Pressed by market globalization and concomitant competition, more and more manufacturers are relying on their suppliers to provide raw materials and component parts so as to focus on their core competence. As a result, the coordination of activities across a network of suppliers becomes critical to quickly respond to dynamic market conditions. In this paper, a novel framework combining mathematical optimization and the contract net protocol is presented for make-to-order supply network coordination. Interactions among organizations are modeled by a set of interorganizational precedence constraints and the objective is to achieve the organizations' individual and shared goals of fast product delivery and low inventory. These interorganizational constraints are relaxed by using a set of interorganizational prices that represent marginal costs per unit time for the violation of such constraints. The overall problem is thus decomposed into organizational subproblems, where individual organizations schedule their activities based on their internal situations and interorganizational prices. Coordination is achieved through an iterative price-updating process carried out in a distributed and asynchronous manner. With prices dynamically updated and schedules adjusted, this approach coordinates activities to fulfill existing commitments while maintaining agility to take on new orders. Numerical testing results show that interorganizational prices converge and prices may change as new orders arrive to reflect the new pressure on deliveries.

In view of today's "time-based competition," scheduling manufacturing operations using the most advanced scheduling tools has become a crucial issue for manufacturers. This can be achieved by using an Internet-based scheduling system. The main considerations in designing such a system are how to provide an effective scheduling tool without major investment, and how to ensure fast and easy access for manufacturers who have diversified computational platforms and settings. This paper presents such an Internet-based scheduling system that meets these considerations. The system is a novel combination of judiciously selected components with several architectural design options, and delivers high quality scheduling solutions in a reasonable computational time via a user friendly and secure Internet environment. The testing results are compared for different implementations of scheduling systems and results for problems of different sizes are provided.

Manufacturing scheduling is an important but difficult task. In order to effectively solve such combinatorial optimization problems, the paper presents a Lagrangian relaxation neural network (LRNN) for separable optimization problems by combining recurrent neural network optimization ideas with Lagrangian relaxation (LR) for constraint handling. The convergence of the network is proved, and a general framework for neural implementation is established, allowing creative variations. When applying the network to job shop scheduling, the separability of problem formulation is fully exploited, and a new neuron-based dynamic programming is developed making innovative use of the subproblem structure. Testing results obtained by software simulation demonstrate that the method is able to provide near-optimal solutions for practical job shop scheduling problems, and the results are superior to what have been reported in the neural network scheduling literature. In fact, the digital implementation of LRNN for job shop scheduling is similar to the traditional LR approaches. The method, however, has the potential to be implemented in hardware with much improved quality and speed.

This paper presents an effective approach for job-shop scheduling considering uncertain arrival times, processing times, due dates, and part priorities. A separable problem formulation that balances modeling accuracy and solution method complexity is presented with the goal to minimize expected part tardiness and earliness cost. This optimization is subject to arrival time and operation precedence constraints, and machine capacity constraints. A solution methodology based on a combined Lagrangian relaxation and stochastic dynamic programming is developed to obtain dual solutions. A good dual solution is then selected by using "ordinal optimization", and the actual schedule is dynamically constructed based on the dual solution and the realization of random events. The computational complexity of the overall algorithm is only slightly higher than the one without considering uncertainties, and a dual cost is proved to be a lower bound to the optimal expected cost for the stochastic formulation considered.