Linear Programming Problem for Aberdeen OilTeck Firm

This report presents the case of Aberdeen OilTeck firm which engaged in the business of manufacturing of rig cleaning equipment that is used in Oil and Gas Industry. The company is producing two types of rig cleaning equipment: RigCleaner and RigBuster. The report discusses the issues related to current production schedule, increase of production capacity, and the optimum product mix point. It also suggests the adoption of overtime wage payment policy to enhance profitability.

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Case Study: Linear Programming Problem

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Introduction:
This report presents the case of Aberdeen OilTeck firm which engaged in the business of
manufacturing of rig cleaning equipment that is used in Oil and Gas Industry. The company
is producing two types of rig cleaning equipment: RigCleaner and RigBuster. Currently the
company has produced 1000 units of RigCleaner and 1500 units of Rigbuster. However, there
is a demand of 3000 units of RigCleaner and 3500 units of RigBuster in market. The
production of two units had to undergo processing in various departments such as Engine
Assembly, Metal Processing and the individual product’s assembly.
Issues related to current production schedule:
The analysis of present production data of Aberdeen has revealed that the company is not
utilising its maximum capacity of Metal stamping and RigCleaner Assembly department.
Both the said departments had surplus hours remained after producing the 1000 and 1500
units of RigCleaner and RigBuster department respectively. Hence, the current production
mix of the company cannot be said to be optimum. To determine the optimum product mix
use of Linear Programming function has been made and it has be found that in order to best
utilise the operating capacity of the company and to achieve maximum profitability, the
product mix of 2000 units of RigCleaner and 1000 units of RigBuster must be maintained
(Dantzig, 2016).
The new product mix will increase the profits of the company by $ 4800000. With the
existing product mix company could only meet its variable costs and fixed costs and no
profits were generated in the business. However, by rescheduling the production mix, the
profit of $ 48000000 could be made, given the total production capacity.

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Issues related to increase of production capacity:
At the optimum production mix point also, the demand of the market could not be fulfilled
completely due to the limitation of production capacity of the company as a whole. The factor
that will be constraint in engine assembly and metal stamping departments of the company
will be machine hours as they are being operated at the maximum capacity. The labour
resource is easily available in the market and this can deployed in the quantum in which it is
necessary to serve the total external market demand.
The capacity of engine assembly department is utilised in full as the number of required
hours to produce the current production mix is equal to the number of available hours.
However, when it comes to producing the units, up-to the external market demand, the
company does not have sufficient capacity.
At the level of optimum mix i.e. 2000 units for RigCleaner and 1000 units of RigBuster, the
best product mix, with the increase in the capacity of engine assembly department by one
hour i.e. from 4000 hours to 4001 hours will remain same because metal stamping which is
also an indispensible process which is required to be undertaken in the manufacturing of both
the products, would be operated at its maximum capacity. Hence, it would not be possible to
stretch its capacity even marginally.
At the existing production level, only total costs of operating the business are being recovered
and no profits are earned. However, to earn the profits the company must utilise the operating
capacities of all its departments to the maximum extent. The company has an alternative
option of purchasing either of its equipment from the external market and rent out the spare
capacity for the production of other equipment.

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The maximum rent that the company must pay for each machine hour of its engine assembly
department’s capacity would be $ 300 as this is the rate at which the company is able to
deploy its engine assembly’s machine hour while producing the equipment internally.
In the present case, the department which is entrusted with the function of engine assembly
will be operated at its 100 % capacity. However, the capacity of RigCleaner Assembly
department and RigBuster Assembly department are under -utilised. Therefore, it would be a
better option to purchase either of the equipment’s engines from outside market so that spare
capacity can be utilised for the production of other equipment’s engine.
the company is presently producing 1000 units of Rigcleaner. However, the optimum units
that it must produce for RigCleaner are 2000 units to maximise the production efficiencies in
this area. On the other hand, the RigBuster is being produced in the quantum of 1500 units
whereas only 1000 units are required to achieve the optimum production of the given
capacities. Hence, the capacity utilised in producing additional 500 units (1500-1000) of
RigBuster must be rented out so that additional units of RigCleaner could be produced. In
such case maximum 1000 hours can be rented out. This has been calculated by multiplying
the spare capacity with the machine hours required to produce per unit of RigBuster.
Since the market demand of both the equipment manufactured by the company is more than
the units of such equipment that could be optimally produced using the 100% capacity of the
company. Hence, it can be said that it would be beneficial for the company to encourage
overtime working in the engine assembly department (Dantzig & Thapa, 2006).
Now, it was to be determined whether to use overtime working in RigCleaner’s production or
RigBuster’s Equipment. Since contribution per unit of RigBuster is more than that of

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RigCleaner, the overtime capacity must be utilised in producing RigBuster. Though the
utilisation of overtime hours for the production of RigBuster will enhance the labour rate per
hour by $100 per unit and the fixed overheads by $ 1.3 million, yet it will entail the
profitability of $ 5000000 and hence the company must go for the adoption of overtime wage
payment policy.
Conclusion:
From the above analysis it can be said that company’s is currently not optimising its
production efficiencies and hence it is required to reschedule its production mix to achieve
desired profitability and to meet more demand of its products in market.

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References:
Dantzig, G., 2016. Linear programming and extensions. Princeton university press.
Dantzig, G.B. and Thapa, M.N., 2006. Linear programming 1: introduction. Springer Science
& Business Media.