Cost Analysis Shipping Problem

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handy21

New Member
Joined
Jun 16, 2013
Messages
3
In need of some help with the formulas needed so solver and calculate my answer! Any help would be greatly appreciated!!

The Cost-Less Corp. supplies its four retail outlest from its four plants.
The shipping cost per shipment from each plant to each retail outlet is given below.

problem%203-25%20table.bmp

Plants 1, 2, 3, and 4 make 10, 20, 20, and 10 shipments per month, respectively. Retail outlets 1, 2, 3, and 4 need to receive 20, 10, 10, and 20 shipments per month, respectively.

The distribution manager, Randy Smith, now wants to determine the best plan for how many shipments to send from each plant to the respective retail outlest each month. Randy's objective is to minimize the total shipping cost.

Formulate this problem as a transportation problem on a spreadsheet and then use the Excel Solver to obtain an optimal solution.
 

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Vidar said:
Hmmm, sounds like homework. You should try to do it yourself.
Click to expand...
Thanks for the , I actually have the table set up with the objective function and constraints just need help with the sum product formulas.[TABLE="width: 508"]
<colgroup><col width="70" style="width: 53pt; mso-width-source: userset; mso-width-alt: 2560;"> <col width="68" style="width: 51pt; mso-width-source: userset; mso-width-alt: 2486;"> <col width="70" style="width: 53pt; mso-width-source: userset; mso-width-alt: 2560;" span="4"> <col width="64" style="width: 48pt;" span="4"> <tbody>[TR]
[TD="class: xl73, width: 278, bgcolor: transparent, colspan: 4"]Cost-Less Corp Problem[/TD]
[TD="width: 70, bgcolor: transparent"][/TD]
[TD="width: 70, bgcolor: transparent"][/TD]
[TD="width: 64, bgcolor: transparent"][/TD]
[TD="width: 64, bgcolor: transparent"][/TD]
[TD="width: 64, bgcolor: transparent"][/TD]
[TD="width: 64, bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"]Unit Cost[/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent, colspan: 2"]Retail Outlet[/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, colspan: 2"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"]1[/TD]
[TD="class: xl65, bgcolor: transparent"]2[/TD]
[TD="class: xl65, bgcolor: transparent"]3[/TD]
[TD="class: xl65, bgcolor: transparent"]4[/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"]Plant[/TD]
[TD="bgcolor: transparent, align: right"]1[/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 500 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 600 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 400 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 200 [/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]2[/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 200 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 900 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 100 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 300 [/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]3[/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 300 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 400 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 200 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 100 [/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]4[/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 200 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 100 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 300 [/TD]
[TD="class: xl66, bgcolor: #92CDDC"] $ 200 [/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="class: xl67, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl65, bgcolor: transparent"]1[/TD]
[TD="class: xl65, bgcolor: transparent"]2[/TD]
[TD="class: xl65, bgcolor: transparent"]3[/TD]
[TD="class: xl65, bgcolor: transparent"]4[/TD]
[TD="class: xl65, bgcolor: transparent"]Shipped[/TD]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"]Quantities[/TD]
[TD="bgcolor: transparent, align: right"]1[/TD]
[TD="class: xl71, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="bgcolor: transparent, align: center"]#VALUE![/TD]
[TD="bgcolor: transparent"]<=[/TD]
[TD="class: xl69, bgcolor: #92CDDC, align: right"]10[/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]2[/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"]<=[/TD]
[TD="class: xl69, bgcolor: #92CDDC, align: right"]20[/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]3[/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"]<=[/TD]
[TD="class: xl69, bgcolor: #92CDDC, align: right"]20[/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]4[/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="class: xl70, bgcolor: yellow"] [/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"]<=[/TD]
[TD="class: xl69, bgcolor: #92CDDC, align: right"]10[/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"]>=[/TD]
[TD="bgcolor: transparent"]>=[/TD]
[TD="bgcolor: transparent"]>=[/TD]
[TD="bgcolor: transparent"]>=[/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"]Needed[/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl69, bgcolor: #92CDDC, align: right"]20[/TD]
[TD="class: xl69, bgcolor: #92CDDC, align: right"]10[/TD]
[TD="class: xl69, bgcolor: #92CDDC, align: right"]10[/TD]
[TD="class: xl69, bgcolor: #92CDDC, align: right"]20[/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl68, bgcolor: #F79646"]Cost[/TD]
[TD="class: xl68, bgcolor: #F79646, align: right"]0[/TD]
[TD="class: xl68, bgcolor: #F79646"] [/TD]
[/TR]
</tbody>[/TABLE]
 
Upvote 0
The constraints show be =, not >=

The total shipping cost is the sumproduct of the blue and yellow tables.
 
Upvote 0
shg said:
The constraints show be =, not >=

The total shipping cost is the sumproduct of the blue and yellow tables.
Click to expand...
Thanks, I believe the math is right now on it.[TABLE="width: 465"]
<colgroup><col width="70" style="width: 53pt; mso-width-source: userset; mso-width-alt: 2560;"> <col width="68" style="width: 51pt; mso-width-source: userset; mso-width-alt: 2486;"> <col width="70" style="width: 53pt; mso-width-source: userset; mso-width-alt: 2560;" span="4"> <col width="70" style="width: 53pt; mso-width-source: userset; mso-width-alt: 2560;"> <col width="64" style="width: 48pt;" span="2"> <tbody>[TR]
[TD="width: 70, bgcolor: transparent"] Unit Cost
[/TD]
[TD="width: 68, bgcolor: transparent"][/TD]
[TD="width: 70, bgcolor: transparent"][/TD]
[TD="class: xl63, width: 140, bgcolor: transparent, colspan: 2"]Retail Outlet[/TD]
[TD="width: 70, bgcolor: transparent"][/TD]
[TD="width: 70, bgcolor: transparent"][/TD]
[TD="width: 128, bgcolor: transparent, colspan: 2"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"]1[/TD]
[TD="class: xl63, bgcolor: transparent"]2[/TD]
[TD="class: xl63, bgcolor: transparent"]3[/TD]
[TD="class: xl63, bgcolor: transparent"]4[/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"]Plant[/TD]
[TD="bgcolor: transparent, align: right"]1[/TD]
[TD="class: xl64, bgcolor: #92CDDC"] $ 500 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"] $ 600 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"] $ 400 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"] $ 200 [/TD]
[TD="class: xl70, bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]2[/TD]
[TD="class: xl64, bgcolor: #92CDDC"] 200 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"]900 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"]100 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"]300 [/TD]
[TD="class: xl70, bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]3[/TD]
[TD="class: xl64, bgcolor: #92CDDC"] 300 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"]400 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"]200 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"]100 [/TD]
[TD="class: xl70, bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]4[/TD]
[TD="class: xl64, bgcolor: #92CDDC"] 200 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"]100 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"]300 [/TD]
[TD="class: xl64, bgcolor: #92CDDC"]200 [/TD]
[TD="class: xl70, bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="class: xl65, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl63, bgcolor: transparent"]1[/TD]
[TD="class: xl63, bgcolor: transparent"]2[/TD]
[TD="class: xl63, bgcolor: transparent"]3[/TD]
[TD="class: xl63, bgcolor: transparent"]4[/TD]
[TD="class: xl63, bgcolor: transparent"]Total $[/TD]
[TD="class: xl63, bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"]Shipped[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"]Quantities[/TD]
[TD="bgcolor: transparent, align: right"]1[/TD]
[TD="class: xl69, bgcolor: yellow, align: right"]0[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]0[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]0[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]10[/TD]
[TD="class: xl71, bgcolor: transparent, align: right"]2000[/TD]
[TD="bgcolor: transparent"]=[/TD]
[TD="class: xl67, bgcolor: #92CDDC, align: right"]10[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]2[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]10[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]0[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]5[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]5[/TD]
[TD="class: xl71, bgcolor: transparent, align: right"]4000[/TD]
[TD="bgcolor: transparent"]=[/TD]
[TD="class: xl67, bgcolor: #92CDDC, align: right"]20[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]3[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]10[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]0[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]5[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]5[/TD]
[TD="class: xl71, bgcolor: transparent, align: right"]4500[/TD]
[TD="bgcolor: transparent"]=[/TD]
[TD="class: xl67, bgcolor: #92CDDC, align: right"]20[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent, align: right"]4[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]0[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]10[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]0[/TD]
[TD="class: xl68, bgcolor: yellow, align: right"]0[/TD]
[TD="class: xl71, bgcolor: transparent, align: right"]1000[/TD]
[TD="bgcolor: transparent"]=[/TD]
[TD="class: xl67, bgcolor: #92CDDC, align: right"]10[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"]=[/TD]
[TD="bgcolor: transparent"]=[/TD]
[TD="bgcolor: transparent"]=[/TD]
[TD="bgcolor: transparent"]=[/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[TD="bgcolor: transparent"][/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"]Needed[/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl67, bgcolor: #92CDDC, align: right"]20[/TD]
[TD="class: xl67, bgcolor: #92CDDC, align: right"]10[/TD]
[TD="class: xl67, bgcolor: #92CDDC, align: right"]10[/TD]
[TD="class: xl67, bgcolor: #92CDDC, align: right"]20[/TD]
[TD="bgcolor: transparent"][/TD]
[TD="class: xl66, bgcolor: #F79646"]Cost[/TD]
[TD="class: xl66, bgcolor: #F79646, align: right"]11500[/TD]
[/TR]
</tbody>[/TABLE]
 
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