MT296 Unit 3 Inventory Model Application Example

Three Hundred Five Bags or a Full Truck: A Unit 3 Inventory Model Application for Potato Flakes

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Purdue University Global

MT296: Supply Chain Management Applications

Unit 3 Inventory Model Application

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[Date]

The pierogi maker, its supplier, prices and costs are composite and illustrative; the sources cited are real.

Assumptions

The plant uses dehydrated potato flakes in its pierogi filling at a steady rate year round, because filling is made daily and stored frozen in batches; the seasonal swing in finished pierogi is absorbed in the plant's production schedule, not in flake purchases. That makes flakes a good fit for the economic order quantity model, which assumes demand for the item is constant and known, that each order arrives all at once, that ordering cost per order and holding cost per unit are constant and that there are no stockouts.

The inputs come from the purchasing and accounting records.

Annual use: 6,720 bags of 50 pounds

Price: $71 a bag

Ordering cost: $118 per order, covering the buyer's time to place the order, receiving and the moisture test the plant runs on each lot

Carrying rate: 24 percent a year of the item's value, covering capital, dry storage space, insurance and spoilage, which gives $17.04 per bag per year

Calculation 1: The Economic Order Quantity

Plugging the plant's figures into the formula gives the square root of (2 × 6,720 × $118) ÷ $17.04, about 305 bags.

At 305 bags, the plant would order about 22 times a year, roughly every 16.6 days. Annual ordering cost is about $2,600 and annual holding cost about $2,599, for a total of $5,198. At the optimum the two are equal, which is a check on the arithmetic. Jacobs and Chase (2020) point out that the total cost curve is shallow around its lowest point, so an order a little larger or smaller than the formula's answer barely changes the bill.

Calculation 2: Rounding to Pallets

The supplier ships on pallets of 40 bags, so 305 bags is not a practical order. Eight pallets, 320 bags, is the nearest full-pallet quantity. At 320 bags, ordering cost falls to about $2,478 and holding cost rises to about $2,726, for $5,204, only $6 a year more than the exact formula.

Calculation 3: The Truckload Discount

The supplier offers a 2 percent discount, $69.58 a bag, for full-truckload orders of 800 bags. The formula alone cannot weigh this, because it assumes a constant price. Silver et al. (2017) describe the standard approach for an all-units discount: compute the total annual cost, purchase price included, at each price break and choose the lowest. The comparison has to include purchase cost.

Eight-pallet orders: purchase $477,120; ordering and holding $5,204; total $482,324

Truckload orders: purchase $467,578; ordering $991 for about 8.4 orders a year; holding $6,680, since the average inventory doubles to 400 bags at a slightly lower value per bag; total $475,248

The truckload raises ordering and holding cost from about $5,200 to about $7,671, but cuts purchase cost by $9,542. The net saving is about $7,076 a year against eight-pallet orders, or $7,070 against the exact formula quantity.

The formula finds the cheapest way to hold flakes; the discount makes it cheaper to hold more of them.

How Sensitive Is the Answer?

Two inputs carry the most uncertainty. The carrying rate of 24 percent includes an estimate for spoilage that the plant has never measured closely. If the true rate were 30 percent, the truckload's holding cost would rise by about $1,670 and the eight-pallet option's by about $680, so the saving would fall to about $6,100, still clearly positive. The carrying rate would have to exceed roughly 67 percent before the truckload lost its advantage, a rate no reasonable estimate of spoilage and capital cost supports for a dry ingredient. The ordering cost of $118 includes the moisture test; if the lab could test a truckload with one sample rather than two, the truckload's advantage would grow slightly. In both directions the recommendation holds, because the discount is large relative to the change in holding and ordering costs.

Can the Plant Hold 800 Bags?

The truckload only works if the plant can store it. At 800 bags delivered and used over about 43 days, the dry storage room must hold up to 800 bags at once, 20 pallets. The room holds 26 pallets, but it also stores flour, so the warehouse lead confirmed that 20 pallets of flakes fit if flour deliveries move to weekly. Flakes keep well for many months in dry storage, so 43 days of supply raises no quality concern. Chopra (2019) notes that quantity discount decisions often depend on storage and shelf life as much as on price.

Recommendation

The plant should buy potato flakes by the full truckload of 800 bags, saving about $7,000 a year, and move flour deliveries to weekly to make room. Purchasing should confirm the supplier's discount in writing for at least a year, since the saving depends entirely on it. If storage becomes tight, eight-pallet orders are the fallback, costing almost exactly what the formula predicts.

References

Chopra, S. (2019). Supply chain management: Strategy, planning, and operation (7th ed.). Pearson.

Jacobs, F. R., & Chase, R. B. (2020). Operations and supply chain management (16th ed.). McGraw-Hill.

Silver, E. A., Pyke, D. F., & Thomas, D. J. (2017). Inventory and production management in supply chains (4th ed.). CRC Press.