Acceptance sampling Plan

College of Management, NCTU

Operation Research I

Fall, 2008

Chap8 The Transportation and Assignment Problems
Example: Three canneries and four warehouse
Shipping Cost per Truckload
Output
Warehouse
1
2
3
4
464
513
654
867
75
1
Cannery
352
416
690
791
125
2
995
682
388
685
100
3
80
65
70
85
Allocation xij = the number of truckloads to be shipped from cannery i to warehouse j.

The Transportation Problem
Distribute goods from sources to destinations with minimum cost. si : number of units being supplied by source i. dj : number of units being received by destination j. cij : cost per unit distributed from source i to destination j. xij : amount distributed from source i to destination j.
Parameter table for the transportation problem:
Cost per Unit Distributed
Supply
Destination
1
2
…
n c11 c12 c1n s1
…
1
Source
c21 c22 c2n s2 …
2
…
…
…
…
…
…
cm1 cm2 sm
…
cmn m d1 d2 … dn Demand
Any problem (whether involving transportation or not) fits the model for a transportation problem if it can be described completely in terms of a parameter table. Jin Y. Wang

Chap8-1

College of Management, NCTU

Operation Research I

Fall, 2008

Formulation m Min Z =

n

∑∑ c i =1 j =1

n

S.T.

∑x j =1

ij

m

∑x i =1

ij

ij

xij

= s i , for i = 1, 2, …, m

= d j , for j = 1, 2, …, n

xij ≥ 0 , for all i and j

The feasible solutions property: A transportation problem will have feasible m solution if and only if

n

∑s = ∑d i =1

i

j =1

j

.

Integer solution property: For transportation problems where every si and dj has an integer value, all the basic variables in every basic feasible solution
(including an optimal one) also have integer values.
We will discuss the reasoning after introducing the solution algorithm.
Another example (production schedule) – with a dummy destination
Scheduled
Maximum
Unit Cost
Unit Cost