Let's break down the problem step by step, then show how to fill in the Excel fields: ### **A. Calculating Number of Racks (Kanbans) Needed Between Painting and Glazing** #### **Step 1: Calculate Daily Expected Demand** - **Units to be completed per shift:** 290 units - **Shift duration:** 8 hours (480 minutes) - **Units per rack:** 5 - **Racks needed per shift:** \[ \text{Racks per shift} = \frac{290\ \text{units}}{5\ \text{units/rack}} = 58\ \text{racks} \] #### **Step 2: Calculate Container Waiting Time (days)** - **Average waiting/handling time per rack:** 9 minutes - **1 day = 480 minutes (8-hour shift)** - **Waiting time in days:** \[ \text{Waiting Time (days)} = \frac{9\ \text{minutes}}{480\ \text{minutes/day}} = 0.01875 \] #### **Step 3: Calculate Processing Time (days)** - **Glazing rate:** 1 rack every 15 minutes - **Time to process 1 rack:** 15 minutes - **Processing time in days:** \[ \text{Processing Time (days)} = \frac{15\ \text{minutes}}{480\ \text{minutes/day}} = 0.03125 \] #### **Step 4: Policy Variable (α)** - **Given:** α = 0.15 #### **Step 5: Kanban (Rack) Calculation Formula** The **Kanban formula** is: \[ \text{Number of Kanbans} = \left( \frac{\text{Daily Demand} \times (\text{Waiting Time} + \text{Processing Time})}{\text{Units per Rack}} \right) \times (1 + \alpha) \] Plug in the numbers: - **Daily Demand:** 290 units - **Waiting Time:** 0.01875 days - **Processing Time:** 0.03125 days - **Units per rack:** 5 - **Policy variable:** 0.15 \[ \text{Number of Kanbans} = \left( \frac{290 \times (0.01875 + 0.03125)}{5} \right) \times (1 + 0.15) \] \[ = \left( \frac{290 \times 0.05}{5} \right) \times 1.15 \] \[ = \left( \frac{14.5}{5} \right) \times 1.15 \] \[ = 2.9 \times 1.15 = 3.335 \] **So, you would need at least 4 racks (since you can't have a fraction of a rack) between painting and glazing.** --- ### **B. Significance of Correct Number of Racks (Kanbans)** - Ensures **smooth material flow** without overproduction or excessive waiting. - Too few racks = **starvation** at glazing, lost production time. - Too many racks = **excess WIP inventory**, higher costs, and less responsiveness. - Correct Kanban count **optimizes inventory, reduces lead time, and improves responsiveness to customer demand.** - **Operational competitiveness** is enhanced by minimizing waste, improving throughput, and reducing costs. --- ### **Excel Table Fill-In** | | Value | |--------------------------|----------------------| | Daily Expected Demand | 290 | | Quantity in Standard Container | 5 | | Container Waiting Time (days) | 0.01875 | | Processing Time (days) | 0.03125 | | Policy Variable | 0.15 | --- ### **Summary Table for Excel** | Field | Value | |-------------------------------|------------| | Daily Expected Demand | 290 | | Quantity in Standard Container| 5 | | Container Waiting Time (days) | 0.01875 | | Processing Time (days) | 0.03125 | | Policy Variable | 0.15 | | **Number of Kanbans/Racks** | **4** | You can use this table as your Excel input. If you need an Excel formula, you can use: ```excel =ROUNDUP(((290*(0.01875+0.03125))/5)*(1+0.15), 0) ``` This will yield **4 Kanbans/Racks**. --- If you need a template or the calculation steps in Excel, let me know!

Certainly! Here's a detailed breakdown of each part of the calculation, including all steps and reasoning, followed by the final answer. --- ### **Part A: Calculating the Number of Racks (Kanbans) Needed** #### **1. Determine the Daily Demand in Units** - **Units to be completed per shift:** 290 units - **Shift length:** 8 hours = 480 minutes - **Units per rack:** 5 units **Racks needed per shift:** \[ \text{Racks per shift} = \frac{\text{Units per shift}}{\text{Units per rack}} = \frac{290}{5} = 58\ \text{racks} \] This means each shift requires moving 58 racks from painting to glazing. --- #### **2. Calculate the Container Waiting Time (in days)** - **Average waiting/handling time per rack:** 9 minutes - **Total minutes in a day (shift duration):** 8 hours = 480 minutes **Waiting time in days:** \[ \text{Waiting Time} = \frac{9\ \text{minutes}}{480\ \text{minutes/day}} = 0.01875\ \text{days} \] This represents the average time a rack spends waiting before being processed in days. --- #### **3. Calculate the Processing Time per Rack (in days)** - **Processing rate:** 1 rack every 15 minutes **Processing time for one rack:** \[ \text{Processing Time} = \frac{15\ \text{minutes}}{480\ \text{minutes/day}} = 0.03125\ \text{days} \] --- #### **4. Incorporate the Policy Variable (\(\alpha\))** Given: \[ \alpha = 0.15 \] This accounts for safety stock or buffer (to prevent stockouts). --- #### **5. Calculate the Number of Kanbans (Racks) Needed** The general **Kanban formula** is: \[ \boxed{ \text{Number of Kanbans} = \left( \frac{\text{Daily Demand} \times (\text{Waiting Time} + \text{Processing Time})}{\text{Units per Rack}} \right) \times (1 + \alpha) } \] **Plugging in the values:** - Daily demand (units): **290** - Waiting time: **0.01875 days** - Processing time: **0.03125 days** - Units per rack: **5** - Safety factor: **1 + 0.15 = 1.15** **Calculation:** \[ \text{Number of Kanbans} = \left( \frac{290 \times (0.01875 + 0.03125)}{5} \right) \times 1.15 \] \[ = \left( \frac{290 \times 0.05}{5} \right) \times 1.15 \] \[ = \left( \frac{14.5}{5} \right) \times 1.15 \] \[ = 2.9 \times 1.15 = 3.335 \] Since the number of racks must be a whole number, **round up** to **4** racks. --- ### **Final Result for Part A:** **Number of racks (Kanbans) needed between painting and glazing:** \[ \boxed{\textbf{4 racks}} \] --- ### **Part B: Significance of Correct Number of Racks (Kanbans)** - **Operational Flow:** Correct Kanban size ensures smooth flow of materials. Too few racks cause delays (starvation at the glazing station), reducing throughput. - **Inventory Management:** Too many racks increase Work-In-Progress (WIP), leading to higher storage costs and potential waste. - **Responsiveness:** Proper Kanban levels allow the system to respond quickly to demand changes, improving flexibility. - **Cost Efficiency:** Minimizing excess WIP reduces inventory holding costs and improves cash flow. - **Competitive Advantage:** Well-calibrated Kanban systems help Olde World maintain high efficiency, reduce lead times, and lower costs, thus enhancing its competitiveness. --- ### **Excel Data Summary** | Field | Calculation / Value | |------------------------------|--------------------------------------------| | Daily Expected Demand | **290 units** | | Quantity per Standard Container | **5 units** | | Container Waiting Time (days) | **=9/480 = 0.01875** | | Processing Time (days) | **=15/480 = 0.03125** | | Policy Variable (\(\alpha\)) | **0.15** | | **Number of Kanbans (rounded up)** | **4** | --- ### **Excel Formula for Number of Kanbans:** ```excel =ROUNDUP(((290 * (0.01875 + 0.03125)) / 5) * (1 + 0.15), 0) ``` This formula yields **4** as the required number of racks (Kanbans). --- **Summary:** - **Part A:** 4 racks - **Part B:** Proper Kanban sizing ensures smooth operations, reduces costs, and enhances Olde World’s competitiveness. If you'd like, I can prepare a detailed Excel sheet template with these calculations!