Third Party Logistics

$29$

Cose $9-1$

Pool Distribution by Younger Water, Inc.

Youmyer Water is a small producer of bottled drinking water with its only manufacturing plant located in Ainheapolis, MN$.$ Every week, the company ships $4,000$ units $($carton boxes$)$ of its products from Minzeapolis to Omaha, NE using TL shipments. The company management, however, is unhappy with the high cost of transportation. Bottled water is a product with low value per unit, so that if the transportation cost is high the company would make very small profit.

One day, Dennis Okamoto, a transportation manager of Younger Water, was told by the management to look for ways to reduce transportation cost. He pondered about this issue while eating lunch at a local restaurant. Dennis was always unhappy with how his shipments have utilized trucks' hauling capacities. Water bottles are "high density" products, meaning that its weight is heavy relative to its volume. This means that when water bottles are loaded onto a truck, the trucks' weight capacity is reached well before the volume capacity is reached. Typically, his product occupies only about $50$ percent of volume capacity when it reaches $100$ percent of weight capacity, which means that a truck that is fully loaded with water bottles typically is half empty $($in volume$).$ Dennis has always thought that this is a waste of space, and wondered how he could have a better utilization of truck capacity, in both weight and volume dimensions. If he can somehow resolve this issue, he may be able to reduce the cost of transportation for Younger Water drastically.

One idea which came to Dennis is to use a $3$PL to perform pool distribution with another shipper. Specifically, he was thinking about having the $3$PL consolidate his products with low$-$density products of another shipper. Dennis believes that by shipping the mix of these two different products in the same truck $($combining high$-$ and low$-$density products in a truck$),$ the capacity utilizations in both weight and volume can be improved to near $100$ percent. Dennis decided to talk to a $3$PL about his idea.

The $3$PL which Dennis contacted told him that there is a client $($shipper$)$ who ships about the same amount of products in the same lane as Younger Water $($Minneapolis to Omaha$)$ every week. This shipper, Zebra Snacks, is a producer of potato chips, which is a low$-$density product, so it is a good candidate for consolidation of shipments with Younger Water. After obtaining detailed information about Zebra Snacks, Dennis created the following table, which shows the details of each product, along with the characteristics of the trucks used by the $3$PL $($where shipper Y refers to Younger Water and shipper $Z$ refers to Zebra Snacks$).$ Dennis was told by the $3$PL that the cost of shipment for both shippers is $$1,000$ per TL shipment $($per truck dispatched$).$

Parameters

$\backslash$table$[[,$shipper $Y,$shipper $Z$