commit f43adb1382399f90937cb769d886cf195dd2312b Author: vickeygorham73 Date: Thu Sep 17 08:21:56 2026 +0200 Add Tutorial: Optimization for Better Decisions diff --git a/Tutorial%3A-Optimization-for-Better-Decisions.md b/Tutorial%3A-Optimization-for-Better-Decisions.md new file mode 100644 index 0000000..6a5913b --- /dev/null +++ b/Tutorial%3A-Optimization-for-Better-Decisions.md @@ -0,0 +1,7 @@ +
Optimization requires that we define, in quantitative terms, a model that specifies all the ways, times or places our resources may be allocated, and all the significant constraints on resources and uses that must be met. Here is the way to do that. Every day, in business, government, and even our personal lives, we make decisions about how to best use the resources - such as time and money - available to us. It is challenging enough for us to decide which items to buy with our available funds, or which of several priorities we should tackle this morning. For even medium-size organizations, this challenge is multiplied many times over: How to best [schedule](https://sportsrants.com/?s=schedule) every hour for a staff of 30 people in a call center? How to load packages on a fleet of 100 trucks, and which routes they should drive to make deliveries in the least time? How to assign crews and aircraft to 1,000 airline flights, as they move across the country throughout a day?
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These decisions - how to allocate (usually limited) resources to different uses, when there are so many options, with so many interrelationships - are prime candidates for optimization. At leading firms, all the foregoing decisions are [routinely](https://discover.hubpages.com/search?query=routinely) made with the aid of optimization. To use optimization, we need to define, in quantitative terms, a model that specifies all the ways, times or places our resources may be allocated, and [Top Source Media website](https://hamsokhanpodcast.com/understanding-answer-engine-optimization-the-future-of-search/) all the significant constraints on resources and uses that must be met. Then a solver searches for and finds the best resource allocation decisions. Our quantified decision variables are the amount of resources allocated to each individual use - for example, [Top Source Media Minneapolis](https://jme-training-academy.com/index.php/Case_Study:_Enhancing_Online_Visibility_Through_Search_Engine_Optimization) the number of call center employees working on each shift, or the number of packages of a given size loaded onto each truck. To determine what "best" means, we must define a quantity called the objective that we can calculate from the values of decision variables-for example, costs that we’d like to minimize or profits to be maximized.
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To complete the model, we must define each constraint, or limit on the ways resources may be allocated, that reflects the real-world situation. Let’s consider a very simple example of a call center employee scheduling problem, shown in Figure 1 (this example Excel model is included with Frontline’s Analytic Solver software). Our problem is to schedule enough employees to work each day of the week (decision variables) to handle our predicted call volume (a constraint), while minimizing total payroll cost (our objective). Our personnel policy, that employees should work five consecutive days and have two consecutive days off, determines the possible ways that resources can be used: There are seven possible weekly schedules, each one starting on a different day of the week. These are labeled A, B, C through G in the Excel model. For example, employees on Schedule A have Sunday and Monday off, then they work Tuesday through Saturday. Our decision variables - the number of employees working on each schedule - are in cells D15:D21; they are summed in cell D22.
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In this simple model, all employees are paid at the same rate, $40 per day at cell N15. 5 (5 working days per week). We must meet a constraint that the number of employees working each day of the week is greater than or equal to the "Minimum Required Per Day" figures in row 25. We assume here that we actually know these numbers - in many real-world call centers, the call volumes per day are uncertain, and we have only a range or probability distribution for each one. In this tutorial, we’re covering only conventional or [Top Source Media](http://navinal.net/bbs/board.php?bo_table=free&wr_id=428063) deterministic optimization; in a future tutorial, we’ll describe stochastic optimization, where we must allocate resources under conditions of uncertainty in the objective and/or constraints (something that Frontline’s software can handle very well). The 1s and 0s in the middle of the worksheet help us calculate the number of employees we’ll have in the call center on each day of the week. For example, on Sunday we’ll have the employees on Schedules B through F, but those on Schedules A and G will have the day off.
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