What to Expect

In this chapter you will find a brief overview of the tasks to be performed, a compact statement of the underlying model to be built, and a glimpse of the output you will produce.

Scope of one-hour tutorial

Summarizing your work

Once you have read the short problem description and the associated mathematical model statement, you will be asked to complete a series of tasks that make up this one-hour tutorial, namely:

• create a new project in AIMMS,

• enter all identifier declarations,

• enter the data manually,

• save your data in a case,

• build a small procedure,

• build a single page with

  • header text,

  • a standard table and two bar charts with input data,

  • a composite table and a stacked bar chart with output data,

  • a button to execute the procedure, and

  • a scalar object with the optimal value,

• perform a what-if run.

Problem description and model statement

Problem description

Truckloads of beer are to be shipped from two plants to five customers during a particular period of time. Both the available supply at each plant and the required demand by each customer (measured in terms of truckloads) are known. The cost associated with moving one truck load from a plant to a customer is also provided. The objective is to make a least-cost plan for moving the beer such that the demand is met and shipments do not exceed the available supply from each brewery.

Data overview

The following table provides the data for the problem described in the previous paragraph.

Table 1 Input data for beer transport problem

Customers Plants	Unit Transport Cost					Supply
	Amsterdam	Breda	Gouda	Amersfoort	Den Bosch
Haarlem	131	405	188	396	485	47
Eindhoven	554	351	479	366	155	63
Demand	28	16	22	31	12

Identifier declarations

The following declarations list the identifiers that are part of the mathematical program to be built.

\[\begin{split}\begin{align} & \textbf{Indices:} \\ &&& \text{$p$} & & \text{plants} \\ &&& \text{$c$} & & \text{customers} \\[0.5pc] & \textbf{Parameters:} \\ &&& \text{$S_p$} & & \text{supply at plant $p$} \\ &&& \text{$D_c$} & & \text{demand by customer $c$} \\ &&& \text{$U_{pc}$} & & \text{unit transport cost from $p$ to $c$} \\[0.5pc] & \textbf{Variables:} \\ &&& \text{$x_{pc}$} & & \text{transport from $p$ to $c$} \\ &&& \text{$z$} & & \text{total transport cost} \\[0.5pc] \end{align}\end{split}\]

Fig. 1 The Netherlands

Model summary

The mathematical model summary below captures the least-cost plan to transport beer such that the demand is met and shipments do not exceed available supply.

\[\begin{split}\begin{align} z = \sum_{pc} U_{pc} x_{pc} & & & \\ \end{align}\end{split}\]

\[\begin{split}\begin{align} \sum_c x_{pc} & \leq S_p & & \forall p \\ \sum_p x_{pc} & \geq D_c & & \forall c \\ x_{pc} & \geq 0 & & \forall (p,c) \\ \end{align}\end{split}\]

Using explicit names

Even though the above notation with one-letter symbols is typical of small mathematical optimization models, it will not be used to represent the model in AIMMS. Instead, explicit names will be used throughout to avoid any unnecessary translation symbols. The number of symbols needed to describe practical applications is generally large, and a clear naming convention supports the understanding and maintenance of large models.