York-Perry Industries (YPI) manufactures a mix of affordable guitars (A, B, C) t
ID: 433162 • Letter: Y
Question
York-Perry Industries (YPI) manufactures a mix of affordable guitars (A, B, C) that are fabricated and assembled at four different processing stations? (W, X, Y, Z). The operation is a batch process with small setup times that can be considered negligible. The product information (price, weekly demand, and processing times) and process sequences are shown below. Purchased parts and raw materials (shown as a per-unit consumption rate) are represented by inverted triangles. YPI is able to make and sell up to the limit of its demand per week with no penalties incurred for not meeting the full demand. Each workstation is staffed by one highly skilled worker who is dedicated to work on that workstation alone and is paid $11 per hour. The plant operates one 8-hour shift per day and operates on a 5-day work week (i.e., 40 hours of production per person per week). Overhead costs are $9,000/week.
The senior management team wants to improve the profitability of the firm by accepting the right set of orders. Currently, decisions are made using the traditional method, which is to accept as much of the product with the highest contribution margin as possible (up to the limit of its demand), followed by the next highest contribution product, and so on until all available capacity is utilized. Because the firm cannot satisfy all the demand, the product mix must be chosen carefully. Jay Perry, the newly promoted production supervisor, is knowledgeable about the theory of constraints and the bottleneck-based method for scheduling. He believes that profitability can indeed be improved if bottleneck resources are exploited to determine the product mix. What is the change in profits if, instead of the traditional method that YPI has used thus far, the bottleneck method advocated by Jay is used for selecting the product mix? What is the profit if the traditional method is used for determining YPI's product mix?
(Note: When determining the product mix, if the number of units to produce is not a whole number, be sure to round down to the next whole number before proceeding with any profit calculations.)
The profit using the traditional method is $_______. (Enter your response rounded to the nearest whole number.)
What is the profit if the bottleneck-based method is used for determining YPI's product mix? (Note: When determining the product mix, if the number of units to produce is not a whole number, be sure to round down to the next whole number before proceeding with any profit calculations.)
The profit using the bottleneck-based method is $__________. (Enter your response rounded to the nearest whole number.)
Calculate the change in profit. By using the bottleneck-based method, profit _________(increases/decreases) by $______. (Enter your response rounded to the nearest whole number.)
Product A Step 1 Station WW (13 min) Step 2 Station Z (11 min) Step 3 Station X (9 min) Product: A Price: $95/unit Demand: 64 units/wk %9 Raw materials Product B Purchased part Step 1 Station Step 2 Station Y (13 min) Step 3 Station Z (8 min) Product: B Price: $85/unit Demand: 54 units/wk $7 (9 min) Raw materials Product C Purchased part Step 1 Station X (10 min) Step 2 Station W (19 min) Step 3 Station Y (6 min) Product: C Price: $105/unit Demand: 64 units/wk $16 Raw materials Purchased partExplanation / Answer
Traditional Method
Step 1: Compute capacity of each station
= 5 days a week * 8 hours a day * 60 minutes per hour = 2400 minutes per week
Step 2: Determine bottleneck station
Workload of each station = SUMPRODUCT of demand of each product* processing time
Workload of station W = 64*13 + 54*9 + 64*19 = 2534 minutes
Workload of station X = 64*9 + 54*0 + 64*10 = 1216 minutes
Workload of station Y = 64*0 + 54*13 + 64*6 = 1086 minutes
Workload of station Z = 64*11 + 54*8 + 64*0 = 1136 minutes
Workload of station W (2534 minutes) is greater than its capacity (2400 minutes)
Therefore, station W is the bottleneck.
Step 3: Determine contribution margin of each product
Contribution margin (CM) = Price - Raw material cost - Purchase part cost
CM of product A = 95 - 9 - 5 = 81
CM of product B = 85 - 7 - 5 = 73
CM of product C = 105 - 16 - 6 = 83
Product C gives the highest CM, following by A and B. Therefore production is proritized in the same order.
Step 4: Determine optimal product mix
Production of C and A is scheduled first upto the demand. Thereforeafter, remaining time of bottleneck station is used for product B
Remaining time of bottleneck station W after production of C and A as per weekly demand = 2400 - 64*19 - 64*13 = 352 minutes
Production of B = 352/9 = 39 complete products.
Optimal product mix is: A = 64, B = 39, C = 64
Profit using traditional method = Contribution margin from the three products - Labor cost - Overhead cost
= 64*81 + 39*73 + 64*83 - 4*8*5*11 - 9000
= $ 2583
Bottleneck Method
In this method, we use contribution margin per minute of bottleneck station to prioritize product mix.
CM of product A per minute of bottleneck station W = (95 - 9 - 5)/13 = 6.23
CM of product B per minute of bottleneck station W = (85 - 7 - 5)/9 = 8.11
CM of product C per minute of bottleneck station W = (105 - 16 - 6)/19 = 4.37
CM of product B per minute of bottleneck station W is the highest, following by A and C. Therefore, production is scheduled in the same priority.
Minutes remaining after production of B and A to weekly capacity = 2400 - 54*9 - 64*13 = 1082 minutes
Production of product C = 1082/19 = 56.95 ~ 56 compete units
Optimal product mix: A = 64, B = 54, C = 56
The profit using the bottleneck-based method = 64*81 + 54*73 + 56*83 - 4*8*5*11 - 9000
= $ 3014
by using the bottleneck-based method, profit increase by $ 3014 - 2583 = $ 431
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