This assigned project aims to enable a student to analyze the given quantitative information and use mathematical models/formulas taught in class to solve a set of connected questions on topics such as forecasting, capacity requirements planning, inventory, bill of materials in MRP, and scheduling. By doing so, a student can apply course concepts to enhance quantitative reasoning abilities or skills for effective decision-making.

Jewelry manufacturing industries are mostly labor-intensive, requiring high operator involvement. Jewelry items such as brooches, rings, bracelets, and earrings are meant for adornment and can be worn by individuals.

A jewelry company reveals the following production information, as shown in Table 1, including the different types of each product name, processing times, and due dates. The production department does not consider product setup times on machines for its production.

| Product Name | Product Type | Processing Time/Hour | Minutes Until Due |
|--------------|--------------|----------------------|-------------------|
| Bracelets | A | 0.5 | 15 |
| Rings | B | 0.2 | 18 |
| Brooches | C | 0.7 | 55 |
| Earrings | D | 0.1 | 12 |
| | E | 0.3 | 12 |
| | F | 0.5 | 21 |
| | G | 0.6 | 33 |
| | H | 0.9 | 54 |
| | I | 0.7 | 44 |
| | J | 0.3 | 20 |
| | K | 0.4 | 33 |
| | L | 0.2 | 14 |

Table 1. Processing times and due dates of product types.

The receiving department at the company orders materials for producing each finished product type. For example, one unit of product type A of bracelets requires one unit of material type A1, three units of material type A2, and two units of material A3. Each unit of material A2 needs one unit of material A21, one unit of material A3 needs three units of A31, and one unit of material A31 needs five units of material A311.

Moreover, the purchase costs and quality (quality scale is out of 100) of materials required from suppliers to build the finished product are shown in Table 2.

| Product Type | Measures | Supplier 1 | Supplier 2 | Supplier 3 |
|--------------|----------|------------|------------|------------|
| A1 | cost | $4.0 | $4.5 | $4.7 |
| A2 | quality | 60 | n/a | n/a |
| A3 | cost | $3.9 | $3.5 | $3.0 |
| A21 | quality | 40 | 55 | 40 |
| A31 | cost | $2.9 | $3.7 | $2.5 |
| A311 | quality | 40 | 40 | n/a |

Table 2. Purchase costs and quality of materials.

The production manager sets each machine to be available for 2000 hours per year (i.e., a department works one 8-hour shift per day, 250 days per year). Each machine costs $15,000.

Additionally, the marketing department provides the following customer demand information about product type A of bracelets, as shown in Table 3.

| Month | Demand |
|--------|--------|
| Jan | 500 |
| Feb | 550 |
| Mar | 610 |
| Apr | 620 |
| May | ? |
| Jun | ? |
| Jul | ? |
| Aug | ? |
| Sep | ? |
| Oct | ? |
| Nov | ? |
| Dec | ? |

Table 3. Available customer demand values.

Finally, the management of inventory at the company, which plays a significant role in meeting customer demand and smoothing production requirements, estimates the following:
- Setup costs per order include $150 for fixed cost transportation (trucking) and $200 for other order expenses.
- Annual holding cost is 6% of the cost per unit of product type A of bracelets.
- Shortage cost is 25% of the cost per unit of product type A of bracelets.
- Lead time is one month.
- Demand rate is assumed to be 470 units per month.
- Starting (beginning) inventory for January is 1500 units.
- No safety stock is specified.

Based on the given information, a student needs to act as a decision-maker on behalf of the company by addressing the following prompts:

1. Assuming April as the current month of the year, there seems to be missing data about the customer demand for product type A of bracelets for the rest of the year. This causes a problem in planning the production capacity. Do you agree? Why? How would you handle this situation, and show your answer quantitatively? (Due February 20, 2022, by midnight)

2. Based on how you have handled prompt 1, what should the total annual capacity requirements (i.e., total processing time needed) in hours be? (Due March 6, 2022, by midnight)

3. If you need to allocate resources such as workers and machines, how many machines do you need to handle the required volume? (Due March 6, 2022, by midnight)

4. Do you have any idea about how much the total machines required would cost you? (Due...)