Chapter 4.14, Problem 1P

Explanation of Solution

Modifying the formulation of the Mondo problem:

Suppose,

$i_t$=Inventory at the end of quarter ‘t’.

$p_t$=Number of motorcycles produced quarter ‘t’.

z=Cost

Here, the user can write,

$\begin{array}{l}{X}_t=X_t\text{'}-X_t\text{'}\text{'}\\ i_t=i_t\text{'}-i_t\text{'}\text{'}\end{array}$

Where,

$X_t$=Amount by which quarter t production exceeds quarter t-1 production.

$X_t\text{'}$=Increase in quarter t production over quarter t-1 production.

$X_t\text{'}\text{'}$=Decrease in quarter t production over quarter t-1 production.

$i_t\text{'}\text{'}$=Amount of demand that is unmet at the end of quarter t.

Therefore, the objective function is,

  $\begin{array}{l}\min z=400(p_1+p_2+p_3+p_4)+100(i_1\text{'}+i_2\text{'}+i_1\text{'}\text{'}+i_2\text{'}\text{'}+i_3\text{'}+i_4\text{'})+120(i_3\text{'}\text{'}+i_4\text{'}\text{'})+\\ 600(X_1\text{'}\text{'}+X_2\text{'}\text{'}+X_3\text{'}\text{'}+X_4\text{'}\text{'})+700(X_1\text{'}+X_2\text{'}+X_3\text{'}+X_4\text{'})\end{array}$

Subject to,

$i_1=i_1\text{'}-i_1\text{'}\text{'}(inventoryinmonth\mathrm{1</}$