These two constraints also need to be expressed as equations. You might say, for example, that because you must maintain your team’s expertise in both raw land development and residential contracting that you want to develop at least 10 lots every year and build at least 5 houses. Suppose that as a matter of policy you want to maintain a certain level of activity both in developing lots and building houses. Typically, you also have policy constraints when you work with an optimization-modeling problem. Again, the less than or equal to symbol is represented by the This formula says the result of the formula 80 times the number of lots plus 200 times the number of houses must be less than or equal to the bulldozer-hours limit of 3,000. The bulldozer capacity constraint can be expressed as follows: The less than or equal to symbol is represented by the This formula says the result of the formula $50,000 times the number of lots plus $25,000 times the number of houses must be less than or equal to the working capital limit of $1,200,000. For example, the working capital constraint can be expressed as follows: These two constraints can also be expressed as equations.
The fact that you have a single bulldozer available for only 3,000 hours each year also limits the number of lots and houses you can annually sell because every lot requires 80 hours of bulldozing and every house requires 200 hours of bulldozing.
Your working capital of $1,200,000 limits the number of lots and houses you can annually sell because every lot requires a $50,000 cash investment and every house requires a $25,000 cash investment. To continue with the fictional case of residential development, suppose that you have two principal limiting fac- tors: working capital and bulldozer capacity.
Of course, any objective function is limited by certain constraints. Your princi- pal financial objective is to maximize your profits, and this objective can be expressed as an objective function, or equation, that you want to maximize: Suppose that you make $20,000 on each home you build and $15,000 on each building lot you develop and then sell. You create and sell two products: building lots and houses. Suppose, for example, that you’re a residential real estate developer and contractor. While this abstract definition sounds complicated, at least at the conceptual level, optimization modeling makes common sense once you provide a concrete example.ĮasyRefresher: How Optimization Modeling Works With an optimization-modeling problem, you want to optimize an objective function but at the same time recognize that there are constraints, or limits. Nelson Leave a Comment Excel’s Solver tool lets you solve optimization-modeling problems, also commonly known as linear programming programs. Optimization Modeling with Solver in Excelīy Stephen L.
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