BUSI 2113: Production and Operations Management

Unit 2 Exercises

Questions

1. Walmart Canada debuted a new checkout system called "fast lane" that lets customers avoid cashiers and registers. Here's how it works: My Walmart users scan items with their phones as they shop. Once a user is finished shopping, they click "checkout" to receive a barcode. Next, the customer scans the order barcode at one of four scanning stations in the fast lane. This action charges the credit card the My Walmart user has on file. Finally, just before exiting the store, customers present their mobile receipts to a worker tending the fast lane. The system has debuted in a newly opened store in Toronto that Walmart says will serve as a prototype for future store renovations. Assume the new fast lane setup will replace 2 old cashier lanes that were staffed by a cashier and bagger on each lane. One worker mans all 4 scanning stations (answering questions, checking for un-scanned items, taking coupons, etc). Checkout on the new lanes takes 2 minutes (customers bag their own orders) while
checkout with the old lanes took only 45 seconds. In addition, the electricity costs for both setups are $0.05 per checkout while bagging (material) costs are $0.10 per checkout with the old system and $0.15 for the new system. The new lanes also require $100/shift in capital costs. Assume that the lanes are always in use for 8 hours per day (1 shift) and that a worker makes $10/hour.

(a) How many checkouts did the old system provide in a shift?
(b) How many checkouts does the new system provide?
(c) What is the multifactor productivity for each system?

2. Below is a network diagram that represents a university revamp project. The project manager analyzes this project using the critical path (CP) method. Activity durations are indicated on the network.

(a) Which is the CP?
(b) Calculate the duration of the CP.
(c) Calculate the amount of slack time at activity H.
(d) If activity I were delayed by ten time-units, what would be the impact on the project duration?

3. Consider the network described in the table below.

Draw the network diagram and answer the following questions.
(a) Calculate the expected duration of each activity.
(b) Calculate the expected duration and variance of the critical path.
(c) Calculate the probability that the project will be completed in more than 28 time units.

4. The client of a project has requested the project team to crash 8 hours of time. The table below provides the necessary information about the possible project crashing.
(a) What is the crash cost for 8 hours of time-savings?
(b) Assume the team calls the client and asks for a project extension, reducing the amount of time they
need to crash. The project team has a $20 crash budget. Is the budget sufficient to crash 4 hours of
time?

Unit 4 Exercises

Questions

1. Use exponential smoothing with trend adjustment to forecast demand for period 11. Let α = 0.5, ???? = 0.3, and let the initial trend value be 12 and the initial forecast be 200.

2. A restaurant has tracked the number of meals served at lunch over the last four weeks. The data show little in terms of trends, but do display substantial variation by day of the week. Use the following information to determine the seasonal (daily) indices for this restaurant. Round all numbers in your calculations to four decimal places.

3. WZ Inc. is an event planning and promotion company who organizes events of different sizes for their clients. Planning and managing events have more than their fair share of frustrations and stressors. From last-minute changes to procrastinating clients, the profession isn’t for the faint of heart. Luckily, executing a successful event makes everything else (like the crazy long hours) worth it. There is a major event planning project due in 8 weeks. The penalty for planning the event late is $14 000 per week, since any delay will cause the venue to open later than anticipated, and cost the client significant returns. If the company uses its inside event planner to complete the planning, it will have to pay them overtime for all work. WZ Inc. has estimated that it will cost $12 000 per week (wages and overhead), including late weeks, to have the event planners finish the job. WZ is also considering outsourcing the planning work to other event planning companies. A bid of $92 000 has been received for the completed event plan. Yet another option for completing the job is to conduct a joint planning by having a third party complete all the preliminary work at a cost of $56 000. WZ would then complete the rest of the planning at an estimated cost of $30 000.

WZ has estimated the following probabilities of completing the project within various time frames when using each of the three options. Those estimates are shown in the following table:

What is the best decision based on an expected monetary value criterion?

4. Montreal Hardware Co. is making a make-or-buy decision. The market feedback shows that the optimal price for this item is $10 each. If the item is outsourced to Laval Hardware Co, there is virtually no cost other than the $6 per unit that they would pay Laval Hardware Co. Internally, they have two choices. Process A requires an investment of $120,000 for design and equipment, but it results in a $4 per unit cost. Process B requires only a $100,000 investment, but its per unit cost is $5. Regardless of whether the item is subcontracted or produced internally, there is a 50% chance that they will sell 50,000 units, and a 50% chance that they will sell 100,000 units. Draw the decision tree appropriate to the alternatives and outcomes stated. Using the decision tree and EMV, what is their best choice?

Unit 8 Exercises

Questions 

1. The computer lab at State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. Students arrive at the help desk at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.
a) What is the average time a student is in the lab?
b) What is the average number of students in the lab?
c) What is the average number of students waiting to receive service?
d) What is the average time a student is in the queue?
e) What is the probability that there are no students at the computer lab?
f) What percentage of the time is the help desk busy?
g) What is the probability that there are exactly 2 students in the lab?
h) By how much would your answer to part (a) be reduced if a second help desk, which could do the same work, were added?

2. A fabric factory has 5 weaving machines in use. These weaving machines need repair after about 20 hours of use. Breakdowns have been determined to be Poisson distributed. Jim, the maintenance worker can service a weaving machine in an average of 2 hours, following an exponential distribution. Weaving machine downtime costs $120 per hour. Jim is paid $25 per hour. a) What is the average time a weaving machine is waiting to be repaired? b) What is the average number of weaving machines in the repairing area? c) What is the total hourly costs?

3. William’s Window Hardware is looking for a new supplier for its casement window operators. William consider price and reputation as the most important criteria. He considers reputation to be four times more important than price. William has narrowed his choices to two suppliers. On a 10-point scale, he has assigned Rideau’s Windows Supply a score of 9 on price and 4 on reputation. He has assigned Ian and Family a score of 3 on price and 6 on reputation. Apply the factor weighting technique to help William choose a new window operator supplier.

Unit 10 Exercises

Questions

1. A standing desk consists of a desk top, four legs, and two adjustment motors. Each leg fastens to the desk top with one fastener set. Each adjustment motor requires two fastener sets for attachment to the legs. Currently there is one order outstanding, to make 180 standing desks. There are 500 legs and 20 desk tops in inventory. There are no other large items in inventory, and no scheduled receipts.
(a) Draw the product structure tree.
(b) Calculate the net requirements to fulfill the outstanding order.

2. The following table shows the bill of material for Product A. The gross requirements for A are 200 units in week 6 and 250 units in week 8. Develop the MRP tables for each item for an 8-week planning period. Use the lot-for-lot lot-sizing rule. 

Assessment Summary

This assessment involves exercises across multiple units, covering topics in operations management, project management, forecasting, decision analysis, queuing theory, supplier selection, and materials planning (MRP). Students are expected to demonstrate understanding by solving quantitative problems, drawing network diagrams, calculating productivity, forecasting demand, evaluating decision alternatives, and preparing bills of materials.

Key Pointers to be Covered:

1. Unit 2: Operations and Project Management

   • Calculate checkouts and multifactor productivity for different systems (Walmart case study)
   • Draw network diagrams, determine critical paths, slack times, and project impacts
   • Analyze project crashing costs and budget sufficiency

2. Unit 4: Forecasting and Decision Making

   • Apply exponential smoothing with trend adjustment
   • Compute seasonal indices for demand data
   • Evaluate make-or-buy and project outsourcing decisions using probability and cost analysis

3. Unit 8: Queuing and Supplier Selection

   • Apply Poisson and exponential distributions to calculate waiting times, queue lengths, and service probabilities
   • Assess cost implications of machine downtime and service rates
   • Apply factor weighting techniques for supplier selection

4. Unit 10: Materials Planning

   • Draw product structure trees and calculate net requirements
   • Develop MRP tables using lot-for-lot lot-sizing rule

Approach by Academic Mentor

The Academic mentor guided the student step by step, ensuring comprehension of both concepts and methods:

1. Understanding Requirements:

   • Reviewed each unit’s exercises to clarify the objectives and expected outputs.
   • Highlighted the formulas, distribution assumptions, and decision-making frameworks relevant to each question.

2. Step-by-Step Problem Solving:

   • Unit 2:

     • Calculated checkouts per shift and multifactor productivity using time, labor, and cost data.
     • Constructed network diagrams, identified critical paths, calculated slack times, and assessed the effect of delays.
     • Evaluated project crashing costs and confirmed budget sufficiency using clear formulas.
   • Unit 4:
     • Applied exponential smoothing with trend adjustments to forecast demand.
     • Calculated seasonal indices for restaurant demand using observed data.
     • Built decision trees and applied Expected Monetary Value (EMV) analysis for make-or-buy decisions.
   • Unit 8:
     • Applied queuing theory formulas to compute waiting times, probabilities, and utilization of help desks.
     • Calculated downtime costs and maintenance requirements for machines.
     • Used factor weighting to select the optimal supplier.

   • Unit 10:

     • Drew product structure trees to visualize components and subassemblies.
     • Calculated net requirements and developed MRP tables to manage inventory planning effectively.

3. Outcome Achievement:

   • Students obtained structured answers with accurate calculations, clear diagrams, and logical reasoning.
   • Applied quantitative and analytical techniques to real-world scenarios, demonstrating mastery of operations, project, and materials management principles.

Learning Objectives Covered

• Apply operations and project management tools to analyze system productivity and project scheduling.
• Use forecasting techniques to predict demand and manage seasonal variations.
• Conduct decision analysis using probability, EMV, and decision trees.
• Apply queuing theory to optimize service operations and calculate associated costs.
• Evaluate supplier selection criteria using factor weighting and cost-benefit analysis.
• Develop materials planning and MRP tables to manage production and inventory efficiently.

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