We show for the general dynamic lot sizing model how minimal forecast horizons may be detected by a slight adaptation of an earlier 0(n log n) or 0(n) forward solution method for the model. A detailed numerical study indicates that minimal forecast horizons tend to be small, that is, include a small number of orders. We describe a new planning approach to ensure stability of the lot sizing deci...

Fixed-horizon planning considers a weighted graph and asks to construct path that maximizes the sum of weights for given time horizon T. However, in many scenarios, is not fixed, but stopping chosen according some distribution such expected If stopping-time known, then ensure robustness, by an adversary as worst-case scenario. A stationary plan every vertex always chooses same outgoing edge. Fo...

We consider an infinite horizon production planning problem with non-stationary, convex production and inventory costs. Backlogging is allowed unlike related previous work and inventory cost is interpreted as backlogging cost when inventory is negative. We create finite horizon truncations of the infinite horizon problem and employ classic results on convex production planning to derive a close...

The use of automatically learned knowledge for a planning domain can significantly improve the performance of a generic planner when solving a problem in this domain. In this work, we focus on the well-known SAT-based approach to planning and investigate two types of learned knowledge that have not been studied in this planning framework before: macro-actions and planning horizon. Macro-actions...

In this paper, we propose to combine imitation and reinforcement learning via the idea of reward shaping using an oracle. We study the effectiveness of the nearoptimal cost-to-go oracle on the planning horizon and demonstrate that the costto-go oracle shortens the learner’s planning horizon as function of its accuracy: a globally optimal oracle can shorten the planning horizon to one, leading t...

SINCE typical mobile robotic vehicles have mobility sensors (such as LADAR or stereo) that can only acquire data up to a few tens of meters, a navigation system has no knowledge about the world beyond this sensing horizon. As a result, path planners that rely only on this knowledge to compute paths are unable to anticipate obstacles sufficiently early and has no choice than to plan inefficient ...

A model predictive control (MPC) strategy is developed to determine the optimal solution of the short-term refinery production planning problem. The main objective of the proposed algorithm is to maximize the total profit and to minimize the costs regarding the refinery process over a planning horizon. The refinery planning problem is solved in discrete time over a pre-determined prediction hor...

This paper provides a replacement policy for warranty products with different failure rate from the consumer’s viewpoint. Assume that the product is replaced once within a finite planning horizon, and the failure rate of the second product is lower than the failure rate of the first product. Within warranty period (WP), the failed product is corrected by minimal repair without any cost to the c...

We consider a dynamic facility location model in which the objective is to find a planning horizon, x*, and a first period decision, XI*, such that XI* is a first period decision for at least one optimal policy for all problems with planning horizons equal to or longer than x*. In other words, we seek a planning horizon, "r*, such that conditions after x* do not influence the choice of the opti...