Let’s break down the problem and simulate the 10-week operation step-by-step, as requested. --- ### **Step 1: Problem Restatement** - **Inventory Policy:** Order 10 refrigerators when only 2 are left at week's end. - **Initial Inventory:** 5 units. - **Demand per week:** Random, based on probabilities. - **Lead time for orders:** Random, based on probabilities. - **Holding cost:** $1/unit/week for leftover inventory. - **Stockout cost:** $40 each time demand cannot be met. - **Simulation period:** 10 weeks. --- ### **Step 2: Setup for Simulation** #### **A. Demand Distribution** | Demand (units) | Probability | |:--------------:|:-----------:| | 0 | 0.20 | | 1 | 0.40 | | 2 | 0.20 | | 3 | 0.15 | | 4 | 0.05 | #### **B. Lead Time Distribution** | Lead Time (weeks) | Probability | |:-----------------:|:-----------:| | 1 | 0.15 | | 2 | 0.35 | | 3 | 0.50 | --- ### **Step 3: Simulate 10 Weeks** Let’s create a table to organize our calculations. #### **Variables to track each week:** - Beginning Inventory - Demand (random) - Ending Inventory - If order is placed (when inventory = 2 at week’s end) - Lead Time (random, if order is placed) - Arriving Order (if lead time completes) - Holding cost - Stockout cost --- #### **Step 4: Generate Random Numbers (or Assume Values)** If not provided, we can assume random values for illustration. Here, let’s **assume the following sequence for demand and lead time** (you can use random numbers or dice for real simulation): | Week | Demand | Lead Time (if order placed) | |------|--------|----------------------------| | 1 | 1 | | | 2 | 2 | | | 3 | 4 | 2 | | 4 | 3 | | | 5 | 2 | 3 | | 6 | 1 | | | 7 | 2 | 1 | | 8 | 0 | | | 9 | 1 | | | 10 | 3 | | --- ### **Step 5: Fill Out Simulation Table** Let’s simulate week by week. | Wk | Begin Inv | Demand | Ending Inv | Order Placed? | Lead Time | Arriving Order | Stockout? | Holding Cost | Stockout Cost | |----|-----------|--------|------------|---------------|-----------|----------------|-----------|--------------|---------------| | 1 | 5 | 1 | 4 | No | | | No | $4 | $0 | | 2 | 4 | 2 | 2 | Yes | 2 | | No | $2 | $0 | | 3 | 2 | 4 | -2 | No | | | Yes | $0 | $40 | | 4 | 0 | 3 | -3 | Yes | 3 | | Yes | $0 | $40 | | 5 | 0 | 2 | -2 | Yes | 3 | | Yes | $0 | $40 | | 6 | 0 | 1 | -1 | Yes | 1 | | Yes | $0 | $40 | | 7 | 0 | 2 | -2 | Yes | 1 | 10 | Yes | $0 | $40 | | 8 | 8 | 0 | 8 | No | | | No | $8 | $0 | | 9 | 8 | 1 | 7 | No | | | No | $7 | $0 | | 10 | 7 | 3 | 4 | No | | | No | $4 | $0 | **Notes:** - When inventory drops below zero, all units are sold, but unmet demand triggers a stockout cost. - Orders arrive after the lead time. For instance, 10 units ordered in week 2 arrive at the end of week 4. --- ### **Step 6: Calculate Totals** - **Total Holding Cost:** $4 + $2 + $0 + $0 + $0 + $0 + $0 + $8 + $7 + $4 = **$25** - **Total Stockout Cost:** $0 + $0 + $40 + $40 + $40 + $40 + $40 + $0 + $0 + $0 = **$200** - **Average Weekly Holding Cost:** $25 / 10 = **$2.50** - **Average Weekly Stockout Cost:** $200 / 10 = **$20.00** --- ### **Step 7: Final Answers** #### **a. Average Weekly Stockout Cost:** **$20.00** #### **b. Average Weekly Holding Cost:** **$2.50** --- ## **Summary Table** | Cost | Total over 10 weeks | Average per week | |-----------------|--------------------|------------------| | Holding | $25 | $2.50 | | Stockout | $200 | $20.00 | --- ### **Explanation** - **Holding cost** is the sum of leftover units at each week's end, multiplied by $1. - **Stockout cost** is $40 each time demand couldn’t be met. - We simulated 10 weeks, tracking inventory, order arrivals, and costs. - **Actual results may vary** if you use actual random numbers or a different sequence. --- **If you want to see the simulation with actual random numbers or have a specific random seed, let me know!**