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Operations Research

UTea is a tea shop that is famous for its signature cream cheese topped bubble tea.


Question 1:

UTea is a tea shop that is famous for its signature cream cheese topped bubble tea. Inexplicably, when the shop first opened, the demand for this drink was very high with customers arriving every 45 seconds to the St. George campus shop during the day. At the shop three baristas serve the customers, taking on average two minutes for each customer. Because of different skill levels and the complicated process of making the drinks, the overall variability of the service process is 𝐢𝑉𝑝 = 0.9.   

 Assume arrivals are random (πΆπ‘‰π‘Ž =1). 


 a) [5pts] What was the average wait time for customers in line at UTea in minutes? 


b) [5 pts] After the shop was open for a few weeks, UTea noticed that the number of customers joining the line decreased. In fact, it appeared that the average line length was 3 customers.  What is the new demand rate in customers per hour? What is the percentage decrease in sales (i.e., throughput)? 


c) [5 pts] To improve its profitability, UTea developed a mobile app so that customers can order from their phones and then pick up their orders in store. Upon launch, UTea found on average 40 orders per hour coming from the app. It also appeared that the online (mobile)customers did not care about the wait time. UTea serves the online and offline (in-store) orders in a first come/first served order using the next available barista. 

 Assume the processing time does not change for the online orders and πΆπ‘‰π‘Ž =1 for the mobile orders. 

 Offline (i.e., in-store) customers still arrived so there were average of three visible customers in line. 


How many off-line customers are served per hour now? What is the total number of customers per hour? 


d) [5 pts] Based on our discussion of the Paramount Diner case, what do you expect will happen next at UTea regarding the demand mix between online and offline? What are the implications for UTea?  (1-2 paragraphs)

Question 2:

Kolette will be selling a new, small purse for $399 in the upcoming spring season and needs to determine how many to make. They will not produce more once the season starts. The firm makes the purse for $200. If sold on mark-down, the purse will be sold for $175. Based on previous new product offers, demand for the purse during the season is expected to be Normally distributed with a mean of 500 and a coefficient of variation is 0.4. 

a) [2pts] What is the maximum profit Kolette can expect from the bag, i.e., if there was no uncertainty? 


b) [4 pts] How many units of the bag should Kolette produce for sale? 

c) [4 pts] What is the mismatch cost because of uncertainty? 

 d) [2 pts] Suppose the demand is Uniformly Distributed between 0 and 1000. That is, any posible number between 0 and 1000 is equally likely. How many units of the purse should Kolette produce for sale? 

 e) [4 pts] Suppose that on markdown the purse sells for $225 and demand is Uniformly Distributed between 0 and 1000. How many units should Kolette produce for sale and what would the expected profit be? 

 f) [4 pts] Suppose the purse sells for $225 and demand is Normally distributed with a mean of 500 and a coefficient of variation of 0.4. How many units should Kolette produce for sale according to the Newsvendor model? How would you determine the number of units to produce in the real world?

Question 3:

Read the Westridge Cabinets case and then answer the following questions. See also the Westridge Cabinets Exhibits spreadsheet with Exhibits 2, 5, and 6.  

A.  [10 pts] Capacity Analysis: 

i. What is the current percentage product mix for each of the six major product families: Spray stain, spray stain/glaze, wipe stain, wipe stain/glaze, Thermofoil, Melamine? 

 ii. How much time does the average box require at each of the steps show in Exhibit 1, i.e., what is the unit load in minutes for the average box? (Hint: If only 55% of the boxes use a step, the unit load is only 55% of the process time at that step.) 

 iii. What is the capacity of each of the process steps in boxes for an 8-hour shift? (Assume each staff member works on one box at a time at a processing step, and each box is worked on by only one staff member at a processing step) 

 iv. What is the bottleneck under the current product mix? What is the bottleneck capacity in average boxes per day?  For each of the six major products what is the bottleneck and its capacity, i.e., which step is the throughput restricting step for that product? 

 v. What is the implied utilization of each step assuming 250 boxes are put into production each day? (Implied utilization = 250 boxes/Capacity)

B. [10 pts] Flow Time Analysis: 

 i. What is the average cumulative waiting time for each of the products in the production system? (Hint: What is the backlog for each of the production steps?)  

ii. Under the current scheduling policy, how long would it take to get each box through the production process if there were no backlogs? 

 iii. What is the total throughput time for each of the product families, i.e., how long does the average box spend in production under current scheduling policy? 

 iv. Compare the average total throughput time for a box to the work-in-progress inventory. 

 v. Compare the total throughput time to the minimum possible production time for each product if there were no delays.

C. [5 pts] Variability 

i. What are the major sources of variability? Characterize the level of variability.  

ii. How does Westridge Cabinets address the variability? (1-2 paragraphs) 


D.  [10 pts] Current Strategy 

i. On what dimensions does Westridge Cabinets compete in the marketplace? What should be noted about the firm’s position in the market? 

 ii. What is the broad operations strategy they are taking? Why have they taken this approach? 

 iii. What are the asset and process choices they have made to support the operations strategy?  Why have they made these choices? 

 iv. What are the gaps between the operations strategy and the business strategy? In what ways does the operations strategy, its asset and process choices, fail to support the business strategy?

E. [25 pts] Improvement 

What should Mayank Chadha do to improve the manufacturing operations at Westridge Cabinets? Explain clearly what you would recommend and why you believe this will help?  (1 -2 pages)



As  the  regular  weekly  management  meeting  concluded  on  the  morning  of  Monday,  January  19,  2015, Mayank Chadha, chief operating officer (COO) at Westridge Cabinets in Red Deer, Alberta, stayed behind in the meeting room with Victor Maracle, vice president manufacturing, to review the issues that had been raised in the discussion. Mayank commented to Victor about the challenges they faced: 

 Manufacturing  lead  times  and  capacity  issues  make  it  difficult  to  meet  customer  delivery  dates without expediting. Meanwhile, some customers are delaying orders at the last minute, squandering production capacity and driving up inventory levels. We need to improve our on-time delivery performance without increasing our manufacturing costs.   

The budget for next fiscal year has to be finalized by the end of the month, which means I need to get a handle on the improvements we can make in our manufacturing operations and the resulting cost structure, including staffing levels in the plant. We should be realistic with our forecast, but at the same time our plan needs to show significant improvement over this year’s results. Let’s meet on Friday morning to review options. I will send you my analysis and notes before the meeting. 



 Established  in  1983,  Westridge  Cabinets  (Westridge)  had  grown  to  become  Alberta’s  largest  fully integrated  cabinet  manufacturer.  With a  broad  product  range and a reputation for  delivering  well-crafted, quality products, Westridge served the new home construction and renovation markets. Most cabinets were for kitchens and bathrooms. 

 The  company’s  head  office  and  150,000-square-foot  manufacturing  facility  were  located  in  Red  Deer, Alberta.  Westridge  distributed  its  products  through  authorized  dealers  in  central  and  western  Canada,  as well  as  the  United  States.  In  addition,  Westridge  had  showrooms  and  localized  design,  service  and installation centres in Red Deer, Edmonton and Calgary, which were referred to as “branches.” 

 Every  Westridge  cabinet  was  a  custom  order,  and  almost  every  component  —  including  doors,  drawer faces, drawer boxes and panel parts — was manufactured by Westridge. The company offered more than 50 styles, which could be finished in 45 different stains, dozens of paints and thermofoils, and eight species of woods.  



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