Linear Programming

1 Linear Programming The first example of linear programming would be optimizing transportation rules. In the first instance, firms have supply chain networks of suppliers and intermediaries, ensuring that raw materials and other inputs get to the business for subsequent processing or utilization. The movement of goods or services from one point to the next benefits from linear optimization models that will eliminate most waste and provide several alternative arrangements to prioritize different aspects of such a network. If response becomes a priority and competitors are moving fast in their rivalry, then such a factor could be adjusted for the output from the model to be relevant. The same is true for other possible constraints used in the model to make a practice decision-making solution for transport routes in a supply chain network.

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2 Secondly, we can also use inventory management as another application area where optimization models are helpful. Stocks fly off the shelves faster than the team responsible for restocking can keep up, and the business ends up making losses because of lost revenue. When new stock arrives and is ready for sale in stores, the demand is no longer there, and the business has to incur expenses for storage and maintenance of related services. On the other hand, optimization will best use available warehousing and transport regarding stock storage and movement to ensure they align with demands from the distribution side of the business or the lower ends of its value chains. The linear optimization model increases the propensity to have the right fit for the different expectations, resulting in a smooth inventory flow across various demand cycles, business conditions, and inventory availability conditions.

The last application area would be production planning and scheduling, where in factory settings, machines, workers, and processes are in harmony due to linear optimization models.

The production capacity is the primary constraint. However, this capacity is also a function of the workers available, the status of their productivity, the technologies in use, the way they contribute to worker productivity, and the challenges to be expected, such as weather, since they affect the production process. There are also forward-facing services depending on the stock demand, the strategies for pushing towards production goals, and any challenges or opportunities arising. While the plan to be productive is often straightforward, the real-world conditions are dynamic, and that is where the optimization model shines. Multiple constraints, such as input, capacity, time, and demand, fit into a specific objective function. They can pave the way for automation to give a business competitive advantages (Anderson et al., 2016).

Reference

3 Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. L., Fry, M. J., & Ohlmann, J. W. (2016). Quantitative methods for business with CengageNOW (13th ed.).

Cengage Learning.

4 Discussion #2 I can think of the ride-hailing industry where companies offering automated taxi-hailing features seek to optimize operations. The overall basis is to match customer numbers with drivers, focusing on location, time, and car type. The things worth minimizing are wait times, travel distance, and operating expenses. Based on this problem understanding, I can develop a solution based on the shortest route linear programming model for such a business case.

Companies in this industry seek to optimize their operations and earn the most revenue for the longest time. They can benefit from dynamic ride matching, where passenger activity is continuously analyzed with all relevant meta-data, such as history, location, and driver conditions, which results in optimal matches. The next aspect of the condition is route optimization. The model feeds into the car routing application the best available options, and drivers can add other conditions as needed. The biggest gain is using linear programming concepts in programming other applications and automation solutions for the stakeholders in this ride-hailing setup.

If well implemented, the model should result in tons of benefits, as Anderson et al. (2016) alluded to, such as lower wait times overall, as drivers can be scheduled to take breaks when their demand is at its lowest. Drivers will take more daily jobs and maximize their earnings since they do not match the demand cycles. Other indirect effects would be enhanced service reliability levels and noticeable persistence in the optimization, which can translate to higher viability of additional features that rely on this model. For instance, if a driver assist feature is to be improved, it relies on the model. It can be more sustainable than an alternative improvement that fails to utilize linear programming practices.

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Reference Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. L., Fry, M. J., & Ohlmann, J. W. (2016). Quantitative methods for business with CengageNOW (13th ed.).

Cengage Learning.