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Stateline Shipping and Transportation Company

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Stateline Shipping and Transportation Company
Strayer university | Stateline shipping and Transportation Company | [Type the document subtitle] | | | 9/3/2012 |

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1. Objective function:
Min Z= 12Xkw + 15Xkl + 17Xkd + 14Xdw + 9Xdl + 10Xdd + 13Xmw + 20Xml + 11Xmd + 17Xsw + 16 Xsl + 19Xsd + 7Xcw + 14Xcl + 12Xcd + 22Xaw + 16Xal + 18Xad

Supply from 6 plants: 35,26,42,53,29,38
Demand from 3 waste sites: 65,80,105

2. Using POM QM to solve the problem, the cost for shipping the waste directly from the 6 plants to the 3 waste disposal sites is $ 2822.

3. Transshipment model
Let Xij = number of barrels transported from the plan i to the waste sites j i= k,d,m,s,c,a j= w,l,d
Xij ≥ 0

In/Out constraints
Xkk+Xkd+Xkm+Xks+Xkc+Xka=Xkw+Xkl+Xku
Xdk+Xdd+Xdm+Xds+Xdc+Xda=Xdw+Xdl+Xdu
Xmk+Xmd+Xmm+Xms+Xmc+Xma=Xmw+Xml+Xmu
Xsk+Xsd+Xsm+Xss+Xsc+Xsa=Xsw+Xsl+Xsu
Xck+Xcd+Xdm+Xcs+Xcc+Xca=Xcw+Xcl+Xcu
Xak+Xad+Xam+Xas+Xac+Xaa=Xaw+Xal+Xau
Xkw+Xdw+Xmw+Xsw+Xcw+Xaw=Xww+Xwl+Xwu
Xkl+Xdl+Xml+Xsl+Xcl+Xal=Xlw+Xll+Xlu
Xku+Xdu+Xmu+Xsu+Xcu+Xau=Xuw+Xul+Xuu

Supply constraints
Xkk+Xkd+Xkm+Xks+Xkc+Xka=35
Xdk+Xdd+Xdm+Xds+Xdc+Xda=26
Xmk+Xmd+Xmm+Xms+Xmc+Xma=42
Xsk+Xsd+Xsm+Xss+Xsc+Xsa=53
Xck+Xcd+Xcm+Xcs+Xcc+Xca=29
Xak+Xad+Xam+Xas+Xac+Xaa=38

Demand constraints
Xww+Xwl+Xwu ≤65
Xlw+Xll+Xlu ≤ 80
Xuw+Xul+Xuu ≤ 105

4. Solving the problem in excel, the cost for multi-shipping is $ 2630.

5. Rachel have to drop and pick up some loads at the various plants and waste sites because it could save $192 in expense for Stateline Shipping and Transport Company. Rachel is observing to complete routes with the minimum amount of cost associated with them. Considerations were either direct shipment from the plant to waste disposal or drop off to the plant so that another truck could pick up the shipment. If she were to ship straight to the waste plant she’s facing a larger cost. By using a drop off operation to the waste plant her cost is fewer. In the first model when shipping directly from the plant to
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