Analytics Exercise $21-3($Algo$)$

Recently, Phil Harris, the production control manager at Brunswick, read an article on time$-$phased requirements planning. He was curious about how this technique might work in scheduling Brunswick's engine assembly operations and decided to prepare an example to illustrate the use of time$-$phased requirements planning.

Phil's first step was to prepare a master schedule for one of the engine types produced by Brunswick: the Model $1000$ engine. This schedule indicates the number of units of the Model $1000$ engine to be assembled each week during the last $12$ weeks and is shown on the next page. Next, Phil decided to simplify his requirements planning example by considering only two of the many components that are needed to complete the assembly of the Model $1000$ engine. These two components, the gear box and the input shaft, are shown in the product structure diagram below. Phil noted that the gear box is assembled by the Subassembly Department and subsequently is sent to the main engine assembly line. The input shaft is one of several component parts manufactured by Brunswick that are needed to produce a gear box subassembly. Thus, levels $0,1,$ and $2$ are included in the product structure diagram to indicate the three manufacturing stages that are involved in producing an engine: the Engine Assembly Department, the Subassembly Department, and the Machine Shop.

The manufacturing lead times required to produce the gear box and input shaft components are also indicated in the product structure diagram. Note that two weeks are required to produce a batch of gear boxes and that all the gear boxes must be delivered to the assembly line parts stockroom before Monday morning of the week in which they are to be used. Likewise, it takes three weeks to produce a lot of input shafts, and all the shafts that are needed for the production of gear boxes in a given week must be delivered to the Subassembly Department stockroom before Monday morning of that week.

In preparing the MRP example Phil planned to use the worksheets shown and to make the following assumptions:

$1.$ Twenty two gear boxes are on hand at the beginning of Week $1,$ and eight gear boxes are currently on order to be delivered at the start of Week $2.$

$2.$ Forty five input shafts are on hand at the start of Week $1,$ and $25$ are scheduled for delivery at the beginning of Week $2.$ Model $1000$ master schedule

Model $1000$ product structure

Engine assembly

Crankcase

Gear box

Lead time $\backslash (=2\backslash )$ weeks Used: $1$ per engine

Input shaft

Lead time $\backslash (=3\backslash )$ weeks

Used: $2$ per gear box

a$.$ Initially, assume that Phil wants to minimize his inventory requirements. Assume that each order will be only for what is required for a single period. Calculate the net requirements and planned order releases for the gear boxes and input shafts. Assume that lot sizing is done using lot$-$for$-$lot $($ L $4$ L $).($Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$ a$.$ Initially, assume that Phil wants to minimize his inventory requirements. Assume that each order will be only for what is required for a single period. Calculate the net requirements and planned order releases for the gear boxes and input shafts. Assume that lot sizing is done using lot$-$for$-$lot $($L$4$L$).($Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$

Gear Box Requirements Input Shaft Requirements

Phil would like to consider the costs that his accountants are currently using for inventory carrying and setup for the gear boxes and input shafts. These costs are as follows: Gear Box Requirements

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Week: & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & $9$ & $10$ & $11$ & $12\backslash \backslash$

$\backslash$hline Gross requirements & $18$ & $5$ & $12$ & $10$ & $0$ & $17$ & $22$ & $10$ & $0$ & $9$ & $5$ & $20\backslash \backslash$

$\backslash$hline Scheduled receipts & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline Projected available balance & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline Net requirements & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline Planned order receipt & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline Planned order release & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Input Shaft Requirements

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Week: & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & $9$ & $10$ & $11$ & $12\backslash \backslash$

$\backslash$hline Gross requirements & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline Scheduled receipts & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline Projected available balance & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline Net requirements & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline Planned order receipt & $0$ & $0$ & $0$ & $58$ & $0$ & $0$ & $0$ & $68$ & $0$ & $0$ & $0$ & $0\backslash \backslash$

$\backslash$hline Planned order release & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$