Distribution Models: Transshipment and Assignment Model

San Beda College

Graduate School of Business

Final paper to be submitted to:

Prof.Lundag

_______________________________

In partial fulfillment of

The requirements for the course

Operations research

_______________________________

Joffrey Maranan

“That in all things, God may be glorified.”

Aug. 2014

Distribution models

I. Transshipment

The transshipment model is an extension of the transportation model in which intermediate transshipment points are added between the sources and destinations.

An example of a transshipment point is a distribution center or warehouse located between plants and stores.

II. Assignment Model

* The Assignment Model arises in a variety of decision making situations. Typical assignment problems involve assigning employees to task, assigning sales personnel to sales territories, or assigning job to machines.

* A distinguishing feature of this distribution model is that assignments must be on a one-to-one basis; that is one employee or job must be assigned to one and only task.

* It is frequently used to look for the assignments that Minimize time or cost, or Maximize profit.

Example

* As in transportation models, we denote the variable by Xij, where i = job (supply point) number and

j = machine (demand point) number. Each Xij can take only of two values: 1 or 0. In general,

Xij = 1 if job is assigned to machine j and

Xij = 0 if job is not assigned to machine j.

Assignments of four jobs to the four machines must be on a one-to-one basis.

* Following the mathematical model for the given assignment problem. The first four constraints are the supply constraints, and the last four are the demand constraints.

* Mathematical Model

Minimize C = 5x11 +10x12 + 11x13 + 8x14 + 7x21 + 8x22 + 10x23 + 7x24 + 4x31 + 7x32 + 7x33 + 6x34 + 9x41 +

12x42 + 13x43 + 13x44

Subject to

X11 + X12 + X13 + X14 = 1 JOB 1 supply constraint

X21...