Question

Weiss’s paint store uses a (Q, R) inventory control system to control its stock level. For a particular popular white latex paint, historical data show that the distribution of monthly demand is approximately normal, with mean 28 and standard deviation 8. Replenishment lead time for this paint is about 14 weeks. Each can of paint costs the store $6. Although excess demands are backordered, the store owner estimates that unfilled demands cost about $10 each in bookkeeping and loss of goodwill costs. Fixed costs of replenishment are $15 per order, and holding costs are based on a 30% annual rate of interest.

a) Follow the Q, R policy identified in a), what is the inventory level when the order with size of Q (identified in a) arrives if there was $150 loss in bookkeeping and loss of goodwill due to unfilled demands in last cycle?

b) Follow the Q, R policy identified in a), what is the inventory level when the order with size of Q (identified in a) arrives if the inventory at the end of last cycle is 21?

Answer 1

Solution:-

Given:-

Month to month request: d=28, s=std. deviation=8

Lead time = L = 14 weeks= 14/4 =3.5 months

Cost of paint= C=$6 each

Cost of loss of altruism =$10 each

Obtainment cost= P= $15/request

Stock holding cost= h= 30% yearly per cost of every thing put away.

Yearly demand= D= 28*12=336

Optimal Lot Size =

=

=74.83

Optimal Lot Size=75 units

Accepting 95% assistance level, z= normiverse(95%) = 1.96

safety syock =

Be that as it may, sl = sexually transmitted disease deviation of lead time = 0

Safety stock =

safety stock =29.33= 30 units

Reorder point=ROP= lead time * month to month utilization + wellbeing stock = L*d +SS

ROP = 3.5*28+30 =128 units

A):-

In this way, so as to limit anticipated all out cost, the ideal part size is 75 units and the reorder point is 128 units.

Since there was lost generosity and accounting worth $150, it infers that there was loss of 150/10 i.e 15 units in the stock.

So when the request amount of EOQ = 75 units shows up to the parcel,

The stock level becomes = EOQ-delay purchased amount

=75-15 = 60 units.

In this way, the stock levels in the provided situation of delay purchase becomes 60 units to oblige for the misfortune.

B):-

Stock toward the finish of last cycle = 21 units.

Ideal arranged amount = 75 units.

Accordingly the new stock level after the given condition = EOQ + Inventory toward the finish of last cycle

=75+21= 96 units

In this way the new stock level after the given condition is 96 units.