Scaling Assembly Operations Efficiently Using MILP Optimisation (Line Balancing)

A local custom Laptop manufacturer assembles Laptops from sourced parts using a 4-step process, staffed by 4 operatives. Fig.1 shows the tasks of each operative, and the durations at each station. The 3rd step is a bottleneck in the process, with 8 mins duration.

Assuming no variability or downtime, they can theoretically produce 60 units in an 8 hour day. They are looking to scale their operations to meet expected demand in the future. They would like to see various options for scaling up the operations.

Now there are several ways in which production could be scaled, such as:

• Run more than one shift per day (2x, or 3x)
• Create an additional line in the same facility, an annexe, or a different location
• Redesign the line with more number of stations (eg. 6, 8, 12, etc)

Multiple options could be worked out using the scaling levers mentioned above. But they will need to be properly evaluated with respect to their feasibility, risks, actual production output, operating costs, investment required and the ROIC (return on the invested capital) before a final choice could be made.

In this article, I would like to focus on redesigning the line by increasing the number of assembly stations and the number of operatives. Any new line design must also be properly balanced to ensure there is no major bottleneck in the process.

In order to redesign the line, we need task dependencies. Task dependencies are shown below in Fig.2. Arrows in the diagram indicate dependencies between the tasks. For example, tasks C, D and E cannot start unless B is complete. And tasks C, D, E can be carried out in any sequence, or in parallel.

In Fig.2 we have 12 tasks, and the total duration required to assembly a Laptop ready for delivery is 28 mins. The problem of distributing N tasks into M number of stations, as evenly as possible across the stations, is known as "Assembly Line Balancing Problem".

Dividing the total assembly time of 28 mins into 6 stations gives us 4.67 mins each. Since the longest task in the list has 5 mins duration, we could perhaps expect to design a line with a max load of 5 mins in each station. Can we achieve it? Let's see.

The "objective function" of the problem is to minimise the difference between maximally and minimally loaded stations in the assembly line (see Fig.3).

Besides, we must subject the problem to the following constraints:

• Each task must be assigned to a station, and not to more than 1 station.
• Each station must have at least 1 task assigned. Number of stations M is known.
• Allocation of tasks to stations must meet the precedence constraints. For example, task H must be either in the same station as the task G, or in a subsequent station.

This problem can be is solved using an optimisation method called Mixed Integer Linear Programming (MILP), which is a powerful tool to solve, not only Assembly Line Balancing problems, but also many other problems related to Production, Manufacturing and Supply Chain Management, besides other disciplines and applications.

Applying MILP to the Laptop Assembly problem gave the following results for 6 scenarios, for number of stations M = 2, 3, 4, 5, 6 and 8 (see Table 1). Each station has 1 operative.

In the above table, the column "Station Durations" indicates the sum of task times in each station. "Calc Capacity (Units/Day)" is determined by dividing 480 mins (in a day) by the bottleneck duration. "Simulated Units / Day" is obtained via Discrete Event Simulation (DES), which is a more reliable estimate than any hand calculation.

Even without considering downtime or variability of task durations, DES gives a lower value than the hand-calculated value because of the start-up and shut-down transients in the operations. When variability, downtime, rework and other complexities are present, DES becomes all the more important.

The financial results - Margin (￡) and Margin Per Unit (￡) - are calculated by assuming the following financial figures. Sale Price = ￡500 per unit. Material Cost = ￡450 per unit. Labour Cost = ￡15 per operative per hour. Each station has an operating cost of ￡250 per day, and there is an overhead of ￡1,000 for the manufacturing facility.

It is clear from the chart above that output (Units / Day) does increase with the number of stations (and operatives), but NOT in a linear fashion. Besides, option D, with 6 stations has the highest Operating Margin (￡), but it doesn't always increase proportionately.

The results depend on the cost structure of the operations, and the MILP solution obtained for the Assembly Line Balancing Problem. What it means is that it is not always possible to distribute the work evenly in all scenarios. Whilst the option D has a bottleneck duration of 6 mins, it doesn't decrease proportionately for option E (6 mins) and option F (5 mins).

Three more line designs have been analysed for further analysis:

• Option G - It's a 2x replication of Option 5 in the same facility.
• Option H - which is Option E, with 1 operative each added to stations 1, 2, 5 and 6.
• Option J - which is Option F, with stations 1-2, 4-5 and 6-7 joined together, and staffed with 3, 2 and 3 operatives respectively (see Fig.5).

The results for Options G, H and J, each with 10 operatives, are shown in the Table 2 below. Option H has the best results, for all parameters - Units / Day. Margin and Margin Per Unit.

Note that Line Redesign illustrated in this example is not the only way to scale operations. As indicated earlier, there are other ways, such as increasing the number of shits, replicating lines, locations, etc, or a combination of them all, each having it's own advantages and disadvantages. The key is to come up with the best options, and calculate the figures - both operational and financial - and evaluate them against factors such as feasibility, investment required, and risks.

Do not use spreadsheets and hand-calculations. They are not reliable especially in cases where MILP optimisation and DES are more suited. You will need a proper, thorough, and scientific analysis, in order to make practical decisions.

Get in touch if you need help to scale up your operations, or make them efficient. Contact, Moses Gummadi at [email protected], or send a DM in my LinkedIn profile.