Analysis by department heads

Discuss about the Coverage Based on Integer Linear Programming.

The company departments heads carried out analysis on their respective areas in order to come out with proper and effective results of enhancing production in the company.

Firstly, Jaan a production manager conducted a random sampling as a part of the consignment whose aims was to determine the quality of beans. The estimation was about 20% of the consignment which was Grade “A” that is regarded as the best available, what remained was Grade “B”. The agreed delivered price to the factory is $ 18,000 per tonne of powder. However, the standard used by Jaan were personal hence it could have never been documented rating system, moreover, there was on the relationship between Jaan’s rating and the agreed purchase price per tonne.

Secondly, Ian the sale manager of Noccio determined all the premium bars that Noccio could have managed to produce. This premium bar was manufactured from the finest powder and ingredients, essentially, other two products had a limitation on markets..

Finally, Mal finance head prepared a pro-form statement about profit. Where calculation of profit contribution of each product was done, on its analysis he noted that the chocolate sauce product hard to make losses that year.

The total revenue is determined by multiplying the sales volume in box  in the optimum product mix table by their  respective sales revenue in sales cost per unit table.

Optimum Product Mix:
Particulars	Premium Bars	Chocolate Sauce	Dark Couverture	Total Consumption
Maximum Demand	37777	50000	80000
Sales Volume (in box)	37777	0	80000
Cocoa Powder (kgs/Box)	0.18	0.2	0.25
Total Cocoa Powder Required	6799.86	0	20000	26799.86
Sales & Cost Details per Unit:
Particulars	Premium Bars	Chocolate Sauce	Dark Couverture
Sales Revenue	$12	$14	$11

Particulars	Premium Bars	Chocolate Sauce	Dark Couverture	TOTAL
Total Sales Revenue	$453,324	$0	$912,000	$1,365,324

The total cost is determined from the addition of the direct labour, variable overhead, variable selling, Cocoa, packaging and allocated overhead.

Direct Labor	$133,731	$0	$129,600	$263,331
Variable Overhead	$27,199	$0	$62,400	$89,599
Variable Selling	$45,332	$0	$91,200	$136,532
Cocoa	$122,397	$0	$360,000	$482,397
Packaging	$79,332	$0	$184,800	$264,132
Allocated Overhead	$407,992	$0	$828,000	$1,235,992
Total Costs	$439,724	$0	$883,200	$1,322,924

The total value of the Cocoa powder required was determined by multiplying the sales volume in boxes by the kilogram of Cocoa powders in box, and the value of the Cocoa powder required in production of premium bars were 6799.86, while for the chocolate sauce was 0 and finally for the Dark Couverture was 20000, therefore the total consumption for all this values was 26799.86

Particulars	Premium Bars	Chocolate Sauce	Dark Couverture	Total Consumption
Maximum Demand	37777	50000	80000
Sales Volume (in box)	37777	0	80000
Cocoa Powder (kgs/Box)	0.18	0.2	0.25
Total Cocoa Powder Required	6799.86	0	20000	26799.86

Using a linear programing solver the profit of the value $480,000 was determined when the sales volume of premium bars were 33333, while the sales volume chocolate sauce is 0 and the sales volume of the dark couverture was 80000.

Objective Cell (Max)
	Cell	Name	Original Value	Final Value
	$E$41	Net Profit TOTAL	40800	40799.88
Variable Cells
	Cell	Name	Original Value	Final Value	Integer
	$B$15	Sales Volume Premium Bars	33333.33	33333	Integer
	$C$15	Sales Volume Chocolate Sauce	0	0	Integer
	$D$15	Sales Volume Dark Couverture	80000	80000	Integer
Constraints
	Cell	Name	Cell Value	Formula	Status	Slack
	$B$17	Total Cocoa Powder Required Premium Bars	5999.94	$B$17<=$B$5	Not Binding	0.06
	$C$17	Total Cocoa Powder Required Chocolate Sauce	0	$C$17<=$B$8	Not Binding	30000
	$D$17	Total Cocoa Powder Required Dark Couverture	20000	$D$17<=$B$6	Not Binding	4000
	$E$17	Total Cocoa Powder Required Total Consumption	25999.94	$E$17<=$B$8	Not Binding	4000.06
	$C$15	Sales Volume Chocolate Sauce	0	$C$15<=$C$14	Not Binding	50000
	$D$15	Sales Volume Dark Couverture	80000	$D$15<=$D$14	Binding	0
	$B$15:$D$15=Integer

The net profit determined must be too be equivalent to getting the difference between the total revenue and the total cost

Net profit = $1,311,996 – $1,271,196 = $40,800

Using the linear programing solver the value of the total cocoa powder required in premium bars is 5999.94, while the total cocoa powder required in Chocolate sauce is 0, while the total cocoa powder required in dark couverture is 2000, while the total Cocoa Powder Required Total Consumption 25999.94 also the sales volume Chocolate Sauce is 0 and finally the sales Volume Dark Couverture is 80000

Constraints
	Cell	Name	Cell Value	Formula	Status	Slack
	$B$17	Total Cocoa Powder Required Premium Bars	5999.94	$B$17<=$B$5	Not Binding	0.06
	$C$17	Total Cocoa Powder Required Chocolate Sauce	0	$C$17<=$B$8	Not Binding	30000
	$D$17	Total Cocoa Powder Required Dark Couverture	20000	$D$17<=$B$6	Not Binding	4000
	$E$17	Total Cocoa Powder Required Total Consumption	25999.94	$E$17<=$B$8	Not Binding	4000.06
	$C$15	Sales Volume Chocolate Sauce	0	$C$15<=$C$14	Not Binding	50000
	$D$15	Sales Volume Dark Couverture	80000	$D$15<=$D$14	Binding	0

Optimum product mix

When determining the number of boxes that would be produced for each of the product, it was found that 33333 boxes would be required in order to pack the premium chocolate bars and 80000 boxes would be required in order to pack the dark couverture. In case of packing the chocolate sauce, there are no boxes required and therefore in an overall manner it is observed that there is a requirement of 113333 boxes in order to pack all the chocolates and thereafter offer for sales in the market. The linear program for the same is given below:

Max 12A + 14B + 11C

Where, 0.18A <= 6000 kgs.

0.2B <= 30000 kgs.

0.25C <= 24000 kgs.

0.18A + 0.2B + 0.25C <= 30000 kgs.

The total amount of cocoa powder that was purchased for the purpose of manufacturing was 30000 units and the overall expense for the same was $540,000. However, it is observed that the overall consumption of cocoa that was used in order to manufacture the chocolate bars, chocolate sauce and dark couverture was found to be 25999.94 units. Therefore there has been an observation that approximately 4000 units of cocoa remains unused and therefore gets wasted and the cost that was associated with the amount of cocoa was an additional expense. Therefore, steps and strategies were required to be taken with the help of which the wasted cocoa can be used or this amount can be reduced as well.

Particulars	Unit	Amount
Grade A	6000	$108,000
Grade B	24000	$432,000
Total Cocoa Powder (in kgs.)	30000	$540,000
Additional Cocoa (in kgs.)	800
Total Cocoa Powder (in kgs.)	30800	$540,000

Optimum Product Mix:
Particulars	Premium Bars	Chocolate Sauce	Dark Couverture	Total Consumption
Maximum Demand	37777	50000	80000
Sales Volume (in box)	37777	0	80000
Cocoa Powder (kgs/Box)	0.18	0.2	0.25
Total Cocoa Powder Required	6799.86	0	20000	26799.86

Itn accordance to the current strategy which was a fixed volume agreement, there have been wastage of approximately 4000 units of cocoa for which a certain amount of money was invested. The maintenance of the fixed volume agreement refers to the fact that in each month and year the company would be purchasing the same unit of cocoa irrespective of the fact that whether they are able to optimally make use of the total amount of cocoa purchased. Hence, it is agreeable that variable volume contract can be taken into consideration. Therefore, it would be better for the company to shift their intention from the fixed volume agreement to the variable volume of contract in which the company would be able to purchase the raw material based on the demand in the market and the amount of production they would undertake. In this manner, the unit of cocoa can vary according to the demand of the final product and thereby the amount of wastage can be reduced and the additional cost that was added with the wasted material can be mitigated. It is even seen that the company would be able to optimally make use of their resources and in this manner would be able to enhance their operational activities and their effectiveness in production.

Sales and cost details per unit

In case variable volume contracts were undertaken, it could be essential for Steve to negotiate a different pricing model because of the fact that the supplier want to sell a specific amount of unit. In this manner, the incorporation of a different pricing model was essential with the help of which an effective price for the product could be created with the help of which the supplier was able to gain certain amount out of the expected money they have anticipated and a price that would be over the actual rate but would be less than the overall money paid earlier which was inclusive of the unit of cocoa that remained wasted. A price that would be able to satisfy the demands of the customer and the supplier would be an effective one for the maintenance of the current relationship and none of them facing an impact for the change in the purchase agreement.

It was found out that the amount of production would increase and the overall consumption of use of the cocoa powder would increase from 25999.94 units to 26,799.86 units. In this manner it was found that the overall consumption would increase and there would be a rise in the total net profit for the company by $1,600. Hence, taking up the additional 800 kg would be beneficial. The company can purchase 6000 units by not changing the basis of the solution. The linear program for the same is stated below:

Max 12A + 14B + 11C

Where, 0.18A <= 6800 kgs.

0.2B <= 30000 kgs.

0.25C <= 24000 kgs.

0.18A + 0.2B + 0.25C <= 30800 kgs.

The extent of sensitiveness for the preferred product was similar to the product mix that was available earlier because of the fact that with the addition of the extra 800 kg only the extent of overall consumption has changed but the sales and cost has remained similar to the one that was seen earlier.    

Conclusion

In conclusion allocation of the cost of powder to the three products raised some discomfort, it was not realistic for cocoa powder to be allocated to each product using the same cost in every kilogram, this was considered from the point of view that Premium Bar only contained Grade A while Couverture was Grade B. Suggestion were raised on if it was good for the company to be more aggressive in negotiations with the suppliers in terms of paying less for grade B powder. After calculation of the marginal contribution in regard to price different between Grade A and B

It is recommended that for the company to enhance its profit then the company should reduce investment in premium bar and in that case more effort and concentration should be placed majorly supplying it on chocolate cafes, chocolate sauce and couverture.

Reference

Ezzati, R., Khorram, E. and Enayati, R., 2015. A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Applied mathematical modelling, 39(12), pp.3183-3193.           

Zhang, Y., Sun, X. and Wang, B., 2016. Efficient algorithm for k-barrier coverage based on integer linear programming. China Communications, 13(7), pp.16-23.