Linear programming (LP)
Linear programming is a methodology used in the operational management to solve problems on market allocation. In market research and management as well, LP has played a vital role in solving problems which arise from scheduling, financial planning, transportation, capital budgeting among others. Marker researchers have greatly benefited from using LP by gaining flexibility, creating applications and optimization algorithms and gaining reliability (Dorfman, 2012). Researchers have produced measurable improvements in market performance. One can count immeasurable benefits from using LP, as the mathematics contains powerful capabilities which helps in cost reduction, effective use of resources, risk reductions and improves profitability (Dorfman, 2012). In addition, managers counts benefits from optimization by gaining skills on how to focus on critical uncertainties and ways to speed up responses. In market research, LP gives solution to optimization problems where it is used in workload assignments, inventory routing and scheduling task (Dorfman, 2012). In problem solving, LP has a simple linear combination which is used in optimization problems. LP has benefits which arise from real time application such as production planning, plant layout, logistic management and equipment acquisition. It also provides computational advantages from its special structure.
For example, a market researcher can use LP in market optimization. Customers use various channels to attain the maximum value from competitors and enterprises. They buy products on cheaper channel and for this reason; the big question with marketers is how to connect customers regularly. The important thing here is to optimize budget allocation in order to achieve the objective. This is where the LP will be applied in problem formulation. For example in this case, there is a scarcity of resources and the client is focusing on allocation of optimal resources. In this example, the client is a carpenter who makes furniture (tables and chairs) but does not get higher profits as he expects. The carpenter is interested to know what he is supposed to do or else the number of chairs and tables he should make in a weekly basis to maximize net income ( Arsham, 2011).
In LP, X2 and X2 stands for tables and chairs and F1 and F2 stand for fixed costs. Therefore;
Maximize 9X1 + 6X2 – [(1.5X1 + X2) + (2.5X1 + 2X2) + F1 + F2],
Maximize 5X1 + 3X2
Maximize 5 X1 + 3 X2
=2 X1 + X2 £ 40 labor constraint
=X1 + 2 X2 £ 50 material constraint
Reference
Dorfman, R. (2012). Linear Programming and Economic Analysis. Dover Publications.
Arsham HOSSEIN (2011). Deterministic Modeling: Linear Optimization with Application,9th Edition. 2011.
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