This research deals with a multi-job Integer batch scheduling problem on a single machine with different due dates. Every job demanded one or more parts, and the single machine processed the job into a number of batches. The objective is to minimize total actual flow time, defined as the total flow time of all jobs starting from the arrival to the common due date. The decisions are to determine the sequence of jobs, the number of batches, batch size, and sequence of all batches on a single machine. This research proposes three algorithms, developed based on the longest due date rule (The P1-LDD Algorithm), the adjacent pairwise interchange method (The P2-API Algorithm), and the permutation method (The P3-PM Algorithm). The numerical experience shows that the three algorithms produce an outstanding solution. The P1-LDD Algorithm fits to solve a simple problem. The P2-API Algorithm has superior to solve a big complicated problem. The P3-PM Algorithm has the best performance to solve small complicated problems.

This paper discusses an integrated model of batch production and maintenance scheduling on flow shop with two deteriorating machines producing single item to be delivered at a due date. The model describes the trade-off between production and maintenance costs as the production run length increases on two machines. The objective function of the model is to minimize the total cost consisting of in process and completed part inventory costs, setup costs, preventive & corrective maintenance costs and rework costs on two machines. The step-wise optimization algorithm is developed to solve a mixed integer quadratic programming. Comparison with the practice and the model sensitivity analysis are demonstrated to clarify how the algorithm works.

This research discusses an integer batch scheduling problems for a single-machine with position-dependent batch processing time due to the simultaneous effect of learning and forgetting. The decision variables are the number of batches, batch sizes, and the sequence of the resulting batches. The objective is to minimize total actual flow time, defined as total interval time between the arrival times of parts in all respective batches and their common due date. There are two proposed algorithms to solve the problems. The first is developed by using the Integer Composition method, and it produces an optimal solution. Since the problems can be solved by the first algorithm in a worst-case time complexity O(n2n-1), this research proposes the second algorithm. It is a heuristic algorithm based on the Lagrange Relaxation method. Numerical experiments show that the heuristic algorithm gives outstanding results.