Chapter 3, Problem 58RP

Explanation of Solution

LP formulation:

• Assume the following,
  • Let “${\text{Pr}}_{\text{w}}$” be the employees assigned to data preparation department during week “w”.
  • Let “${\text{En}}_{\text{w}}$” be the employees assigned to data entry during week “w”.
  • Let “${\text{F}}_{\text{w}}$” be the unprocessed forms exist at the end of week “w”.
  • Let “${\text{F}}_{\text{w}}\text{'}$” be the forms awaiting data entry at the beginning of week “w”.
  • Let “${\text{Dp}}_{\text{j}}$” be the forms processed in data preparation department during week “j”.
  • Let “${\text{De}}_{\text{j}}$” be the forms processed in data entry department during week “j”.
• Consider that all forms come at the beginning of the week and also consider that the forms, which are prepared during week “j”, are passed to data entry at the starting of week “$\text{j+1}$”.
• The correct Linear Programming (LP) formulation is as follows,

  $\min z=200(P{r}_1+{\text{En}}_{\text{1}}+P{r}_2+{\text{En}}_2+P{r}_3+{\text{En}}_3+P{r}_4+{\text{En}}_4+P{r}_5+{\text{En}}_5)$

  $\begin{array}{l}\text{S}\text{.T}\text{.}\\ {\text{F}}_1\text{=40000}-{\text{Dp}}_1\\ {\text{F}}_2{\text{=F}}_1\text{+30000}-{\text{Dp}}_2\\ {\text{F}}_3{\text{=F}}_2\text{+60000}-{\text{Dp}}_3\\ {\text{F}}_4{\text{=F}}_3{\text{+Pr}}_4\\ {\text{F}}_{}\end{array}$