Sherman Motor Company.docx

SHERMAN MOTOR COMPANT CASE ANALYSIS BACKGROUND: Sherman Motor Company manufactures two specialised models of truck in a single plant. It consists of four manufacturing operations: metal stamping, engine assembly, model 101 assembly and model 102 assembly. Out of the four departments Metal Stamping was operating at 56.2% of capacity and model 101 assembly was operating at only 14.8%. The sales manager suggested to stop production of model 101 trucks to improve profitability. However, the production manager suggests against dropping model 101 trucks. He believes that increasing production of model 101 trucks and cutting back on model 102 trucks will improve profitability. PROBLEM: The fundamental problem faced by Sherman motor company was to find an optimized production for both the models so as to maximize the profits because of the high fixed overhead costs. ANALYSIS: From the case we know that not all the manufacturing departments at SMC were working at their full capacity. To determine the optimal product mix, so that all the resources are efficiently used to reduce the costs, we formulate a linear programming model which was solved using excel solver to obtain the results. The main goal is to increase profits so profit maximization becomes the objective function for the LP model. We know Profit = Revenue – Cost. The selling price for model 101 is $2100 and for model 102 is $2000. The variable cost associated with each model is shown in the table below along with the overall fixed overhead cost.

MODEL 101

102

Variable overhead Direct Materials Direct Labour Total Variable Cost Fixed Cost

400 1200 200 1800

425 1000 225 1650 385000

Table 1 COST ANALYSIS

So, the objective function can be written in mathematical terms as Pmax = (2100-1800)*Q101 + (2000-1650)*Q102 -385000 ----------------------------------------- (1) We also have five constraints Metal Stamping

7Q101 + 5Q102 = 17500

-------------------------------------------- (2)

Engine assembly

Q101 + 1.99Q102 = 3333

-------------------------------------------- (3)

Model 101 assembly

Q101 ≤ 2250

--------------------------------------------- (4)

Model 102 assembly

Q101 ≤ 1500

-----------------------------------------------(5)

Also Q101 & Q102 ≥ 0 and integers. Then we use excel solver to determine the optimal solution

Table 2 OPTIMIZED MODEL

Based on Table 2 we can see that in the “optimised model “ if SMC produces 2037 units of model 101 trucks and 648 units of model 102 trucks, then it can maximise its profits and use the make efficient use of the capacity available in facility. From this we can also support the Production manager claims that producing model 101 more will increase profits, which is

about $469,174. The pro-forma profit/loss statement for the optimised model is shown in Exhibit 2. Now, if SMC management decides to outsource the engines, the constraints related to engine assembly (eqn. 3) and the associated variable cost are ignored. We again use excel solver

Table 3 OPTIMISED MODEL WITH ENGINES OUTSOURCED

From the above Table 3 we can observe that SMC can produce 1429 units of model 101 and 1500 units of model 102 and makes a profit of $1,284,286. The maximum labour and overhead charge that SMC can pay for the additional engines is the difference between profits of Table 2 and Table 3. Outsourcing charge for engines = $1,284,286 - $469,174 = $815,112 This means we if the outsourcing charges are less than $815,112 the SMC should outsource its engine assembly and vice-versa. To determine whether SMC should invest in additional engine capacity we use the sensitivity analysis report from excel solver. The table below shows the sensitivity report of the optimised model.

Table 4 SENSITIVITY ANALYSIS

INCOME STATEMENT With Assumtions* Net Sales $ 5,573,700.00 C.O.G.S $ 4,735,800.00 Contribution $ 837,900.00 SG & A* $ 695,457.00 NIBT $ 142,443.00 Tax* $ 75,494.79 Net Income $ 66,948.21

In order to generate more profits SMC should produce more model 101 trucks, but

since there is a resource constraint it is advisable to invest in additional engine capacity as is evident from Table 4. The shadow price represents the profit generated per unit increase in capacity of the limiting constraint. It is clear from the table above that if SMC has enough funds then it would be wise to invest in additional engine capacity as it generates the highest profit among all the other departments. Also, investing in both metal stamping and engine assembly is recommended as both them have some profits associated with per unit capacity increase, whereas there is no point in investing in model 101 and 102 assembly as its shadow price is zero i.e, no amount of capacity increase will have an effect on profits. CONCLUSION: To conclude, we recommend the SMC should increase the units produced of model 101 trucks and should not take the sales managers advice. Also, if the management decides to outsource engine assembly in order to remove the capacity constraint, we recommend doing so only if the cost of outsourcing is less than $815,112. If the cost is greater than this price then do not outsource. We would also recommend investing in additional engine capacity to maximise profits as is evident from Table 4 shadow price.

APPENDIX EXHIBIT 1 : Pro-forma profit/loss statement for “optimised model”