Establishing direct link between shop floor operations and profitability
In my perspective, an optimal manufacturing operations should be economically choosing machining conditions to meet required specifications. What the word “economically” means here is that the algorithm should be taking costs into account as well. To many, it may seem to be simply a matter of selection however this planning is a decision-making process to fully AND economically utilize the manufacturing environment and available resources in production.
The current state and its drawback
I made a post on LinkedIn a couple of weeks ago regarding advising a footwear manufacturing company on opportunities to leverage manufacturing analytics. While this scenario would have been too futuristic for them (so did not include this in my proposal), I ended up using data from their shoe buckle manufacturing line to experiment. This line manufactures Steel buckles of all sizes for many shoe lines for both Men and Women. A sample data file for parameters collected for this line are below and the cost explanation is in the Appendix section (Appendix B). We will focus on this line, which is a cutting operation, to discuss our expert system algorithm.
The way it currently works in most manufacturing processes is that the decision maker usually starts by identifying feasible range of system parameters. For this specific line, the first priority is usually given to the determination of feasible ranges of three cutting parameters to assure the product quality:
- Cutting speed
- Depth of cut
Afterwards, alternative plans may be formed within the identified feasible ranges to guarantee that these alternative plans are meaningful and practical. The final plan selected for a given part is a function of a preset goal.
With a Smart Fcatory setup, manufacturing planning is not only a matter of core operations data. Cost analysis to evaluate the variable and fixed costs associated with the manufacturing operations is critical to a good plan. The planning should also be related to making an apprasisal for the justification of possible technical and economical benefits from adopting new manufacturing technologies.
The Architecture for the Simulation experiment
The figure below shows the high level structure of my solution. Any data that was not provided by the company, I made something up for the experiment. The first element in the architecture is a classic scenario generator, like the ones you have in simulation models, which is built on the manufacturing system to provide qualified plans. The second element is a cost analyzer to identify and evaluate components of fixed and variable costs. The third element is an optimizer to select the optimal plan based on the prescribed criterion from the management. The fourth element is the comparator to test the optimality and to assess the validity of adopting new and advanced machining operations from an economic perspective.
The feedback path from the comparator to the alternative generator determines the direction and amount of change in the three cutting parameters for improvement, and thuse closes the optimizing loop. The whole loop interacts with its surrounding environment mainly through the market which reflects the demand and price of the part to be machined. The corresponding system dynamics diagram is below:
Applying the theory to real life
Raw Data from buckle line (sanitized, specifically the cost data is made up to respect client confidentiality): BuckleLine
The key relationships that among various parameters have been shown in the graph below (generated using visme.co, check out the site, very useful for generating graphs to wow your boss 😎 Accidentally stumbled upon this website):
This graph above captures relationships between production time as a function of Machining time, Fractional tooling time and Auxiliary time. Key relationships are summarized below. Would be interested to see what other granualr relations can you find from the attached data ?
Relation between production time and cutting speed
The production time is found to fluctuate as the cutting speed varies from 30 m/min to 145 m/min. It reaches its minimum value of 3.08 min/piece at a cutting speed of 95 m/min. If the first five columns of data in our table are observed, as shown in the graph below, the machining time decreases significantly as the cutting speed used grows large. However, with the same increase in cutting speed, the fractional tool changing time needed for maintaining a workable cutting edge during machining increases accordingly.
This is due to a short tool life resulting from machining at a high cutting speed. In fact, the minimum production time is a compromise between the machining time and the fractional tool changing time, both of which are functions of cutting speed.
Relation between Total Unit cost and cutting speed
Before you go further, please refer to the primer on cost calculations used in the experiment in the appendix of this post.
The total unit cost is also found to vary as the cutting speed increases from 30 m/min to 145 m/min. It reaches its minimum value of INR 4.07/piece at cutting speed = 75 m/min. The drivers behind this are:
- A lower unit fixed cost as compared to those produced at cutting speeds lower than 75m/min. This cost is listed as INR 1.89/piece.
- A lower unit vaiable cost as compared to those produced at cutting speeds higher than 75 m/min. This cost is listed as INR 2.19/piece.
Relation between operating profit and cutting speed
Obviously a major goal of manufacturing is to support the organization to attain profits. A system dynamic example depiction of role of profit during manufacturing operations and the cost analysis of the experiment is shown below as well in the form of a graph.
Appendix A: Our case study example
If you are a manufacturing professional, you know that cutting speed plays a major role in both quality of machined parts and machining tools. In this case study, we will analyze cost and productivity of machining operations run under different cutting speeds. The parameters for our case study are:
- Material: AISI 1035 steel
- Diameter 56mm (initial) 60mm (final)
- Length: 250mm
- Material: Carbide
- (tr abd vr): (100 min, 80 m/min)
- exponent n: 0.2
- Tool cost: INR 25/piece
- Changing time: 15 min
- Capacity: 175 hours/month
- Fixed Cost: INR 6000/month
- d limit: 2mm
- Feed: 0.25 mm/rev
- Auxiliary Time: 25% (Machining time)
- Monthly Demand: 4000 pieces
- Wage Rate: INR15/hr
- Overhead: INR10/hour
- Holding Cost: INR 1/piece
- Revenue: INR 9/piece
Appendix B: Identifying relationships to costs:
MT = Machine Time
PT = Production time
TL = Tool Life
Machining Cost = (Wage Rate + Overhead) X MT
Tooling Cost = MT/TL x (Tool Cost) + MT/TL x (Changing Time) x (Ware Rate + Overhead)
Auxiliary Cost = (Wage Rate + Overhead) x (Auxiliary Time)
Inventory Cost = Holding Cost [ ((No of Machines)(Capacity Hours) x 60)/PT – Monthly Demand]
where Production Time = PT = MT + MT/TL x (Changing time) + Auxiliary Time
Unit Inventory Cost = Inventory Cost / ((No. of Machines)(Capacity Hours) X 60 /PT)