Scheduling Problems Depending On Allocated Resource

As a branch of operation research, scheduling theory has a profound practical background and broad application prospects. With the development of processing methods, objective functions and solution methods, modern scheduling problems have developed in diversify directions in recent years. It is more complex and significant for modern scheduling problems in practical application. This paper studies modern controllable scheduling problems with varying processing times, the main contents can be summarized as follows:Chapter 1 firstly introduces the definition, classification and solution of schedul-ing problems and the characteristic of modern scheduling problems, secondly intro-duces the research background of several scheduling problems, finally summarizes the main contributions in this paper.Chapter 2 concerns scheduling problems on a single machine with truncated learning effect, deteriorating effect and resource allocation. We assume that the actual processing time depends on the truncation learning effect, deteriorating ef-fect and the amount of resource allocated simultaneously. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately for minimizing three cost functions (total cost function, cost of completion, control-ling cost):(1)minimizing total cost function for linear (convex) resource allocation model; (2)minimizing cost of completion under the limitation of controlling cost for convex resource allocation model; (3)minimizing controlling cost under the lim-itation of cost of completion for convex resource allocation model. We prove that these problems have polynomial solutions respectively.Chapter 3 considers scheduling problems on a single machine with learning effect, deteriorating effect and resource allocation under group technology (GT) assumption. We assume that the actual processing time depends on the job po-sition, the group position, the starting time and the amount of resource allocated concurrently, and the actual setup time of group depends on the group position and the amount of resource allocated concurrently. The linear and convex resource allocation functions are examined for minimizing the weighted sum of makespan and total resource cost. We prove that the problems have polynomial solutions under the condition that the number of jobs in each group is the same.Chapter 4 discusses unrelated parallel machines scheduling problems involving resource dependent processing times and deteriorating effect simultaneously. We assume that the actual processing time of a job is a function of its starting time and its resource allocation. For the linear and convex resource allocation functions, we find the optimal sequence of jobs and the optimal resource allocation respectively. This chapter focus on the objectives of minimizing two total cost functions. If the number of unrelated parallel machines is a given constant, we show that these problems remain polynomially solvable respectively under the proposed model.Chapter 5 proposes the prospect of the later research work for some resource allocation models in this paper.