Let's break down the problem step by step with all calculations shown: --- ### **Given Data** #### **Parts Moved Between Work Centers (Flow Matrix)** | | A | B | C | D | |-----|-----|-----|-----|-----| | **A** | - | 325 | 600 | 50 | | **B** | 420 | - | 200 | 0 | | **C** | 0 | 0 | - | 750 | | **D** | 0 | 0 | 0 | - | #### **Existing Layout** A ---30'--- B ---30'--- C ---30'--- D --- ## **a) Cumulative "Load x Distance" or "Movement Cost"** For the existing layout, calculate the total movement cost: - **Distance between adjacent centers = 30 feet** - **Distance between centers separated by one center = 60 feet** - **Distance between centers at the ends = 90 feet** Let's create a distance matrix for the current layout: | | A | B | C | D | |-----|-----|-----|-----|-----| | A | 0 | 30 | 60 | 90 | | B | 30 | 0 | 30 | 60 | | C | 60 | 30 | 0 | 30 | | D | 90 | 60 | 30 | 0 | Now, sum up all **Flow x Distance** for each pair (from the flow matrix): #### **A to Others** - A → B: 325 moves × 30 ft = 9,750 - A → C: 600 moves × 60 ft = 36,000 - A → D: 50 moves × 90 ft = 4,500 #### **B to Others** - B → A: 420 moves × 30 ft = 12,600 - B → C: 200 moves × 30 ft = 6,000 - B → D: 0 moves × 60 ft = 0 #### **C to Others** - C → A: 0 moves × 60 ft = 0 - C → B: 0 moves × 30 ft = 0 - C → D: 750 moves × 30 ft = 22,500 #### **D to Others** - D → A: 0 - D → B: 0 - D → C: 0 Now, sum all these values: - 9,750 (A→B) - 36,000 (A→C) - 4,500 (A→D) - 12,600 (B→A) - 6,000 (B→C) - 0 (B→D) - 0 (C→A) - 0 (C→B) - 22,500 (C→D) - 0 (D→A, D→B, D→C) **Total Movement Cost = 9,750 + 36,000 + 4,500 + 12,600 + 6,000 + 22,500 = 91,350** **Answer (a):** Cumulative "load x distance" or "movement cost" = **91,350** --- ## **Center Pair with Highest and Second Highest Moves** ### **Based on the flow matrix:** - **C → D:** 750 moves (highest) - **A → C:** 600 moves (second highest) So, centers **C and D** should be next to each other (highest), and **A and B** should be next (second highest). --- ## **b) Improved Layout** Given: **A and D locations are fixed.** Need to find optimal positions for B and C. **Pairs with highest moves should be adjacent:** - C and D (750 moves) - A and B (420 moves from B to A + 325 moves from A to B = 745, but A to C is 600, which is still high) But since C and D should be adjacent (highest), and A and B should be adjacent (second highest), test both possible placements of B and C between A and D. ### **Possible Layouts:** 1. **A - B - C - D** 2. **A - C - B - D** Let's calculate the movement cost for both: --- ### **Layout 1: A - B - C - D** Distances: - A to B = 30 - A to C = 60 - A to D = 90 - B to C = 30 - B to D = 60 - C to D = 30 Let’s repeat the calculations: #### **A to Others** - A → B: 325 × 30 = 9,750 - A → C: 600 × 60 = 36,000 - A → D: 50 × 90 = 4,500 #### **B to Others** - B → A: 420 × 30 = 12,600 - B → C: 200 × 30 = 6,000 - B → D: 0 × 60 = 0 #### **C to Others** - C → A: 0 × 60 = 0 - C → B: 0 × 30 = 0 - C → D: 750 × 30 = 22,500 **Total = 9,750 + 36,000 + 4,500 + 12,600 + 6,000 + 22,500 = 91,350** --- ### **Layout 2: A - C - B - D** Distances: - A to C = 30 - A to B = 60 - A to D = 90 - C to B = 30 - C to D = 60 - B to D = 30 #### **A to Others** - A → B: 325 × 60 = 19,500 - A → C: 600 × 30 = 18,000 - A → D: 50 × 90 = 4,500 #### **B to Others** - B → A: 420 × 60 = 25,200 - B → C: 200 × 30 = 6,000 - B → D: 0 × 30 = 0 #### **C to Others** - C → A: 0 × 30 = 0 - C → B: 0 × 30 = 0 - C → D: 750 × 60 = 45,000 **Total = 19,500 + 18,000 + 4,500 + 25,200 + 6,000 + 45,000 = 118,200** --- ### **Best Layout** - **A - B - C - D**: 91,350 - **A - C - B - D**: 118,200 So, **A - B - C - D** gives the lowest cost. ### **Where should B and C be located?** - The work center that should be between A and D is **B** (i.e., the layout is: A - B - C - D). --- ## **Final Answers** ### a) Existing layout cumulative "movement cost": **91,350** ### b) Based on the flows: - Centers that should be next to each other (**highest moves**): **C and D** - Centers that should be next to each other (**second highest**): **A and B** - The work center that should be between A and D: **B** - Cumulative distance based on improved layout: **91,350** feet --- **If you have follow-up questions or need a summary table, let me know!**