BUS 2100 Module 5 Paint Stock and a Store Remodel Schedule Example

Paint on the Shelf and a Remodel on Schedule: Stock Control and Critical Path

Student Name

Bachelor of Science in Business Administration, Thomas Edison State University

BUS-2100: Quantitative Skills for Business

Mentor Name

Month Day, Year

Paint on the Shelf and a Remodel on Schedule: Stock Control and Critical Path

The Situation

A composite independent hardware store in Indiana faces two quantitative problems. Its best-selling interior paint either runs out during spring projects or crowds the stockroom after a large order, and the owner plans a remodel of the paint department that must not close it for long. Wisniewski and Shafti (2020) present stock control models and network analysis for exactly these kinds of operational decisions.

Part 1: How Much to Order

The store sells about 4,800 gallons of the paint a year. Placing and receiving an order costs about $45 in staff time, freight paperwork and checking. Holding a gallon in stock for a year costs about $3.60, or 20 percent of its $18 cost, covering storage space, capital tied up and damaged cans. The economic order quantity balances these two costs: the square root of (2 x 4,800 x $45) / $3.60, or the square root of 120,000, about 346 gallons.

Ordering about 346 gallons at a time, roughly every three and a half weeks, saves about $85 a year compared with the current 500-gallon orders. The saving is modest, which reflects a well-known property of the model: total cost changes slowly near the optimum, so an order size somewhat above or below it costs little extra. The larger benefit is space; average stock falls from 250 to about 173 gallons. If the supplier offers pallet pricing at larger quantities, that discount should be compared with the added holding cost before changing the policy.

Part 2: When to Order

Weekly demand averages 96 gallons, with a standard deviation of about 22 gallons, and the supplier's lead time is two weeks. Expected demand during the lead time is 192 gallons. Demand variation over two weeks is 22 x the square root of 2, about 31 gallons. To limit the chance of running out during a lead time to about 2 percent, the store needs a buffer of 2.05 x 31, about 64 gallons, so it should reorder when stock falls to about 256 gallons. The point-of-sale system can flag that level automatically. Silver et al. (2017) note that the right buffer depends on the service level a business chooses, so the owner should revisit it if stockouts remain costly or space becomes tight.

Part 3: Scheduling the Remodel

The paint department remodel has seven activities.

A forward pass gives each activity's earliest start and finish, and a backward pass from the final finish gives the latest times. The project takes 11 weeks along the critical path A, C, D, E, F, G, whose activities have zero float. Fixture ordering, activity B, has one week of float: it can start up to a week late without delaying the remodel. Kerzner (2017) stresses that managers should watch float closely, since a delay that consumes it turns a noncritical activity into a critical one.

Crashing Decision

The department loses about $6,000 in gross margin each week it is partly closed, from demolition through restocking. The flooring contractor can finish in one week instead of two for an extra $2,400. Shortening activity E by a week reduces the A, C, D, E, F, G path to 10 weeks; the other path, A, B, F, G, is also 10 weeks, so both become critical and the project finishes in 10 weeks. Because the $2,400 cost is less than the $6,000 a week saved, the crash is worthwhile. A further week would require shortening both paths, and the store has no affordable way to speed up fixture delivery, so 10 weeks is the practical minimum.

Checking the Results

Two quick checks confirm the work. At the economic order quantity, the annual ordering and holding costs should be equal, and they are, at about $624 each. In the network, the length of the critical path should equal the project's earliest finish, and the sum of A, C, D, E, F and G, 3 + 1 + 2 + 2 + 2 + 1, is 11 weeks. After crashing, both paths equal 10 weeks, which confirms that no further single-activity crash would shorten the project.

Recommendation

The store should order paint in lots of about 350 gallons whenever stock reaches about 256 gallons, and pay for the faster flooring crew to complete the remodel in 10 weeks, monitoring fixture delivery closely since it no longer has float.

References

Kerzner, H. (2017). Project management: A systems approach to planning, scheduling, and controlling (12th ed.). Wiley.

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

Wisniewski, M., & Shafti, F. (2020). Quantitative analysis for decision makers (7th ed.). Pearson.