If each box is a special rectangular box (length × width × height=23 inches × 11.5 inches × 11.5 inches), then how to pack these boxes onto an enough hard base of a (46 inches × 46 inches) square in order to make them reach the stablest/optimal structure as high as they are? This is a practical problem that we are always thinking in our mind. We will give an algorithm to solve the problem:

Step 1: Put 2 boxes on one of the four boundaries (denoted as B1) of the base, with their lengths occupying B1.

Step 2: Put 1 box on each of the neighbored boundaries (denoted as B2 and B3) respectively, with each length side occupying each boundary respectively.

Step 3: Put 2 boxes on the remaining boundary (denoted as B4) of the base, with their lengths occupying B4.

Step 4: Now a 23 inches × 23 inches square is inner (or in the center of) the base. Put 2 boxes into the inner square, with their length sides paralleling to B1 and/or B4. Now we finished the layout of the 1st layer.

Step 5: Determine how many layers that you will lay the boxes, according to your own constraints. Once the number of layers was determined, we will repeat Step 6 to finish the layout onto the inner 23 inches × 23 inches square.

Step 6: Put 2 boxes in the even number of the layer, with their length sides paralleling to B2 and/or B3; put 2 boxes in the odd number of the layer, with their length sides paralleling to B1 and/or B4.

Step 7: Now we lay boxes onto the outside of the inner 23 inches × 23 inches square: repeating Steps 8 then 9 until reaching the maximum number of layers.

Step 8: In the even number of the layer, put 2 boxes on both sides paralleling to B2 and B3 respectively; in the odd number of the layer, put 2 boxes on both sides paralleling to B1 and B4 respectively.

Step 9: In the even number of the layer, put 1 box on both sides paralleling to B1 and B4 respectively; in the odd number of the layer, put 1 box on both sides paralleling to B2 and B3 respectively.

根据上面的算法，下面箱子的摆放方式没有一个是最优的：

模型建立与求解，还是有一套专业技术的 (例如，如何定义变量，如何处理数据为那些是已知数据那些是未知数据等等，熟练的有经验的建模工作者有一套技术)。例如，“the decision we must make”的量一般需要定义为变量，变量下标最多不超过3个，因为变量个数为10的4次方以上时, 实际计算时计算量就较大。原英国数学规划学会会长就出过两本书 <<Model Building in Mathematical Programming>>, <<Model Solving in Mathematical Programming>>，第一本书 (2013年) 第五版可以从网站 https://www.researchgate.net/file.PostFileLoader.html?id=546b5d0bd685cc9e2b8b45d4 下载。