Consider the following example that demonstrates optimization of transportation.<\/p>\n
There are production facilities in Battle Creek, Cherry Creek, and Dee Creek with annual capacities of 500 units, 400 units, and 600 units, respectively. The annual demands at warehouses in Worchester, Dorchester, and Rochester are 300 units, 700 units, and 400 units, respectively. The table below gives the unit transportation costs between the production facilities and the warehouses.<\/p>\n
Worchester Dorchester Rochester<\/p>\n
Battle Creek<\/p>\n
$20\/unit<\/p>\n
$30\/unit<\/p>\n
$13\/unit<\/p>\n
Cherry Creek<\/p>\n
$10\/unit<\/p>\n
$5\/unit<\/p>\n
$17\/unit<\/p>\n
Dee Creek<\/p>\n
$15\/unit<\/p>\n
$12\/unit<\/p>\n
$45\/unit<\/p>\n
How much of the demand at each of the warehouses must be met by each of the production facilities?<\/p>\n
This problem can be modeled as a linear programming model as follows:<\/p>\n
Decision Variables<\/p>\n
Xbw = # of units to be transported from Battle Creek to Worchester<\/p>\n
Xcw = # o<\/p>\n
f units to be transported from Cherry Creek to Worchester<\/p>\n
Xdw = # of units to be transported from Dee Creek to Worchester<\/p>\n
Xbd = # of units to be transported from Battle Creek to Dorchester<\/p>\n
Xcd = # of units to be transported from Cherry Creek to Dorchester<\/p>\n
Xdd = # of units to be transported from Dee Creek to Dorchester<\/p>\n
2<\/p>\n
QSO 635 Module<\/p>\n
Seven<\/p>\n
Xbr = # of units to be transported from Battle Creek to Rochester<\/p>\n
Xcr = # of units to be transported from Cherry Creek to Rochester<\/p>\n
Xdr = # of units to be transported from Dee Creek to Rochest<\/p>\n
er<\/p>\n
Objective Function<\/p>\n
Minimize total annual transportation cost ($):<\/p>\n
= 20*Xbw + 10*Xcw + 15*Xdw + 30*Xbd + 5*Xcd + 12*Xdd + 13*Xbr + 17*Xcr + 45*Xdr<\/p>\n
Constraints<\/p>\n
Demand Constraints<\/p>\n
Xbw + Xcw + Xdw \u2265 300<\/p>\n
(demand at Worchester)<\/p>\n
Xbd + Xcd + Xdd \u2265 700<\/p>\n
(demand at Dorchester)<\/p>\n
Xbr + Xcr + Xdr \u2265 400<\/p>\n
(demand at Rochester)<\/p>\n
Capacity Constraints<\/p>\n
Xbw + Xbd + Xbr \u2264 500<\/p>\n
(capacity at Battle Creek)<\/p>\n
Xcw + Xcd + Xcr \u2264 400<\/p>\n
(capacity at Cherry Creek)<\/p>\n
X<\/p>\n
dw + Xdd + Xdr \u2264 600<\/p>\n
(capacity at Dee Creek)<\/p>\n
Non<\/p>\n
–<\/p>\n
Negativity Constraints<\/p>\n
Xbw, Xcw, Xdw, Xbd, Xcd, Xdd, Xbr, Xcr, and Xdr are \u2265 0<\/p>\n
Integer Constraints<\/p>\n
Xbw, Xcw, Xdw, Xbd, Xcd, Xdd, Xbr, Xcr, and Xdr are integers<\/p>\n
The above model can be solved using the Microsoft Excel Solver tool. Refer to the tutorial on how to use the Solver tool (click on each image for a better display).<\/p>\n","protected":false},"excerpt":{"rendered":"
Consider the following example that demonstrates optimization of transportation. There are production facilities in Battle Creek, Cherry Creek, and Dee Creek with annual capacities of 500 units, 400 units, and 600 units, respectively. The annual demands at warehouses in Worchester, Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-174651","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/174651","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=174651"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/174651\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=174651"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=174651"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=174651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}