The Optimisation of Chorley Fabrics - Essay Example

1. Introduction Chorley Fabrics Ltd. (hereafter CFL) manufactures a range of ten fabric types. Each has its own method of production, marketing, etc.The company uses five different machines to extract the fabrics through two raw materials. The purpose of this paper is to produce a report to aid CFL in the optimisation of its process and the increase in profits through analysing various aspects of the manufacturing process. 2. Basic Information These main attributes include a) the time the machines are in use, b) labour and material concerns or requirements and c) availabilities of the above in addition to labour. Weekly contractual obligations will also need to be taken into consideration, in addition to the maximum market demands for each product. 3. Profits and Costs The table shown below details the initial optimal production schedule: Product Amount Prof/unit Profit X1 15 210 3,150 X2 28 190 5,320 X3 2 105 210 X4 0 120 0 X5 9 150 1,350 X6 4 100 400 X7 3 110 330 X8 24 210 5,040 X9 22 220 4,840 X10 11 160 1,760 Total 22,339 The amount of units to produce was acquired by taking the values of the availability of resources (from another table) and the usage of resources per product. This was divided into the former to get a quotient: the maximum use of resources. Both Stevenson (2005)1 and Middleton (2006)2 explain how to use Excel in this fashion via the Solver tool. After this, the amount of units produced was multiplied by the profit per unit to obtain the value for total profit. Going by the chart above, we can see that only five of these products are produced in significant amounts and are therefore able to make a worthwhile profit. X1, X2, X8, X9 and X10 are the profit bringers, and thus they should be placed on the schedule in order of profit received, starting from the highest: X2, X8, S9, X1 and X10. The others, as there is little profit from them, should be moved to the bottom of the list. X4 can likely be eliminated altogether. 4. Usage of Resources The first table below will show the usage of each resource in relation to each product. Product M/C 1 M/C 2 M/C 3 M/C 4 M/C 5 Mat 1 Mat 2 Labour X1 1.8 1.6 2.8 2.1 2.0 7.0 11.9 1.1 X2 1.2 1.0 3.0 1.1 1.0 7.0 2.0 1.4 X3 2.1 1.2 3.2 1.1 3.0 1.0 18.0 1.2 X4 1.9 2.2 2.9 2.1 0.5 3.0 11.0 1.0 X5 2.1 1.5 2.8 1.2 3.0 1.1 15.0 2.0 X6 1.0 2.0 2.1 1.2 1.5 7.0 10.0 1.0 X7 3.2 4.0 1.2 1.3 1.0 5.0 10.0 2.1 X8 4.8 1.0 0.9 1.3 2.0 7.0 0.0 2.0 X9 5.6 3.3 2.1 2.8 5.0 1.0 10.0 1.1 X10 3.2 2.1 3.8 3.1 6.0 5.0 8.0 2.2 From this, using the SUMPRODUCT formula, which adds the sums of products of corresponding arrays, it can then be determined how much of each resource is used per week. For example, X1 can have 15 units produced, at a cost of 1.8 units in M/C 1. Unit 2 can have have 28 units, at a cost of 1.2 in M/C 2, and so on down the list. All these values are added up to get the total usage of resources. Alternatively, all values in the row corresponding to each product can be added to get the total cost per unit. Resource Usage Available M/C 1 369.75 400 M/C 2 206.75 250 M/C 3 280.00 280 M/C 4 212.82 270 M/C 5 324.00 340 Mat 1 600.00 600 Mat 2 780.00 780 Labour 182.80 229 This table denotes the usage of all resources, based upon the values gained from the procedure described above. Going by this, it can be seen that M/C 3 and both raw materials are used to optimum efficiency. There is no surplus or deficit. M/C 2 and M/C 4, hwever, are lacking; there is a a period of 44.3 hours left over for 2, and a period of 57.2 hours for 4. M/C 1, 3, and 5 are used efficiently; there is little available time left for them. 5. Marginal Benefits Resource Final Value Marginal Benefits Constraint R.H. Side Allowable Increase Allowable Decrease M/C 1 Usage 369.75 0.00 400 1E+30 30.24822533 M/C 2 Usage 206.84 0.00 250 1E+30 43.15699565 M/C 3 Usage 280.00 7.93 280 7.303252788 14.80479303 M/C 4 Usage 212.84 0.00 270 1E+30 57.15903366 M/C 5 Usage 322.01 0.00 340 1E+30 17.99473323 Mat 1 Usage 600.00 13.98 600 65.70689655 61.87637795 Mat 2 Usage 780.00 7.49 780 82.26876513 75.41554703 Labour Usage 181.85 0.00 229 1E+30 47.1511564 The table above depicts each resource item and how much increase may be made. It may be seen that Machines 3, Material 1 and 2 are optimally used, thus the marginal benefits are positive number. For machine 3, the machine time is saturated. Increase in machine time might be a good idea to increase profit about 7.9. However, significance of maintenance and wear-tear has to be considered. As for Machine 1,2,4,5 and labour, the value of marginal benefits are zero. This is because these resources are still beyond optimization. Thus, there should be focus on optimizing these resources. Meanwhile, for Material 1 and Material 2, the usage has reached equivalence with its availability. In order to find market demand, the formula P = Da*Q + Db is used, where P = price, Da is the slope of the equation (or in this case, cost/profit ratio per unit), Q is the quantity of the product to be sold and Db is the price for selling zero units; that is to say, the cost of producing them without garnering any profit. Income will be derived from the equation I = Da*Q^2 + Db*Q, in which the values are the same as for the demand equation. This will be a curve, due to the law of diminishing return on investment. Marginal cost and benefit will then be calculated - marginal meaning the change if one more unit were to be produced or sold. For example, all the resources tallied up for product X1 comes to a cost of 30.1 units. This is its marginal cost. Marginal rate of return, or marginal benefit, abides by the principle that 'it is worthwhile for a producer to continue investing up to the point at which the return per unit invested equals the cost.' (Evans 2005)3 6. Contractual Obligations Final Value Marginal Cost Over Supply Market Demand Allowable Increase Allowable Decrease X1 Min.con 15.07 0.00 15.07 0 15.07121594 1E+30 X2 Min.con 28.00 0.00 23.00 5 23 1E+30 X3 Min.con 2.00 69.26 0.00 2 7.044362292 2 X4 Min.con 0.00 0.00 0.00 0 0 1E+30 X5 Min.con 8.73 0.00 8.73 0 8.726814747 1E+30 X6 Min.con 4.00 89.46 0.00 4 13.07299633 4 X7 Min.con 3.00 44.36 0.00 3 9.554164137 3 X8 Min.con 24.00 0.00 24.00 0 24 1E+30 X9 Min.con 22.00 0.00 20.00 2 20 1E+30 X10 Min.con 10.78 0.00 7.78 3 7.780398441 1E+30 Based on the table above, the products are able to comply with its contractual obligations. Certain products, however, are not optimised in terms of profit, and their continued production is questionable. If the company intends to continue the production of these products, a loss will occur in future. After all, 'a company will not produce a product simply because it is expected to break even.' (Holland 1998) 4 By producing the output where the marginal revenue equals the marginal cost, the firm maximizes economic profits." (Watkins 2006)5 Based on the table above, X3, X6, and X7 are liabilities. For instance manufacturing X6 causes a loss of 89.46. And in producing 4 maximum allowable units, the total loss is equal to 357.84. Final Value Marginal Benefit Marketing Demand Excess Demand Allowable Increase Allowable Decrease X1 Max.con 15.07 0.00 45 29.93 1E+30 29.92878406 X2 Max.con 28.00 53.35 28 0.00 7.404009587 4.639175868 X3 Max.con 2.00 0.00 18 16.00 1E+30 16 X4 Max.con 0.00 0.00 20 20.00 1E+30 20 X5 Max.con 8.73 0.00 27 18.27 1E+30 18.27318525 X6 Max.con 4.00 0.00 34 30.00 1E+30 30 X7 Max.con 3.00 0.00 35 32.00 1E+30 32 X8 Max.con 24.00 105.00 24 0.00 6.888829785 9.599496222 X9 Max.con 22.00 113.63 22 0.00 7.813808769 20 X10 Max.con 10.78 0.00 20 9.22 1E+30 9.219601559 The table above shows the market demand for each product and the amount of each that is currently being manufactured. It also presents the marginal benefits from each product type. Following from this, if a particular product has a final value that is at par with the market demand, this suggests that it has adequate demand and consumer following in the market and is therefore worth continuing. The most viable option is to win more market share for the product; more sales will lead to more profit. X2, X8 and X9 are, as stated before, the most valuable products, whereas the rest hold no benefit. X9 merits special focus. 7. Recommendations Following the discussion on resource utilisation, market demand, and contracts, the following recommendations are put forth: 1. There should be an increase in the usage of M/C2, M/C4, and Material 1 that will enable greater efficiency; Material 1 should be foremost in the list of resources to acquire. An extension of operating time may be considered for the two machines. There should be consistent maintainance to ensure functionality at all times - reduced down time means greater profits. 2. For compliance to contracts, the findings show that Products X3, X6 and X7 are not effective contributors to profit. Therefore, there should be less of these that should be manufactured, if at all. It is recommended that the marginal benefit/cost procedure outlined earlier in this paper be done. 3. X2, X8 and X9 have sufficient market demand to sustain or even grow their market shares. They already have a customer following and patronage. There should thus be focus on these products to grow market demand even further. Advertising and effective marketing programs are the key to growing the market. 8. Conclusion All these areas on resource utilization, availability of resources, and market demand must be prioritised and addressed. In carrying this out, the company shall be able to yield optimal profit from what it has invested. 9. References 1. Stevenson, W.J. 2005. Operation Management, 8th edition, International edition. McGraw Hill Irwin. 2. Evans, Edward. 2005. Marginal Analysis: An Economic Procedure for Selecting Alternative Technologies/Practices. University of Florida. http://edis.ifas.ufl.edu/pdffiles/FE/FE56500.pdf 3. Holland, Robert. 1998. Break-even Analysis. Agricultural Extension Service. University of Tennessee. 4. Middleton, Michael R. 2006. Decision Analysis Using Microsoft Excel. University of San Francisco: School of Business and Management. 5. Watkins, Tom. 2006. Economics: Decision Making. Decision Making Using Marginal Analysis. http://people.eku.edu/watkinst/Economics%20120/The%20Firm%20and%20Profit%20Maximization.doc Read More