Consider an item with the following deterministic, time$-$varying pattern:

Week $123456$

Demand $508018080130120$

Week $789101112$

Demand $18015010100180130$

Suppose the pattern terminates at week $12.$ Other relevant parameters are:

$2$

$1.$ Inventory carrying cost is $0\mathrm{.}2$ $$/$unit$/$week $($note this the same as

p

vr

where v is the cost per unit and

p

r

is cost in dollars of carrying one dollar

worth of inventory through one week $).$ We assume that the carrying cost

is incurred only on the units carried over from one week to the next.

$2.$ Fixed cost per replenishment is $$50.$

$3.$ Initial inventory is $60$ units. Also, the lead time for the item is $2$ weeks.

$4.$ There is a scheduled receipt for the item m in week $2($i$.$e$.$ at the beginning of

week $2)$ of $75$ units.

Plan just the immediate replenishment $($i$.$e$.,$ plan just one inventory cycle$)$ using

the lot$-$size rules listed below. Present your plan in a time$-$phased $($i$.$e$.,$ MRP$)$

table showing the immediate inventory cycle for each rule $($no need to redraw the

table if the current rule gives a Q that is the same as in an earlier table$).$

Fixed lot size of $($adjusted$)$ EOQ

Least unit cost

Silver$-$meal heuristic $($least cost per period$)$

Fixed cycle time of $($adjusted$)$ TEOQ.

Part$-$period balance