Inventory Control Systems Questions and Answers

Answer: D

The main objective of the EOQ (economic order quantity) model is to minimise the total inventory costs. It finds the order size at which the sum of the ordering cost and the holding cost is least. The model does not aim at maximising sales, minimising lead time or maximising stock availability, which would raise holding cost.

Answer: D

The item that is NOT inventory is CNC milling machines.

Inventory is stock held to be converted into, or sold as, product: raw materials waiting to be processed, work-in-process partly through production, and finished goods awaiting sale. All three appear on the books as current assets.

CNC milling machines are the equipment that does the processing. They are capital goods (fixed assets) used over many years and are not consumed in or sold as the product, so they are not inventory. (A machine-tool maker's unsold machines would be its finished goods, but the question is about the machines as production equipment.)

Answer: C

The economic order quantity is 300 tyres.

With annual demand D, ordering cost per order \(C_{o}\) and carrying cost per unit per year \(C_{h}\):

\[ \begin{aligned} EOQ &= \sqrt{\frac{2DC_{o}}{C_{h}}} \\ &= \sqrt{\frac{2 \times 9600 \times 75}{16}} \\ &= \sqrt{90000} = 300 \end{aligned} \]

At this quantity the annual ordering cost (32 orders × Rs. 75 = Rs. 2400) equals the annual carrying cost (150 average tyres × Rs. 16 = Rs. 2400), which is the check. 212 is what you get by dropping the factor 2, and 64 comes from inverting the cost ratio; 1200 does not follow from the formula.

Answer: A

The correct labelling is Curve P1: Total cost, Curve P2: Holding cost, Curve P3: Setup cost, and Curve P4: Production cost.

In the EOQ model, with order quantity Q, annual demand D, setup cost S per order and holding cost H per unit per year:

• holding cost rises in a straight line with Q, since average stock is Q/2: the dash-dot line P2 through the origin;
• setup (ordering) cost falls as D/Q, steeply at first and then flattening: the hyperbola-like curve P3;
• production or purchase cost per unit does not depend on the order quantity: the flat line P4;
• total cost, the sum of these, is U-shaped with its minimum near where the holding and setup curves cross, at the EOQ: P1.

Every other option gives a straight or flat curve the name of a cost that must curve, or swaps the U-shaped total with a component.

Answer: A

The total cost rises by 2.5%.

In the EOQ model the total of ordering and holding cost, as a fraction of its minimum, depends only on the ratio of the order size to the optimal size \(Q^{*}\):

\[ \begin{aligned} \frac{TC(Q)}{TC(Q^{*})} &= \frac{1}{2}\left(\frac{Q}{Q^{*}} + \frac{Q^{*}}{Q}\right) \\ &= \frac{1}{2}\left(1.25 + 0.8\right) = 1.025 \end{aligned} \]

so the cost is 2.5% higher. The demand and cost figures fix \(Q^{*}\) (about 183 gears with a holding cost of 144 rupees per gear per year), but the percentage change does not depend on them. The cost curve is flat near its minimum, which is why a 25% error in order size costs only 2.5%; 12.5% is half the 25% change in order size and ignores that flatness, and 0 or 5% do not follow from the formula.