You have previously studied methods of balancing manufacturing plants where only a single model is produced. The strength of such a line is that work items can be assigned to stations in such a way as to maximize efficiency, which peaks at a particular rate of output.
The weaknesses of a mono-model line are that it becomes ineffective when demand falls or rises, and that it is only efficient in producing the model for which it was designed. If the market demand changes to require other products, the other products need to be produced.
This can be done by installing separate, dedicated lines for other products, but this is only economical when the additional lines themselves are operating efficiently in meeting the highest demand. That is, there is no solution to the total demand plane with the product mix varying.
planning-and-control-of-production-balancing-of-assembly-lines-1Two solutions to this fluctuating demand problem have been used in the past: multi-model lines and mixed-model lines. Each has its own strengths and weaknesses.
BALANCE OF LINES (ANALYSIS OF PRODUCTION)
The design problem in finding ways to equalize working times across all stations is called the line balancing problem.
There must be certain conditions for online production to be practical:
- The production volume or quantity must be sufficient to cover the cost of line preparation. This depends on the pace of production and the duration of the task. The times required for each online operation should be approximately the same. Precautions should be taken to ensure a continuous supply of material, parts, sub-assemblies, etc., and the prevention of equipment failures.
Typical cases of production line balancing are:
- Once the times of the operations are known, determine the number of operators required for each operation. Know the cycle time, minimize the number of work stations. Know the number of work stations, assign work items to it.
In order to apply line balancing, we will use the following formulas:
EXAMPLE 1:
You want to know the Unit Cost of manufacturing 500 items in an 8-hour shift, where the salary is $ 50, so applying the standard time obtained, we have that for each element we have, taking into account that there is an efficiency of 90 %
| TE min | EP | IP | NOT | NOR | T | TA |
| 3.6451 | 0.9 | 1.0417 | 4.3 | 5 | 0.729 | 0.893 |
| 4.8384 | 0.9 | 1.0417 | 5.6 | 6 | 0.806 | 0.893 |
| 5.6462 | 0.9 | 1.0417 | 6.5 | 7 | 0.807 | 0.893 |
| 2.9780 | 0.9 | 1.0417 | 3.4 | 4 | 0.744 | 0.893 |
| 2,677 | 0.9 | 1.0417 | 3.1 | 3 | 0.893 | 0.893 |
| 4.8832 | 0.9 | 1.0417 | 5.7 | 6 | 0.814 | 0.893 |
| 4.1626 | 0.9 | 1.0417 | 4.8 | 5 | 0.833 | 0.893 |
| 5.2534 | 0.9 | 1.0417 | 6.1 | 6 | 0.876 | 0.893 |
| 0.5768 | 0.9 | 1.0417 | 0.7 | one | 0.577 | 0.893 |
| 0.2562 | 0.9 | 1.0417 | 0.3 | one | 0.256 | 0.893 |
| 0.5928 | 0.9 | 1.0417 | 0.7 | one | 0.593 | 0.893 |
| 17.4420 | 0.9 | 1.0417 | 20.2 | twenty | 0.872 | 0.893 |
| 3.2448 | 0.9 | 1.0417 | 3.8 | 4 | 0.811 | 0.893 |
| 11.0730 | 0.9 | 1.0417 | 12.8 | 13 | 0.852 | 0.893 |
| 4.7268 | 0.9 | 1.0417 | 5.5 | 6 | 0.788 | 0.893 |
| 3.0958 | 0.9 | 1.0417 | 3.6 | 4 | 0.774 | 0.893 |
| 1.7644 | 0.9 | 1.0417 | 2.0 | two | 0.882 | 0.893 |
| 24.3960 | 0.9 | 1.0417 | 28.2 | 28 | 0.871 | 0.893 |
| 5.6566 | 0.9 | 1.0417 | 6.5 | 7 | 0.808 | 0.893 |
| 2.2703 | 0.9 | 1.0417 | 2.6 | 3 | 0.757 | 0.893 |
| 5.3254 | 0.9 | 1.0417 | 6.2 | 6 | 0.888 | 0.893 |
| 2.6378 | 0.9 | 1.0417 | 3.1 | 3 | 0.879 | 0.893 |
| 1.1832 | 0.9 | 1.0417 | 1.4 | two | 0.592 | 0.893 |
| 10.7476 | 0.9 | 1.0417 | 12.4 | 13 | 0.827 | 0.893 |
| 19.5286 | 0.9 | 1.0417 | 22.6 | 2. 3 | 0.849 | 0.893 |
| 2.9600 | 0.9 | 1.0417 | 3.4 | 4 | 0.740 | 0.893 |
| 7.3597 | 0.9 | 1.0417 | 8.5 | 9 | 0.818 | 0.893 |
| 1.7640 | 0.9 | 1.0417 | 2.0 | two | 0.882 | 0.893 |
Since we determine our standard time, for each element of our defined task, which is lamination, polishing, etc., we set the unit cost for the manufacture of 500 items, in an 8-hour work day, observing the situation of the working conditions in
MULTI-MODEL LINES
This approach treats the manufacturing plant as a reconfigurable resource, which produces various models in batches one after the other. Before producing a batch, the lines the equipment (people, tools, material supply) is set up to suit the model or variant required. This process takes time. The batch of products is then produced according to schedule.
The advantage of a multi-model line is that once installed for a particular model it is as efficient as a conventional line. The downside is that setting up takes time, which means lost production and inefficiency.
The problems for the multi-model line planner are:
- How to balance the line for each product separately? This is fairly straightforward, since the function of technological feasibility followed by the use of a standard balancing method (see Helgeson and Birnie or Moodie and Youth). How to order batches to minimize losses from change? It is often the case that changes from one to the other will take less time than the reverse change.
This second problem is not discussed further here: it is a standard ordering problem that the reader will find busy in most texts on operations management.
MIXING-MODEL LINES
The mix-model approach is more realistic in the modern world, given the rise of software-configurable flexible manufacturing equipment. The basic premise is that multiple products are managed by each job site with no stops to switch over between them. This allows a random sequence of the launch to be able to make products in the order and mix that the market demands.
One difficulty is that the job content on each job site can differ from model to model. Another, which follows from this, is that the idle time at each station varies from time to time depending on the sequence of patterns along the line.
The problems for the planner of a multi-model line are again twofold:
- How to balance the line when different products have different working content? How to determine the optimal launch sequence that minimizes losses?
The second problem is an operations management issue that, again, the keen student can investigate from the OM texts. What best or best deal with here is the DESIGN (balancing) of a mix-model line.
BALANCE A MIXING-MODEL LINE
Although the problem may appear daunting, the solution method is absolutely straightforward. There is hardly a deletion warning: it must be technologically feasible to produce the various models on the same line. Thus, it's reasonable to try to mix the production, for example, of 10 different video models, or 15 different TV's on the same line, but these are not realistic to make the tractors and the plane on the same line! Actually, we should talk about different VARIANTS of the same product, rather than totally different PRODUCTS.
There are several ways to go about this, but here and adaptation of the Helgeson and Birnies procedure which is conceptual simple and easy to apply. The contour procedure to solve the problem is this:
- Gather the process and technological data for the product range, i.e. operation times and precedents (what should follow what if the product should go together) Get the demand data on what volume of each product is required and on what a rate. This may be available as absolute variable volumes, or it may be as aggregate volume plus product mix data. Use this information to produce a table of composite process times. The table must contain, for each operation, a process time loaded by the proportion of products using that operation. Thus, an operation that takes 10 minutes in which only 35% of the total demand occurs becomes 3½ minutes. Calculate the cycle time and the minimum number of stations required.Construct a precedence diagram for the composite product, showing which operations depend on each other, taking into account all the variations that will occur. Determine the positional weight (PW) of each operation, just like you for a normal balancing exercise. Use the loaded times to determine PWs. Assign operations to stations, with respect to PWs, precedence, and remaining time on the job site. Depending on the goals and constraints, you may have to repeat this final step several times, trying to minimize the number of job sites, maximize processing performance, or maximize efficiency.Determine the positional weight (PW) of each operation, as you would for a normal balancing exercise. Use the loaded times to determine PWs. Assign operations to stations, with respect to PWs, precedence, and remaining time on the job site. Depending on the goals and constraints, you may have to repeat this final step several times, trying to minimize the number of job sites, maximize processing performance, or maximize efficiency.Determine the positional weight (PW) of each operation, as you would for a normal balancing exercise. Use the loaded times to determine PWs. Assign operations to stations, with respect to PWs, precedence, and remaining time on the job site. Depending on the goals and constraints, you may have to repeat this final step several times, trying to minimize the number of job sites, maximize processing performance, or maximize efficiency.Trying to minimize the number of workstations, maximize throughput or maximize efficiency.Trying to minimize the number of workstations, maximize throughput or maximize efficiency.
How You Can See It All Comes Down To Create A Fictional Composition Product There Is What It Is Not Really But It Has The Characteristics Of The Whole Range, So Applying The Standard Pound Technique. Let's do an example. Thanks go to Vonderembse for your inspiration.
Example: Background Information
A flexible manufacturing plant should be set up to package a range of hospital medical kits. All kits use the same basic elements, but there is variation. In the standard the product contains a set of components, the basic one has a smaller set, while the deluxe version contains the same items as the standard kit but in larger quantity plus a couple of additional items.
The operational and product data of the mixture for the three variants are given in the following table.
| Time (seconds) | |||||
| From Op. Sys. | Description | Standard (50% sales) | Basic
(30% sales) |
Luxury (sales of 20%) | Task (s) that precedes |
| TO | Reveal and place the box | fifteen | 12 | fifteen | - |
| B | Insert the water bottle | 9 | 9 | 9 | TO |
| C | Insert drinking glasses | 7 | 4 | 10 | TO |
| D | Insert wedge | 7 | 0 | 7 | A
(non-basic) |
| AND | Insert divider (s) | 7 | 7 | 9 | B C D |
| F | Fold the dressing gown
and fill in box |
18 | 18 | 24 | AND |
| G | Insert tissues | 6 | 0 | 9 | E
(non-basic) |
| H | Insert the casts | 7 | 7 | 10 | AND |
| I | Put the lid on | 10 | 10 | 10 | F, G, H |
| J | Shrink-wrap box | twenty-one | twenty-one | 28 | I |
| Total times | 107 | 88 | 131 |
Table 1 Operational and product data of the mixture for the three products
An aggregate output of 6,000 units is required from an effective 40 hour work week.
Solution
First, we are going to determine the process times of the product, multiplying the actual process time for each element by the proportion of the demand for that element.
Each of the first three columns shows the basic time of operation, and bold the result when this is multiplied by the demand ratio. The final column shows the sum of these charged times, the operation time of the product which is the effective time for this operation. In this model, the operation times are in seconds and the work sessions are in hours and weeks. You need to be sure that you are consistent in your use of units, using multipliers as appropriate. (make the correct conversions as a good industrial engineer)
|
Basic time (seconds) |
||||||
| From Op. Sys. | Standard (50% sales) | Basic
(30% sales) |
Luxury
(sales of 20%) |
Compound time
(sum of op. Times loaded) |
||
| TO | 15 ® 7.5 | 12 ® 3.6 | 15 ® 3.0 | 14.1 | ||
| B | 9 ® 4.5 | 9 ® 2.7 | 9 ® 1.8 | 9.0 | ||
| C | 7 ® 3.5 | 4 ® 1,2 | 10 ® 2.0 | 6.7 | ||
| D | 7 ® 3.5 | 0 | 7 ® 1.4 | 4.9 | ||
| AND | 7 ® 3.5 | 7 ® 2.1 | 9 ® 1.8 | 7.4 | ||
| F | 18 ® 9.0 | 18 ® 5.4 | 24 ® 4.8 | 19.2 | ||
| G | 6 ® 3.0 | 0 | 9 ® 1.8 | 4.8 | ||
| H | 7 ® 3.5 | 7 ® 2.1 | 10 ® 2.0 | 7.6 | ||
| I | 10 ® 5.0 | 10 ® 3.0 | 10 ® 2.0 | 10.0 | ||
| J | 21 ® 10.5 | 21 ® 6.3 | 28 ® 5.6 | 22.4 | ||
| 107 ® 53.5 | 88 ® 26.4 | 131® 26.2 | 106.1 | |||
Table 2 - compound times of the operation
Next, we determine the minimum number of jobsites needed.
Cycle duration = (hours / week available x 3600) / (week output) = 40 x 3600/6000 = 24 seconds
Ideal number of job sites = job content / compound cycle time
= 1061/24
= 4.42
We cannot have 0.42 of a station, so the minimum number of stations is 5 (five). It is rounded as you can see.
Next, we are going to draw a diagram of the precedence.
Precedence diagram for assembling the medical kit
Note that in this case there are no unique operations to a single variant. If there were, they would be just directed like any other from Op. Sys.. The diagram is constant with the final column
Now let? S determine the positional weights of each operation. The PW of an operation is the sum of the process times for ALL operations that depend on it, plus its own process time. In the table all operations depend on operation A. In the case of a mix-model line, the PWs are calculated from the compound times established earlier. Op A's Pw here is thus 106.1. It shows the PWs for the rest of the ops, aligned in descending order. Notice how the PW changes when parallel operations (B, C, D, and F, G, H) are involved.
| PW Row | Operation | Positional Weight | Commentary |
| one | TO | 106.1 | Op Close-up? all the others depend on it |
| two | B | 80.4 | B, C, D is independent
IYJ depend on each one |
| 7 | H | 40.0 | |
| 8 | G | 37.2 | |
| 9 | I | 32.4 | F, G and H must all precede I |
| 10 | J | 22.4 | From Op. Past, so PW = Op time. |
aligned positional weights of operations
We can now assign operations to the stations in the normal way. The heuristic procedure is:
- At Station I, consider all operations (that is, those for which there are no preceding operations). If there is more than one, select that with the highest PW. Continue to attempt to assign operations to Station I until no more eligible operations exist or will fit in the remaining time. Record idle time, if any. Move to Station II. Repeat attempts to assign eligible operations, in descending order of PW, until there is no eligible operation that will fit. Note that eligibility / precedence always comes before PW; PW is used to break ties. Repeat until all operations have been assigned, even if it means creating more than the theoretical minimum number of stations. Finally,calculate balance delay ratio (= 100-efficiency) available working time and total idle time.
The following table demonstrates the procedure gradually.
| Eligible operation (s) | Selected operation (s) | Compound operation time (sec) | Assigned to the station | Cumulative allotted time (sec) | Idle Time (sec) |
| TO
B C D |
TO
B |
14.1
9.0 |
I
I |
14.1
23.1 |
0.9 |
| C, D
C AND |
D
C AND |
4.9
6.7 7.4 |
II
II II |
4.9
11.6 19.0 |
5.0 |
| F, G, H
G, H |
F (largest PW)
G (H will not fit) |
19.2
4.8 |
III
III |
19.2
24.0 |
0 |
| H
I |
H
I |
7.6
10.0 |
IV
IV |
7.6
17.6 |
6.4 |
| J | J | 22.4 | V | 22.4 | 1.6 |
Step by Step we determine workstations in a Heuristic way
| Station | Assigned Operations | Weather |
| I | A, B | 0.9 |
| II | D, C, E | 5.0 |
| III | F, G | 0 |
| IV | H, I | 6.4 |
| V | J | 1.6 |
| Total time | 13.9 |
Sum of allocated time of workstations
To Calculate the Balancing Time, the cycle time was 24 seconds, so the Total time Working in Balanced Line = Cycle time x Number of Stations
Time Efficiency:
BALANCE OF LINES OF A MANUFACTURING PLANT
The final assembly plant for the Mach 10 one-person sailboat is in Cupertino, California. In this time only 200 minutes are available each day to meet a daily demand for 60 sailboats.
- a) Given the following information draw the precedence diagram and assign tasks to the few possible job sites to meet the demand.
| Homework | Weather | Precedents |
| TO | one | - |
| B | one | TO |
| C | two | TO |
| D | one | C |
| AND | 3 | C |
| F | one | C |
| G | one | D, E, F |
| H | two | B |
| I | one | G, H |
- b) What is the effectiveness of the line? c) Repeat the steps above with 300 minutes of assembly time available each day. What is the effectiveness of the line now? d) Repeat the steps above with 400 minutes of assembly time available each day. What is the effectiveness of the line now?
Answers:
- a) b)
Efficacy = 78%
(multiple provisions in this efficiency are possible)
- c)
Efficacy = 86.7%
(multiple provisions in this efficiency are possible)
- d)
Efficacy = 64.9%
(multiple provisions in this efficiency are possible)
PLANNING AND CONTROL OF PRODUCTION INVENTORY ANALYSIS - PROPOSED PROBLEMS
one) The office manager of a law firm is responsible for ordering copier paper to supply all copiers located on the firm's six floors. The machines require a total of 22 boxes of paper each day, 6 days per week, 52 weeks per year. The paper is ordered from a large distributor at a rate of $ 12 per box. The distributor also bills the firm a $ 20 fulfillment charge for each order placed and imposes a charge charge for the shipment. The paper is shipped in boxes of a dozen boxes, and the distributor determines the cost shipping to the customer at a rate of $ 24 per case. Every time the order paper signs he requires the seller, paid at the rate of $ 10 per hour, 30 minutes to generate and distribute the appropriate paperwork.Since there is not enough room on the premises for the alternate storage space is contracted from another tenant in the building. The tenant charges the firm $ 2.80 plans for each paper box he holds in inventory for one year. All signature purchases are funded at 1 and 1/2% per month, and no shortages from any office supplies are allowed.
- a) The firm is currently ordering 100 boxes of paper at a time. What is the total relevant cost of this policy? b) How many boxes should the firm order under the optimal policy? c) What is the total relevant cost of the optimal policy? d) How many orders are placed each year under optimal policy? e) How many days are there between the orders under optimal policy?
Suppose the firm's partners inform the office manager that they consider the cost of carrying inventory too expensive. They suggest that with some sources, such as copier paper, occassional shortages could be tolerated. Any print job that might be interrupted could be run when the new paper order is received. One of the partners, specializing in the economy, acknowledges that, while he could see no direct negative impact of such shortages on firm revenues, there may be an opportunity cost of some kind. He confidently informs the office manager that an appropriate penalty cost would be $ 2 for each box of paper short.
- f) How many boxes should ask new signature under optimal policy? g) What is the total relevant cost of the new optimal policy? h) How many boxes of each new delivery will be set aside to run accumulated print jobs? i) What percentage of the time is the signature out of the copier's paper stock?
After a few weeks under a new policy another partner approaches the office manager to explain that the policy was not acceptable. She worries about the health of the firm and insists that no more than 5% of the copier's time be out of paper.
- j) What is the imputed penalty charge? k) What is the total relevant cost of the newest optimal policy?
2) The summit steel mill can produce 5,000 tons of steel per week, 52 weeks per year. They have orders for 15,000 tons of steel per month, 12 months per year. Each ton of steel costs $ 600 for raw materials and $ 1,200 for refining and production. All inventories are valued at an internal return rate of 20%, and each time the blast furnace is restarted it costs $ 10,000 top.
- a) How much steel should be produced in a single production run? b) How many days does a production run take? c) How many days pass between the times when the blast furnace is restarted? d) What is the maximum inventory on hand? e) What is the relevant total cost of the optimal policy?
3) DigiTech, a small PC manufacturer, buys high definition color monitors from a high-end supplier. The cost per unit is determined by the following guidelines:
| Number of units ordered | Price by unit |
| 01 to 20 | $ 400 |
| 21 to 30 | 395 |
| 31 to 40 | 390 |
| 41 to 50 | 388 |
| 51 to 100 | 387 |
| 101 to 200 | 386 |
| 201 and up | 385 |
DigiTech has an annual demand for 730 custom computers. Each time the company asks for monitors it incurs a cost of $ 20, and calculates that each monitor held in inventory for a year's cost the firm $ 50.
- a) Without considering quantity discounts, what is the quantity of the economic order? b) Taking quantity discounts in consideration what is the quantity of the economic order?
REFERENCES AND WEB LINKS:
WB Helgeson & DP Birnie, "Assembly Line Balancing using the Ranked Positional Weight Technique", Journal of Industrial Engineering, Vol 12, No 6, Nov-Dec 1961
Moodie and Young, cited in W Bolton, "Production Planning and Control", Longman, 1994.
MA Vonderembse & GP White, "Operations Management - Concepts, Methods and Strategies", West 1996
Download the original file
