The Uncapacitatied Dynamic Single-Level Lot-Sizing Problem under a Time-Varying Environment and an Exact Solution Approach

The dynamic lot-sizing problem under a time-varying environment considers new features of the production system where factors such as production setup cost, unit inventory-holding cost, and unit price of manufacturing resources may vary in different periods over the whole planning horizon. Traditional lot-sizing theorems and algorithms are no longer fit for these situations as they had assumed constant environments. In our study, we investigated the dynamic lot-sizing problem with deteriorating production setup cost, a typical time-varying environment where the production setup is assumed to consume more preparing time and manufacturing resources as the production interval lasts longer. We proposed new lot-sizing models based on the traditional lot-sizing model considering the changing setup cost as a new constraint, called uncapacitatied dynamic single-level lot-sizing under a time-varying environment (UDSLLS-TVE for short). The UDSLLS-TVE problem has a more realistic significance and higher research value as it is closer to reality and has higher computational complexity as well. We proposed two mathematical programming models to describe UDSLLS_TVE with or without nonlinear components, respectively. Properties of the UDSLLS-TVE models were extensively analyzed and an exact algorithm based on forward dynamic programming (FDP) was proposed to solve this problem with a complexity of O (n2). Comparative experiments with the commercial MIP solver CPLEX on synthesized problem instances showed that the FDP algorithm is a global optimization algorithm and has a high computational efficiency.

An Optimal Operation Scheduling for Wind Farm with Storage and Forecasting

In this paper, the optimal schedule for power output of a wind farm with storage units and forecasting system has been studied. Optimal schedule for wind power output aims at maximizing expected schedule income and minimizing cost over the required period. We present a practical method to solve the problems based on forward dynamic programming algorithm. It is demonstrated by simulation that the method presented in this paper can ensure one to get a feasible and profitable schedule for wind farm.

A BATCHING PROBLEM WITH LEARNING EFFECT CONSIDERATIONS

Consider a batch-sizing problem, where all jobs are identical or similar, and a unit processing time (p = 1) is specified for each job. To minimize the total completion time of jobs, partitioning jobs into batches may be necessary. Learning effect from setup repetition makes small-sized batches; on the contrary, job's learning effect results in large-sized batches. With their collaborative influence, we develop a forward dynamic programming (DP) algorithm to determine the optimal number of batches and their optimal integer sizes. The computation effort required by this DP algorithm is a polynomial function of job size.