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...

Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for genera...

This paper discusses why the selection of a finite planning horizon is preferable to an infinite one for a replenishment policy of production inventory models. In a production inventory model, the production rate is dependent on both the demand rate and the inventory level. When there is an exponentially decreasing demand, the application of an infinite planning horizon model is not suitable. T...

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...

Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of weights for a given time horizon T . However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution...

Monotonicity of optimal solutions to finite horizon dynamic optimization problems is used to prove the existence of a forecast horizon, i.e a long enough planning horizon that ensures that a first period optimal action for the infinite horizon and the finite horizon problem agree, regardless of problem parameter changes in the tail. The existence of extremal monotone optimal solutions motivates...

Graph and automata theory are widely used in the algorithmic solution of fundamental problems in verification. Verification problems often boil down to solving reachability questions in graphs, optimization problems, and combinatorial problems in automata. Fundamental algorithmic problems in computer science have been well studied, such as the shortest path problem, the travelling salesman prob...

Minimum cost flow problems in infinite networks arise, for example, in infinite-horizon sequential decision problems such as production planning. Strong duality for these problems was recently established for the special case of linear costs using an infinite-dimensional simplex algorithm. Here, we use a different approach to derive duality results when the costs are convex. We formulate the pr...

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...

Forecast horizons, i.e long enough planning horizons that ensure agreement of first period optimal production decisions of finite and infinite horizon problems regardless of changes in future demand, are shown to exist in the context of production planning under stochastic demand. The monotonicity of first period optimal production decisions with respect to first order stochastic shifts in dema...