Using the Kilbridge and Wester procedure for. Let the cycle time be. First, check if this c is feasible. These labels are the Roman numbers. Tasks that have no predecessors are placed in column I, tasks. Note that this results in a precedence diagram that places.

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In this section we consider several methods for solving the line balancing problem by hand, using Example 6. These methods are heuristic approaches, meaning that they are based on logic and common sense rather than on mathematical proof.

None of the methods guarantees an optimal solution, but they are likely to result in good solutions which approach the true optimum. The manual methods to be presented are : 1. Largest-candidate rule 2. Ranked positional weights method In Section 6. Largest-candidate rule This is the easiest method to understand.

The work elements are selected for assignment to stations simply on the basis of the size of their T e values. The steps used in solving the line balancing problem are listed below, followed by Example 6. List all elements in descending order of T e value, largest T e at the top of the list. Step 2. To assign elements to the first workstation, start at the top of the list and work down, selecting the first feasible element for placement at the station.

A feasible element is one that satisfies the precedence requirements and does not cause the sum of the T e values at the station to exceed the cycle time T c. Step 3. Continue the process of assigning work elements to the station as in step 2 until no further elements can be added without exceeding T c. Step 4. Repeat steps 2 and 3 for the other stations in the line until all the elements have been assigned.

One comment should be made which applies not only to the largest-candidate rule but to the other methods as well. Starting with a given T c value, it is not usually clear how many stations will be required on the flow line. Of course, the most desirable number of stations is that which satisfies Eq. However, the practical realities of the line balancing problem may not permit the realization of this number. Also listed are the immediate predecessors for each element.

This is of value in determining feasibility of elements that are candidates for assignment to a given station. Following step 2, we start at the top of the list and search for feasible work elements. Element 3 is not feasible because its immediate predecessor is element I, which has not yet been assigned, The first feasible element encountered is element 2.

We then start the search over again from the top of the list. Steps 2 and 3 result in the assignment of elements 2, 5, 1, and 4 to station 1. The total of their element times is 1.

Continuing the procedure for the remaining stations results in the allocation shown in Table 6. There are five stations, and the balance delay for this assignment is The solution is illustrated in Figure 6. The largest-candidate rule provides an approach that is appropriate for only simpler line balancing problems.

More sophisticated techniques are required for more complex problems. The technique has been applied to several rather complicated line balancing problems with apparently good success [11]. It is a heuristic procedure which selects work elements for assignment to stations according to their position in the precedence diagram. The elements at the front of the diagram are selected first for entry into the solution. This overcomes one of the difficulties with the largest candidate rule, with which elements at the end of the precedence diagram might be the first candidates to be considered, simply because their T, values are large.

However, our problem is elementary enough that many of the difficulties which the procedure is designed to solve are missing. The interested reader is invited to consult the references, especially [2], 17], or 11], which apply the Kilbridge and Wester procedure to several more realistic problems.

Step 1. Constraint the precedence diagram so that nodes representing work elements of identical precedence are arranged vertically in columns. This is illustrated in Figure 6.

Elements 1 and 2 appear in column I, elements 3, 4, and 5 are in column II, and so on. Note that element 5 could be located in either column II or III without disrupting precedence constraints. List the elements in order of their columns, column I at the top of the list.

If an element can be located in more than one column, list all the columns by the element to show the transferability of the element. This step is presented for the problem in Table 6. The table also shows the T c value for each element and the sum of the T e values for each column.

To assign elements to workstations, start with the column I elements. Continue the assignment procedure in order of column number until the cycle time is reached.

T c in our sample problem is 1. The sum of the T e values for the columns is helpful because we can see how much of the cycle time is contained in each column.

The total time of the elements in column I is 0. We immediately see that the column II elements cannot all fit at station 1. To select which elements from column II to assign, we must choose those which can still be entered without exceeding T c. When added to the column I elements, T s would exceed 1. Accordingly, elements 4 and 5 are added to station 1 to make the total process time at that station equal to T c.

To begin on the second station, element 3 from column II would be entered first. The column II elements would be considered next. Element 6 is the only one that can be entered.

The assignment process continues in this fashion until all elements have been allocated. Table 6. Also, for stations that do have the same elements, the sequence in which the elements are assigned is not necessarily identical.

Station 1 illustrates this difference. In general, the Kilbridge and Wester method will provide a superior line balancing solution when compared with the largest-candidate rule. However, this is not always true, as demonstrated by our sample problem. Ranked positional weights method The ranked positional weights procedure was introduced by Helgeson and Birnie in [6].

A ranked positional weight value call it the RPW for short is computed for each element. The RPW takes account of both the T e value of the element and its position in the precedence diagram.

Then, the elements are assigned to work stations in the general order of their RPW values. For convenience, include the T e value and immediate predecessors for each element. Assign elements to stations according to RPW, avoiding precedence constraint and time-cycle violations. For element I, the elements that follow it in the arrow chain see Figure 6. This RPW value is 3. The reader can see that the trend will be toward lower values of RPW as we get closer to the end of the precedence diagram.

We begin the assignment process by considering elements at the top of the list and working downward. The reader should follow through the solution in Table 6. In the RPW line balance, the number of stations required is five, as before, but the maximum station process time is 0. The corresponding balance delay is The RPW solution represents a more efficient assignment of work elements to stations than either of the two preceding solutions.

However, it should be noted that we have accepted a cycle time different from that which was originally specified for the problem. For large balancing problems, involving perhaps several hundred work elements, these manual methods of solution become awkward.

A number of computer programs have been developed to deal witii these larger assembly line cases. In the following section we survey some of these computerized approaches. Very Helpful! Understood it very well! You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account.

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CASA DE MUNECAS HENRIK IBSEN PDF

## 6.5 METHODS OF LINE BALANCING

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