In this paper, we consider the integration of production, inventory and distribution decisions in a supply chain composed of one production facility supplying several retailers located in the same region. The supplier is far from the retailers compared to the distance between retailers. Thus, the traveling cost of each vehicle from the supplier to the region is assumed to be fixed and there is a fixed delivery (service) cost for each visited retailer. The objective is to minimize the sum of the costs at the production facility and at the retailers. The problem is more general than the One-Warehouse Multi-Retailer problem and is a special case of the Production Routing Problem. Five heuristics based on a Genetic Algorithm are proposed to solve the problem. In particular, three of them include the resolution of a Mixed Integer Program as subproblem to generate new individuals in the population. The results show that the heuristics can find optimal solutions for small and medium size instances. On large instances, the gaps obtained by the heuristics in less than 300 s are better than the ones obtained by a standard solver in two hours.

In this paper, we study a two-echelon supply chain network consisting of multi-outsourcers and multi-subcontractors. Each one is composed of a failure-prone production unit that produces a single product to fulfil market demands with variable production rates. Sometimes the manufacturing systems are not able to satisfy demand; in this case, outsourcing option is adopted to improve the limited in-house production capacity. The outsourcing is not justified by the production lack of manufacturing systems, but is also considered for the costs minimization issues. In the considered problem, we assume that the failure rate is dependent on the time and production rate. Preventive maintenance activities can be conducted to mitigate the deterioration effects, and minimal repairs are performed when unplanned failures occurs. We consider that the production cost depends on the rate of the machine utilization. The aim of this research is to propose a joint policy based on a mixed integer programming formulation to balance the trade-off between two-echelon of supply chain. We seek to assist outsourcers to determine the integrated in-house/ outsourcing, and maintenance plans, and the subcontractors to determine the integrated production-maintenance plans so that the benefit of the supply chain is maximized over a finite planning horizon. We develop an improved optimization procedure based on the genetic algorithms, and we discuss and conduct computational experiments to study the managerial insights for the developed framework.

This paper considers a supply chain management problem which integrates production, inventory, and distribution decisions. The supply chain is composed of one supplier production facility and several retailers located in a given geographic region. The supplier is responsible for the production and the replenishment of the inventory of retailers, in a vendor managed inventory (VMI) context. The distance between retailers is negligible compared to the distance between the supplier and the retailers’ region. Thus, for each vehicle, there is a major fixed cost for traveling to the cluster of retailers and a minor fixed cost for visiting each individual retailer. The problem consists of determining quantities to be produced, quantities to be delivered to retailers, vehicles to be used, and retailers to be serviced by each vehicle. This problem is an extension of the one warehouse multi-retailer problem with the consideration of production planning and storage and vehicle capacity limitations in addition to fixed vehicle utilization costs and retailer servicing costs. The objective is to minimize a total cost composed of production, transportation, and inventory holding costs at the supplier and at the retailers. Two mixed integer linear programming formulations are proposed and six families of valid inequalities are added to strengthen these formulations. Two of these families are new and the others are adapted from the literature. The numerical results show that the valid inequalities considerably improve the quality of the formulations. Moreover, the parameters that influence the most computational times are analyzed

Flexible job-shop scheduling problem (FJSP), which is proved to be NP-hard, is an extension of the classical job-shop scheduling problem. In this paper, we propose a new genetic algorithm (NGA) to solve FJSP to minimize makespan. This new algorithm uses a new chromosome representation and adopts different strategies for crossover and mutation. The proposed algorithm is validated on a series of benchmark data sets and tested on data from a drug manufacturing company. Experimental results prove that the NGA is more efficient and competitive than some other existing algorithms.

The single machine scheduling problem has been often regarded as a simplified representation that contains many polynomial solvable cases. However, in real-world applications, the imprecision of data at the level of each job can be critical for the implementation of scheduling strategies. Therefore, the single machine scheduling problem with the weighted discounted sum of completion times is treated in this paper, where we assume that the processing times, weighting coefficients and discount factor are all described using trapezoidal fuzzy numbers. Our aim in this study is to elaborate adequate measures in the context of possibility theory for the assessment of the optimality of a fixed schedule. Two optimization approaches namely genetic algorithm and pattern search are proposed as computational tools for the validation of the obtained properties and results. The proposed approaches are experimented on the benchmark problem instances and a sensitivity analysis with respect to some configuration parameters is conducted. Modeling and resolution frameworks considered in this research offer promise to deal with optimality in the wide class of fuzzy scheduling problems, which is recognized to be a difficult task by both researchers and practitioners.