Operator assignment model for minimizing total operator cost in a flexible flow shop environment

This research proposes a mix-integer linear programming model for operator assignment in a flexible flow shop environment. The objective is to minimize the total cost of operator transportation and operator exchange between machine. The model was developed considering practical constrain whereas machine are operated semi automatically, allowing an operator to be assigned to more than one machine in a certain period of time. Therefore, number of operator could be less than the number of machine. The proposed model result in a reduction up to 60% for operator transportation and operator exchange compared to current practice. Current output of proposed model will assign operator based on the number of available operator. Further research will be conducted by relaxing the number of operator to increase the operator utilization.


Introduction
This paper arises from a practical case study of a textile industry. One of the textile process is creating a yarn by twisting together of fibers, also known as spinning process. The spinning process is categorized as a flexible flow shop system, which different type of yarn will go through the same stage of machine sequences. In each machine stage there are one or identical parallel machines. Different types of yarn are produced depending on the textile job order and due date. Thus, sequencing of yarn jobs is necessary to fulfill a certain objective. There are studies for job sequencing in a flexible flow shop [1]. In this case study, each machine has different level of automation, thus requiring less of operator time than the process time of the machine. In other words, it is possible that the operator shifts from one machine to another and conduct different jobs. Consequently, the number of operator could be less than the number of machines. Most research on operator assignment consider the number of operator is fixed during a certain time bucket in a planning horizon [2].
This research focus on the operator assignment problem. The objective of the research is to minimize the total cost of traveling and number of operator exchange between assignment, as seen in Figure 1.
The paper will be divided into four sections. The following section will discuss the model development. Section 3 will describe the case study and merit of the proposed model. The last section will point out remarks and further research activity.

Model development
The case study has similar characteristics of the operator assignment problem in an assembly line system [3]. Each operator is assigned certain task within a certain planning horizon. Differences is that operator must move between stations [4]. Gebennini [5] has developed a model for assigning operators into a flexible manufacturing system. The objective function is to minimize operators' walking time.
Gebennini also assumes that an operator may not shift to other machine until the job is finished.
Considering the practical fact that machine has certain level of automation, the proposed model will relax this assumption enabling operator to move to other machine within the same time bucket if it fulfill the operator capacity within the time bucket. The proposed model will also consider a practical constrain for minimizing operator exchange. The objective function of case study is to minimize operator transportation time and operator switching between assignments. The proposed model assumes that that the distance between station is linier in a flow shop layout [6]. The operator origin point will be set at the medium point between the closest and furthest assigned station. The operator skill level and walking speed are assumed the same.

Notation
The following notation of the proposed model. : walking distance of station j assigned to operator k from the medium point of the operator k

Model formulation
The proposed mixed-integer linear model is formulated as follows: (1) Subject to (2) (2) assure that an operator could be assigned at one machine in a certain time;  Constraints (3)-(5) identifies the last station assign to each operator in each time bucket;  Constraints (7)-(8) identifies the first station assign to each operator in each time bucket;  Constraints (9)-(10) calculate the of the operator medium point between station j assigned to operator k in time bucket t;  Constraint (11)-(12) is the binary setting to identify in number of operator exchange;  Constraint (13) is the capacity for each operator for traveling time and assignment time at station j in time bucket t;

Stasiun δjt
The current operator assignment of the company is depicted in Figure 2. The operator assignment is based on trial and error conducted by the supervisor and being refined from time to time.