We give multi-stage stochastic programming formulations for lot-sizing problems where costs, demands and order lead times follow a general discrete-time stochastic process with finite support. We characterize the properties of an optimal solution and give a dynamic programming algorithm, polynomial in input size, when orders do not cross in time.

Production planning is a key area of operations management. An important methodology for production planning is mathematical programming. Traditional mathematical programming models for production planning are deterministic, and cannot provide robust production plans in the presence of uncertainty. As such, deterministic planning models may yield unsatisfactory decisions. Stochastic programming...

In this paper, a novel framework is proposed to study impacts of regulatory incentive on distributed generation (DG) investment in sub-transmission substations, as well as upgrading of upstream transmission substations. Both conventional and wind power technologies are considered here. Investment incentives are fuel cost, firm contracts, capacity payment and investment subsidy relating to wind ...

This study considers pricing, production and transportation decisions in a Stackelberg game between three-stage, multi-product, multi-source and single-period supply chains called leader and follower. These chains consist of; manufacturers, distribution centers (DCs) and retailers. Competition type is horizontal and SC vs. SC. The retailers in two chains try to maximize their profit through pri...

This is a PhD thesis of Blagoj Delipetrev explaining nested dynamic programming, nested stochastic dynamic programming and nested reinforcement learning algorithms that are applied in reservoir optimization problem. Additionally there are also multi-objective version of these algorithms.

the control problem and dynamic programming is a powerful tool in economics and management. we review the dynamic programming problem from its beginning up to its present stages. a problem which was involved in physics and mathematics in i 7” century led to a branch of mathematics called calculus of variation which was used in economic, and management at the end of the first quarter of the 20” ...

This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of Benders decomposition and of its application to two-stage stochastic programming problems (also known in this context as the L-shaped method), then extends this t...