Assembly line balancing

SUMMARY ASSEMBLY LINE BALANCING Introduction An assemly system performs a set of distinct minimum rational work elements for the assembly of a product or products and consists of a set of work stations linked together by a transport mechanism and a detailed specification of how the assembly of the product flows from one station to another. A minimum rational work element (task, hereafter) is the smallest indivisible work element and a work station (station, hereafter) a location along the flow line where the tasks are processed. A task is 'smallest and indivisible' in the sense that it cannot be divided between two or more stations without conflict, and that is separable from other activities, that is it can be performed independently. The time required for the completion of a task is termed the task processing time (process time, hereafter). A station consists of human or robotic operators and/or machinery, equipment and gadgets. The series of stations and the transport mechanism, usually a conveyor belt, is referred to as the assembly line. The conveyor belt moves at each interval of T time units, known as the cycle time, that is a manufacturing item is fed to the first station of the line at a predetermined constant feed rate 1/T. The production rate is therefore 1/T units per time unit. Since the item is available to a station for T time units only, the total time required to perform all the tasks assigned to a station should not exceed T, if the line is to operate smoothly with no delays or interruptions. One of the key issues in the design of an assembly system, therefore, is specification of the tasks to be performed at each individual station. This can not be done arbitrarily because, in addition to the cycle- time restriction, there exist technological sequencing requirements, known as precedence relations, that is the processing of a task may not start until the processing of all its immediate predecessors has been completed. The predence relations are traditionally represented schematically by a precedence network/diagram. Each node of such a network corresponds to a distinct task and, if task i is an immediate predecessor of task j, that is if the processing of task j cannot start until task i is completed this relation is represented by a directed arc (i,j), joining node i to node j. The set of precedence relations is simply a partial ordering of the tasks. To fully utilize the resources, the collection of tasks assigned to a particular station must be chosen so that the idle time at that station is minimal. The assembly line is said to be balanced xvSUMMARY ASSEMBLY LINE BALANCING Introduction An assemly system performs a set of distinct minimum rational work elements for the assembly of a product or products and consists of a set of work stations linked together by a transport mechanism and a detailed specification of how the assembly of the product flows from one station to another. A minimum rational work element (task, hereafter) is the smallest indivisible work element and a work station (station, hereafter) a location along the flow line where the tasks are processed. A task is 'smallest and indivisible' in the sense that it cannot be divided between two or more stations without conflict, and that is separable from other activities, that is it can be performed independently. The time required for the completion of a task is termed the task processing time (process time, hereafter). A station consists of human or robotic operators and/or machinery, equipment and gadgets. The series of stations and the transport mechanism, usually a conveyor belt, is referred to as the assembly line. The conveyor belt moves at each interval of T time units, known as the cycle time, that is a manufacturing item is fed to the first station of the line at a predetermined constant feed rate 1/T. The production rate is therefore 1/T units per time unit. Since the item is available to a station for T time units only, the total time required to perform all the tasks assigned to a station should not exceed T, if the line is to operate smoothly with no delays or interruptions. One of the key issues in the design of an assembly system, therefore, is specification of the tasks to be performed at each individual station. This can not be done arbitrarily because, in addition to the cycle- time restriction, there exist technological sequencing requirements, known as precedence relations, that is the processing of a task may not start until the processing of all its immediate predecessors has been completed. The predence relations are traditionally represented schematically by a precedence network/diagram. Each node of such a network corresponds to a distinct task and, if task i is an immediate predecessor of task j, that is if the processing of task j cannot start until task i is completed this relation is represented by a directed arc (i,j), joining node i to node j. The set of precedence relations is simply a partial ordering of the tasks. To fully utilize the resources, the collection of tasks assigned to a particular station must be chosen so that the idle time at that station is minimal. The assembly line is said to be balanced xvThe simple case described clearly does not represent all the complications of an assembly system and, numerous variations of BALBP have been defined in the literatuure. These will be referred to as the general assembly line balancing problem (GALBP), whether they are deterministic or stochastic. These versions incorporate other complications found in assembly systems such as mixed-models. (Thomopoulos 1967), zoning requirements, must-do-tasks, balance delay, parallel stations, processing alternatives and other extensions. Formulation of SALBP as a mixed-integer program SALBP was first formulated as a mathematical program by Bowman. In the Bowman model, as modified by White, presented here: I denotes the task set, I={1,2,..,i,...,m}, and t. the process time of task i, where iel = {1,2,...,m}. Also P(x) are {immediate predecessors of task i} and the cycle time, is denoted by T. The decision variable is defined as follows : let x.. = I if task i is assigned to station j and x.. = D if it is not, '-'where j=1,2,...,n, and n< m. The following 0-11.program represents SALBP. Program P Minimize n m Z = Z Z ex.. (1) J=1 1=1 1 XJ subject to the following constraints: n Z x,, = 1 ViE I (2) j=1 m ıj Z t x Mn. VJ E^-{n} (6) and M is a sufficiently large positive integer. The objective function (1) represents the "cost" of using the stations and is, therefore, to be minimized. Relation (6) defines such a premium on using and additional station when all the xviitaks can be accommodated.without it, that the minimization of the objective function CD mill result in the minimum number of stations. Constraint (2), known as the "occurrence constrainti' guarantees that every taks is assigned to a station and the "cycle-time" constraint (3) guarantees that the total process time for all the tasks assigned to each station is, at most, the prespecified cycle time. Finally, constraint (4) represents the predecence relations: if x.. = 1, that is if task i is assigned to station k, then, each immediate predecessor h of task i must be assigned to a station j such that j^k, sd that task h may be completed before the processing of task i starts. If, on the other hand, x.. = 0, the immediate predecessor h of i may or may not be assigned to the first k stations. Constraint (5), of course, guarantees that each variable can assume values of 0 or 1 Dnly (that is a task cannot be split among two or more stations). An improved version of program P is given by Patterson and Albracht and an alternative formulation as a- general integer program ming problem has been proposed by Talbot and Patterson. If n* is the optimal number of stations needed, then: m ( î t.) T Keyword: Hazır giyim endüstrisi = Ready made wear industry ; Montaj hattı dengeleme = Assembly line balancing ; Üretim = Production