Business Problems with Yes/No Decisions
In prescriptive analytics, yes or no decisions are modelled with binary variables.
Business problem 1:
A company is considering using magazine outlets for an advertising campaign. The company has identified seven publishers. Each publisher breaks down the subscriber base into a number of groups based on demographics and location. The company has set a budget for the advertising campaign and wants to maximize the number of subscribers exposed to its ads. The company wants to determine which publishers to select and how many groups to purchase from each publisher. Clearly, the selection of a publisher requires a yes or no decision. That is, a publisher is either selected or not. Once a publisher is selected, a second decision must be made regarding the number of subscriber groups to purchase. The model for this problem must take into consideration that no subscriber groups can be purchased from a publisher that has not been selected. It also must consider that when two publishers are competitors, the company wants to select amongst one of them. Finally, the model should take into account that there is a fixed cost for engaging a publisher. This fixed cost is paid for every publisher that the model selects. The binary decision variables can be used to model all these constraints.
Business problem 2:
A company's establishing a new business to serve customers in a region around the Cincinnati, Ohio area. The company has identified 16 key market areas and wants to establish regional offices to meet the goal of being to able to travel to all key markets within 60 minutes. The company has gathered data on travel times, in minutes, between each pair of cities and would like to create a model to answer the following questions. What is the minimum number of regional offices required to meet the company’s goal? Suppose that the company changes the goal to 90 minutes. So what will be the best solution? How many markets can be covered with 4 regional offices within a travel time of 60 minutes? The answers to these questions would help the company establish an original office network that balances service and cost. While being within 60 minutes of all these customers may be desirable, the cost may be too high. A model for this problem would require yes or no variables, one for each location. The value of these variables will indicate whether or not to choose the location to establish a regional office. Given a table of travel times, it can be determined the set of cities covered by a location that is selected for a regional office.
Business problem 3:
Forest planning models prescribe which areas to harvest to identify demand in each period over a planning horizon. Ideally, forest planning models would include environmental concerns related to wildlife protection, erosion, water quality, and preservation of scenic beauty. However, analysts have not found a direct way of formulating these multiple concerns in models to determine harvest patterns. Instead, proxy management options have been established. The most common is the so-called adjacency, or maximum opening harvesting constraint. These constraints establish the maximum contiguous area that may be harvested in a given time period. Neighbouring areas can then be harvested only when the trees in the first area have grown to a minimum size. The resulting patterns help with wildlife protection. For example, elks will not feed on openings created by harvesting unless they are relatively near the protection provided by grown trees. Mandated maximum contiguous areas that can be harvested are between 75 and 125 acres, depending on the country or region. Forest engineers configure harvesting blocks within the maximum allowed area. Models that create visible harvesting patterns require yes or no decisions to select the blocks to be harvested and to impose the adjacency constraints.
Business problem 1:
A company is considering using magazine outlets for an advertising campaign. The company has identified seven publishers. Each publisher breaks down the subscriber base into a number of groups based on demographics and location. The company has set a budget for the advertising campaign and wants to maximize the number of subscribers exposed to its ads. The company wants to determine which publishers to select and how many groups to purchase from each publisher. Clearly, the selection of a publisher requires a yes or no decision. That is, a publisher is either selected or not. Once a publisher is selected, a second decision must be made regarding the number of subscriber groups to purchase. The model for this problem must take into consideration that no subscriber groups can be purchased from a publisher that has not been selected. It also must consider that when two publishers are competitors, the company wants to select amongst one of them. Finally, the model should take into account that there is a fixed cost for engaging a publisher. This fixed cost is paid for every publisher that the model selects. The binary decision variables can be used to model all these constraints.
Business problem 2:
A company's establishing a new business to serve customers in a region around the Cincinnati, Ohio area. The company has identified 16 key market areas and wants to establish regional offices to meet the goal of being to able to travel to all key markets within 60 minutes. The company has gathered data on travel times, in minutes, between each pair of cities and would like to create a model to answer the following questions. What is the minimum number of regional offices required to meet the company’s goal? Suppose that the company changes the goal to 90 minutes. So what will be the best solution? How many markets can be covered with 4 regional offices within a travel time of 60 minutes? The answers to these questions would help the company establish an original office network that balances service and cost. While being within 60 minutes of all these customers may be desirable, the cost may be too high. A model for this problem would require yes or no variables, one for each location. The value of these variables will indicate whether or not to choose the location to establish a regional office. Given a table of travel times, it can be determined the set of cities covered by a location that is selected for a regional office.
Business problem 3:
Forest planning models prescribe which areas to harvest to identify demand in each period over a planning horizon. Ideally, forest planning models would include environmental concerns related to wildlife protection, erosion, water quality, and preservation of scenic beauty. However, analysts have not found a direct way of formulating these multiple concerns in models to determine harvest patterns. Instead, proxy management options have been established. The most common is the so-called adjacency, or maximum opening harvesting constraint. These constraints establish the maximum contiguous area that may be harvested in a given time period. Neighbouring areas can then be harvested only when the trees in the first area have grown to a minimum size. The resulting patterns help with wildlife protection. For example, elks will not feed on openings created by harvesting unless they are relatively near the protection provided by grown trees. Mandated maximum contiguous areas that can be harvested are between 75 and 125 acres, depending on the country or region. Forest engineers configure harvesting blocks within the maximum allowed area. Models that create visible harvesting patterns require yes or no decisions to select the blocks to be harvested and to impose the adjacency constraints.
