We consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints. Examples include production planning and equipment replacement over an infinite horizon. We form the natural dual linear programming problem and prove strong d...

We develop a competitive pricing model which combines the complexity of time-varying demand and cost functions and that of scale economies arising from dynamic lot sizing costs. Each firm can replenish inventory in each of the T periods into which the planning horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carryi...

We consider tactical planning for a particular class of multi-period vehicle routing problems (MPVRP). This problem involves optimizing product collection and distribution from several production locations to a set of processing plants over a planning horizon. Each horizon consists of several days, and the collection-distribution are performed on a repeating daily basis. In this context, a sing...

This paper considers the Dynamic Multi-Period Vehicle Routing Problem which deals with the distribution of orders from a depot to a set of customers over a multi-period time horizon. Customer orders and their feasible service periods are dynamically revealed over time. The objectives are to minimize total travel costs and customer waiting, and to balance the daily workload over the planning hor...

This paper presents a representation of static and moving obstacles, using Velocity Obstacles (VO), for on-line planning in dynamic environments. Each obstacle is mapped to forbidden states by selecting a proper time horizon for the velocity obstacle. The proper choice of the time horizon ensures that the boundary of the mapped obstacle overlaps with the boundary of the set of inevitable collis...

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...

the aim of this study is to propose a new mixed integer linear programming (milp) model to find the minimum required number of yard cranes, rubber tyred gantry cranes (rtgcs), for completion the total amount of works at the end of planning horizon. in other word, we find the optimal number of yard cranes in a container terminal which completes the total amount of works. the paper supports the p...

The hierarchical approach to production planning is classically used to handle the organization and logistics in complex production systems. It distinguishes several decision levels using different descriptions of the production process. The upper-level planning horizon is relatively long, and, since the number of time intervals (or buckets) of this horizon is restricted by computational limita...

When individuals are making decisions regarding the purchase of a durable commodity, the choice of job, or any other decision that has a time duration element to it, these decisions critically depend upon the lifetime or the time horizon of the object being decided upon. The reason that the time horizon is so critical comes from the fact that the worth of each option depends not only upon its i...

Flexible and dynamic supply chain network design problem has been studied by many researchers during past years. Since integration of short-term and long-term decisions in strategic planning leads to more reliable plans, in this paper a multi-objective model for a sustainable closed-loop supply chain network design problem is proposed. The planning horizon of this model contains multiple strate...