Cement Americas

WIN 2016

Cement Americas provides comprehensive coverage of the North and South American cement markets from raw material extraction to delivery and tranportation to end user.

Issue link: https://cement.epubxp.com/i/636168

Contents of this Issue

Navigation

Page 12 of 39

www.cementamericas.com • Winter 2016 • CEMENT AMERICAS 11 FEATURE THE CONSTRAINTS (AKA INPUTS) First, the rules of the game must be established in the form of operating constraints, which form the "dimen- sions of the feld" that the solver will ultimately play in. Demand is viewed as a constraint to a linear program (LP) since a location can only be given so much prod- uct before it exceeds its ability to convert the product into sales. In the client's case, the company had 25 sales locations to consider, each with varying demand for the same product. Another sideline to the feld included margin informa- tion so that output would be based on overall prof- it. Specifcally, this information detailed the individual product, fxed and delivery costs. Finally, the capabili- ties of the network were entered, from plant manufac- turing rates to railcar and truck capabilities. With these rules in place, the team went to work ensuring they could replicate the previous year's operational perfor- mance and thus establish a trustworthy baseline. THE PROCESSING (AKA LINEAR OPTIMIZATION) An optimized solution merely means it is the "best use" of limited resources available. The "best use" usually means something positive (like effciency or proft) is maximized or things to be avoided (like costs) are min- imized. A quick break-down of what happens during a linear optimization is illustrated in the example below. Exhibit 1: The optimization process is just like any process as it contains ingredients (inputs), processing (optimization) and a result (best output). Imagine an operation that wants to minimize the costs of meeting sales demand. The available fnished prod- uct storage capacity in its region is 200 tons between two neighboring manufacturing plants. The only thing preventing infnite production (so far) is how many products could go into each storage silo. Graphically stated on an x and y axis, that scenario is displayed by the blue line in Exhibit 2. The area under that curve represents all the product they can make (Plant 1 + Plant 2 = 200 tons in total). Now, making the example a bit more realistic, we add other operational constraints that cut into what the plants can produce: the supply of raw materials and the amount of available labor. When these constraints are likewise graphed, they cut into the wide open area under the blue line. As more and more limitations are introduced, the area under the curve becomes smaller and smaller. Here's where the solver mechanism adds value: the point of intersection of the innermost constraint lines (which in this case are blue and orange) indicates the optimum amount of tons to produce from each plant (Plant 1= 120; Plant 2= 80) while playing by the rules of the limits. Exhibit 2: The intersection of the innermost con- straints dictates how much freedom the solver has to fnd an optimal solution. The LP takes into account the absolute limits on de- mand, production capacity, delivery trucks, etc. but is also allowed to play with those variables in an adjust- able fashion – within the stated thresholds. The solv- er is merely trying to fnd the point where all most limiting constraints intersect while allowing for the greatest area under the curve (i.e. maximizing proft.) Within a minute, the solving mechanism whips through hundreds of thousands of iterations and sorts through 13,000 adjustable variables until it is sure it has found the best solution. Now it's time to analyze the output. THE OUTPUT One of the best things about a computer program is that it will do what you say. And sometimes, one of the worst things about a program is that it will … do

Articles in this issue

Links on this page

Archives of this issue

view archives of Cement Americas - WIN 2016