Abstract
The problem studied in this paper was inspired from an actual textile company. The problem is more complex than usual scheduling problems in that we compute overtime requirements and make scheduling decisions simultaneously. Since having tardy jobs is not desirable, we allow overtime to minimize the number of tardy jobs. The overall objective is to maximize profits. We present various mathematical models to solve this problem. Each mathematical model reflects different overtime workforce hiring practices. An experimentation has been carried out using eight different data sets from the samples of real data collected in the above mentioned textile company. Mathematical Model 2 was the best mathematical model with respect to both profit and execution time. This model considered partial overtime periods and also allowed different overtime periods on cells. We could solve problems up to 90 jobs per period. This was much more than what the mentioned textile company had to handle on a weekly basis. As a result, these models can be used to make these decisions in many industrial settings.
Highlights
In manufacturing systems, capacity allocation and machine scheduling play an essential role
The capacity planning establishes the number of machines/workers needed in a process layout environment, number of production lines or cells needed in a cellular environment, number of shifts to be utilized, whether
The first table shows the sequence of jobs assigned to each cell; the second table shows the corresponding overtime decisions for the problem; the third table shows the original due day, due shift and due time; revenue generated from each job, processing times, detailed computations of completion times and revised due dates (Di*) based on overtime decisions; and the Gantt chart is given in the corresponding figure
Summary
Capacity allocation and machine scheduling play an essential role. On the other hand, scheduling deals with the detailed allocation of resources established in the capacity planning step to various jobs over a period of time. Scheduling establishes start and completion times of jobs on resources, i.e. machines, cells, production lines and workers. Establishing capacity requirements is a difficult task and it gets even harder when capacity requirements vary from one period to the In this situation, using overtime is a feasible method and many companies use that. Each overtime decision comes with a cost associated with it This all makes the problem difficult to solve and lead to a NP-hard optimization problem where the weekend and weekday overtime decisions as well as cell loading and job sequencing are performed to maximize the overall net profit. We need to mention that if overtime is needed week after week, this may be an indicator that organization needs to re-assess capacity requirements and adjust regular capacity levels, i.e., increase number of cells, number of machines, etc
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