21 research outputs found
Analysis of a stochastic lot scheduling problem with strict due-dates
No full textThis chapter considers admission control and scheduling rules for a single machine production environment. Orders arrive at a single machine and can be grouped into several product families. Each order has a family dependent due-date, production duration, and reward. When an order cannot be served before its due-date it has to be rejected. Moreover, when the machine changes the production of one type of family to another family, a setup time is incurred. The problem is to find long-run average optimal policies that accept or reject orders and schedule the accepted orders. To obtain insight into the optimal performance of the system we model it as a Markov decision process (MDP). This formal description leads to, at least, three tangible goals. First, for small scale problems the optimal admission and scheduling policy can be obtained with, e.g., policy iteration. Second, simple heuristic policies can be formulated in terms of the concepts developed for the MDP, i.e., the states, actions and (action-dependent) transition matrices. Finally, the simulator required to study the performance of heuristic policies for large scale problems can be directly implemented as an MDP. Thus, the formal description of the system in terms of an MDP has considerable off-spin beyond the mere numerical aspects of solving the MDP for small-scale systems
Optimal Control of Production-Inventory Systems with Constant and Compound Poisson Demand
Get PDFIn this paper, we study a production-inventory systems with finite production capacity and fixed setup costs. The demand process is modeled as a mixture of a compound Poisson process and a constant demand rate. For the backlog model we establish conditions on the holding and backlogging costs such that the average-cost optimal policy is of (s, S)-type. The method of proof is based on the reduction of the production-inventory problem to an appropriate optimal stopping problem and the analysis of the associated free-boundary problem. We show that our approach can also be applied to lost-sales models and that inventory models with un onstrained order capacity can be obtained as a limiting case of our model. This allows us to analyze a large class of single-item inventory models, including many of the classical cases, and compute in a numerical efficient way optimal policies for these models, whether these optimal policies are of (s, S)-type or not.
Corrigendum to “Representations for the extreme zeros of orthogonal polynomials” [J. Comput. Appl. Math. 233 (2009) 847–851]
Get PDFWe correct representations for the endpoints of the true interval of orthogonality of a sequence of orthogonal polynomials that were stated by us in the Journal of Computational and Applied Mathematics 233 (2009) 847–851
Optimal policies for Production-Clearing Systems under Continuous-Review
Get PDFIn this paper, we consider a production-clearing system with compound Poisson demand under continuous review. The production facility produces one type of item without stopping and at a constant rate, and stores the product into a buffer to meet future demand. To prevent high inventory levels, a clearing operation occasionally removes all or part of the inventory from the buffer. We prove that an (m, q)-policy, i.e., a policy that clears the buffer to level m as soon as the inventory hits a level q, minimizes the long run average holding and clearing cost. We also derive a numerically very efficient approach to compute the optimal parameters of the (m, q)-policy for models with backlogging and models with lost sales. With these numerical methods we show that tuning the clearing levels m and q in concert can lead to substantial cost savings
An intuitive approach to inventory control with optimal stopping
Get PDFIn this research note, we show that a simple application of Breiman's work on optimal stopping in 1964 leads to an elementary proof that (s,S) policies minimize the long-run average cost for periodic-review inventory control problems. The method of proof is appealing as it only depends on the fundamental concepts of renewal-reward processes, optimal stopping, dynamic programming, and root-finding. Moreover, it leads to an efficient algorithm to compute the optimal policy parameters. If Breiman's paper would have received the attention it deserved, computational methods dealing with (s,S)-policies would have been found about three decades earlier than the famous algorithm of Zheng and Federgruen (1991).</p
Admission policies for the customized stochastic lot scheduling problem with strict due-dates
Get PDFThis papers considers admission control and scheduling of customer orders in a production system that produces different items on a single machine. Customer orders drive the production and belong to product families, and have family dependent due-date, size, and reward. When production changes from one family to another a setup time is incurred. Moreover, if an order cannot be accepted, it is considered lost upon arrival. The problem is to find a policy that accepts/rejects and schedules orders such that long run profit is maximized. This problem finds its motivation in batch industries in which suppliers have to realize high machine utilization while delivery times should be short and reliable and the production environment is subject to long setup times. We model the joint admission control/scheduling problem as a Markov decision process (MOP) to gain insight into the optimal control of the production system and use the MDP to benchmark the performance of a simple heuristic acceptance/scheduling policy. Numerical results show that the heuristic performs very well compared with the optimal policy for a wide range of parameter settings, including product family asymmetries in arrival rate, order size, and order reward. (C) 2011 Elsevier B.V. All rights reserved
Admission policies for the customized stochastic lot scheduling problem with strict due-dates
No full textThis papers considers admission control and scheduling of customer orders in a production system that produces different items on a single machine. Customer orders drive the production and belong to product families, and have family dependent due-date, size, and reward. When production changes from one family to another a setup time is incurred. Moreover, if an order cannot be accepted, it is considered lost upon arrival. The problem is to find a policy that accepts/rejects and schedules orders such that long run profit is maximized. This problem finds its motivation in batch industries in which suppliers have to realize high machine utilization while delivery times should be short and reliable and the production environment is subject to long setup times. We model the joint admission control/scheduling problem as a Markov decision process (MDP) to gain insight into the optimal control of the production system and use the MDP to benchmark the performance of a simple heuristic acceptance/scheduling policy. Numerical results show that the heuristic performs very well compared with the optimal policy for a wide range of parameter settings, including product family asymmetries in arrival rate, order size, and order reward.Scheduling Order acceptance Make-to-order production Stochastic lot scheduling problem Due-dates
Optimal Control of Production-Inventory Systems with Constant and Compound Poisson Demand
Get PDFIn this paper, we study a production-inventory systems with finite production capacity and fixed setup costs. The demand process is modeled as a mixture of a compound Poisson process and a constant demand rate. For the backlog model we establish conditions on the holding and backlogging costs such that the average-cost optimal policy is of (s, S)-type. The method of proof is based on the reduction of the production-inventory problem to an appropriate optimal stopping problem and the analysis of the associated free-boundary problem. We show that our approach can also be applied to lost-sales models and that inventory models with un onstrained order capacity can be obtained as a limiting case of our model. This allows us to analyze a large class of single-item inventory models, including many of the classical cases, and compute in a numerical efficient way optimal policies for these models, whether these optimal policies are of (s, S)-type or not
Optimal Control of Production-Inventory Systems with Constant and Compound Poisson Demand
Get PDFIn this paper, we study a production-inventory systems with finite production capacity and fixed setup costs. The demand process is modeled as a mixture of a compound Poisson process and a constant demand rate. For the backlog model we establish conditions on the holding and backlogging costs such that the average-cost optimal policy is of (s, S)-type. The method of proof is based on the reduction of the production-inventory problem to an appropriate optimal stopping problem and the analysis of the associated free-boundary problem. We show that our approach can also be applied to lost-sales models and that inventory models with un onstrained order capacity can be obtained as a limiting case of our model. This allows us to analyze a large class of single-item inventory models, including many of the classical cases, and compute in a numerical efficient way optimal policies for these models, whether these optimal policies are of (s, S)-type or not
Optimal Control of Production-Inventory Systems with Constant and Compound Poisson Demand
Get PDFIn this paper, we study a production-inventory systems with finite production capacity and fixed setup costs. The demand process is modeled as a mixture of a compound Poisson process and a constant demand rate. For the backlog model we establish conditions on the holding and backlogging costs such that the average-cost optimal policy is of (s, S)-type. The method of proof is based on the reduction of the production-inventory problem to an appropriate optimal stopping problem and the analysis of the associated free-boundary problem. We show that our approach can also be applied to lost-sales models and that inventory models with un onstrained order capacity can be obtained as a limiting case of our model. This allows us to analyze a large class of single-item inventory models, including many of the classical cases, and compute in a numerical efficient way optimal policies for these models, whether these optimal policies are of (s, S)-type or not
