper, a manufacturing/ remanufacturing system composed by two parallel machines, a manufacturing buffer, a recovery buffer and a customer who demands a constant quantity of product. To describe the system, a stochastic fluid model is adopted and which take into account returned products and remanufacturing products. The objective of this paper is to evaluate the optimal manufacturing buffer. This optimal level allows minimizing the total cost which is the sum of inventory and lost sales costs. Infinitesimal perturbation analysis is used for optimization of the manufacturing/ remanufacturing system. The trajectories of the buffer level are studied and the infinitesimal perturbation analysis estimates are evaluated. These estimates are shown to be unbiased and then they are implemented in an optimization algorithm which determines the optimal buffers levels in the presence of returned products and remanufacturing products.

In this paper we propose a new heuristic based approach to determine the optimal non-periodic inspection plan on a finite time horizon for a condition-based maintenance. The considered system consists of a single machine subject to a continuous, monotonous and stochastic degradation which can lead to failure and consequently to a maintenance action. The maintenance actions consist of replacing the main part of the production unit by another spare part. Spare parts are classified by their degradation into several qualities: New spare parts, which are provided by external supplier with a fixed delivery time. Used spare parts which are collected and provided by the maintenance service with fixed remanufacturing time, Depending on decision thresholds, the replacement might be either preventive or corrective. The objective is to determine the order/remanufacturing decision threshold (from which an order/remanufacturing is to be launched) and the preventive maintenance decision threshold to perform the preventive replacement. Our approach aims to minimize the total cost due to replacement, storage, inspection, order/remanufacturing costs and downtime penalty. A simulation-based genetic algorithm is proposed. At the end numerical examples are given to observe the performance of the proposed heuristic.

In this paper, we consider a manufacturer company composed of a single randomly failing and repairable machine that produces a single product. It should satisfy the global market demands in exogenous delivery periodicities where postponement or backlogging of shortage quantities are allowed and generate a penalty cost. This manufacturer is in relationship with n independent contractors. We consider outsourcing costs depend on the rate of non-conforming product, also the production rate dependent failure rate. The aim of this research is to determine the appropriate contractors and the associated quantity for each order which maximize the expected total profit for the manufacturer company. We propose a mathematical model and we develop a genetic algorithm based optimization procedure to solve the proposed model. We discuss and conduct computational experiments to study the managerial insights for the developed strategy.

In this paper, a manufacturing system composed by a single-product machine, a manufacturing stock, a purchase warehouse and a constant demand is considered. A stochastic fluid model is adopted to describe the system and to take into account delivery times. The goal of this paper is to evaluate the two optimal inventory levels: that of the manufacturing stock and that of the warehouse. Those optimal levels allow minimizing the total cost which is the sum of inventory, transportation and backlog costs. Infinitesimal perturbation analysis is used for optimisation of the failure-prone manufacturing system. The trajectories of the inventory levels are studied and the infinitesimal perturbation analysis estimates are evaluated. These estimates are shown to be unbiased and then they are implemented in an optimisation algorithm which determines the optimal inventory levels in the presence of constant delivery time.

In this paper, we consider a repairable production unit subject to random failures, which supplies input to a direct (main) customer. The production unit is submitted to a preventive maintenance action at instants kT (k=1,2,...). The corrective and preventive maintenance actions have random durations. In order to maximize the use of production capacity of the unit, it was decided to allocate it to perform periodic tasks of subcontracting for a contractor. A buffer stock is built up in order to guarantee a continuous supply of customer demand at a constant rate during repair and preventive maintenance actions, and subcontracting periods. We determine analytically the optimal instant to begin subcontracting which minimize the total average cost per time unit.

In this article we treat the problem of the delay of subcontracting and its impact on a system controlled by a policy joining the production and maintenance management. We will study a system made up of a machine M which can break down in a random way, and on which we carry out actions of corrective maintenance of random durations. Indeed, each interval T the machine is subject of actions of preventive maintenance. The system is provider of subcontracting services defined as periodic tasks in each cycle T, during which the machine is allocated to produce for a third party. Our objective is to study analytically this system, and determine the expression of the overcost generated by a delay of subcontracting.

This paper addresses the forbidden state problem of Petri nets (PN) with liveness requirement and uncontrollable transitions. The proposed approach computes a maximally permissive PN controller, whenever such a controller exists. The first step, based on a Ramadge-Wonham-like reasoning (1989), determines the legal and live maximal behavior the controlled PN should have. In the second step, the theory of regions is used to design control places to add to the original model to realize the desired behavior. Furthermore, necessary and sufficient conditions for the existence of control places realizing the maximum permissive control are given. A parameterized manufacturing application of significant state space is used to show the efficiency of the proposed approach.

Forbidden state problem of Petri nets with non-blocking requirement and uncontrollable transitions is addressed in this paper. The approach proposed in this paper combines the Ramadge-Wonham's (1989) approach and the theory of regions, a theory recently proposed for compiling a labelled automaton into a Petri net. It first determines the automaton model of the closed loop system using a Ramadge-Wonham-like approach. It then uses the theory of regions to design a set of control places to add to the initial Petri net to realize the maximum permissive and non-blocking control. Although the proposed approach does not avoid the state explosion problem in its design phase, it does provide a compact representation of the optimum control in terms of control places and hence can be very useful in the implementation of optimum control.

The job shop scheduling problem (JSP) deals with the sequencing operations of a set of jobs on a set of machines with minimum cost. The flexible job shop scheduling problem (FJSP) is a generalization of the JSP, which is concerned with both the assignment of machines to operations and the sequencing of the operations on the assigned machines. The paper first presents an extension of the geometric approach for solving a two-job shop problem, when there is one flexible job and the second job is a job shop job. Based on this extension and the notion of the combined job, an integrated greedy heuristic that simultaneously deals with the assignment and the sequencing subproblems is developed to solve the general case with more than two jobs. The results obtained by the greedy heuristic on existing benchmarks from the literature are promising.

This paper addresses the scheduling and deadlock avoidance of a class of automated manufacturing systems. In such systems, a set of jobs is to be performed on a set of resources and each job requires several operations. An operation may require several types of resources with several units of each type. Further, upon the completion of an operation, its related resources cannot be released until resources needed for the next operation become available. One important characteristic of such systems is the possibility of deadlock. The scheduling problem deals with the allocation of resources such that jobs are completed within a minimal makespan and deadlocks are avoided. We extend the classical geometric approach to solve the two-job case of our model. A greedy algorithm based on this result and the taboo search heuristic are then developed for the general case. Numerical results show that the proposed algorithm is fast and provides good schedules.