
Concept explainers
a)
To determine: The optimal plan using the transportation method.
Introduction: Aggregate planning using transportation method helps to attain minimum cost using the optimal plan. The major advantage of transportation method is to achieve the optimal solution using optimal plans.
a)

Answer to Problem 17P
The optimal plan using the transportation method has been developed.
Explanation of Solution
Given information:
The following information has been given:
Quarter |
| Regular time | Overtime | Subcontract |
1 | 500 | 400 | 80 | 100 |
2 | 750 | 400 | 80 | 100 |
3 | 900 | 800 | 160 | 100 |
4 | 450 | 400 | 80 | 100 |
Initial inventory is given as 250 units, regular time cost is $1 per unit, overtime cost is $1.50 per unit, and subcontract cost is $2 per unit. Carrying cost is given as $0.5 per unit per quarter and backorder cost is $0.5 per unit per quarter. Initial inventory would incur $0.2 per unit.
Develop optimal plan using transportation model:
Develop cost matrix:
Cost matrix | Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | Ending inventory | Supply |
Beginning inventory | 0.2 | 0.4 | 0.6 | 0.8 | 1 | 250 |
Regular time 1 | 1 | 1.2 | 1.4 | 1.6 | 1.8 | 400 |
Over time 1 | 1.5 | 1.7 | 1.9 | 2.1 | 2.3 | 80 |
Subcontract 1 | 2 | 2.2 | 2.4 | 2.6 | 2.8 | 100 |
Regular time 1 | 1.5 | 1 | 1.2 | 1.4 | 1.6 | 400 |
Over time 1 | 2 | 1.5 | 1.7 | 1.9 | 2.1 | 80 |
Subcontract 1 | 2.5 | 2 | 2.2 | 2.4 | 2.6 | 100 |
Regular time 1 | 2 | 1.5 | 1 | 1.2 | 1.4 | 400 |
Over time 1 | 2.5 | 2 | 1.5 | 1.7 | 1.9 | 80 |
Subcontract 1 | 3 | 2.5 | 2 | 2.2 | 2.4 | 100 |
Regular time 1 | 2.5 | 2 | 1.5 | 1 | 1.2 | 400 |
Over time 1 | 3 | 2.5 | 2 | 1.5 | 1.7 | 80 |
Subcontract 1 | 3.5 | 3 | 2.5 | 2 | 2.2 | 100 |
Demand | 500 | 750 | 900 | 450 | 2570 | |
2600 |
Excel worksheet to generate the above table:
Develop optimal plan:
Optimal plan | Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | Ending inventory | Dummy |
Beginning inventory | 100 | 150 | ||||
Regular time 1 | 400 | |||||
Over time 1 | 80 | |||||
Subcontract 1 | 100 | |||||
Regular time 1 | 400 | |||||
Over time 1 | 80 | |||||
Subcontract 1 | 100 | |||||
Regular time 1 | 800 | |||||
Over time 1 | 40 | 100 | 20 | |||
Subcontract 1 | 100 | |||||
Regular time 1 | 400 | |||||
Over time 1 | 50 | 30 | ||||
Subcontract 1 | 100 | |||||
Demand | 500 | 750 | 900 | 450 |
The given demand and supply should be separated and the remaining supply and demand should be used as a dummy value.
b)
To determine: The total cost of the optimal plan.
Introduction: Aggregate planning using transportation method helps to attain minimum cost using the optimal plan. The major advantage of transportation method is to achieve the optimal solution using optimal plans.
b)

Answer to Problem 17P
The optimal cost of the plan is $2,641.
Explanation of Solution
Given information:
The following information has been given:
Quarter | Forecast (units) | Regular time | Overtime | Subcontract |
1 | 500 | 400 | 80 | 100 |
2 | 750 | 400 | 80 | 100 |
3 | 900 | 800 | 160 | 100 |
4 | 450 | 400 | 80 | 100 |
Initial inventory is given as 250 units, regular time cost is $1 per unit, overtime cost is $1.50 per unit, and subcontract cost is $2 per unit. Carrying cost is given as $0.5 per unit per quarter and backorder cost is $0.5 per unit per quarter. Initial inventory would incur $0.2 per unit.
Develop optimal plan using transportation model:
Develop cost matrix:
Cost matrix | Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | Ending inventory | Supply |
Beginning inventory | 0.2 | 0.4 | 0.6 | 0.8 | 1 | 250 |
Regular time 1 | 1 | 1.2 | 1.4 | 1.6 | 1.8 | 400 |
Over time 1 | 1.5 | 1.7 | 1.9 | 2.1 | 2.3 | 80 |
Subcontract 1 | 2 | 2.2 | 2.4 | 2.6 | 2.8 | 100 |
Regular time 1 | 1.5 | 1 | 1.2 | 1.4 | 1.6 | 400 |
Over time 1 | 2 | 1.5 | 1.7 | 1.9 | 2.1 | 80 |
Subcontract 1 | 2.5 | 2 | 2.2 | 2.4 | 2.6 | 100 |
Regular time 1 | 2 | 1.5 | 1 | 1.2 | 1.4 | 400 |
Over time 1 | 2.5 | 2 | 1.5 | 1.7 | 1.9 | 80 |
Subcontract 1 | 3 | 2.5 | 2 | 2.2 | 2.4 | 100 |
Regular time 1 | 2.5 | 2 | 1.5 | 1 | 1.2 | 400 |
Over time 1 | 3 | 2.5 | 2 | 1.5 | 1.7 | 80 |
Subcontract 1 | 3.5 | 3 | 2.5 | 2 | 2.2 | 100 |
Demand | 500 | 750 | 900 | 450 | 2570 | |
2600 |
Excel worksheet to generate the above table:
Develop optimal plan:
Optimal plan | Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | Ending inventory | Dummy |
Beginning inventory | 100 | 150 | ||||
Regular time 1 | 400 | |||||
Over time 1 | 80 | |||||
Subcontract 1 | 100 | |||||
Regular time 1 | 400 | |||||
Over time 1 | 80 | |||||
Subcontract 1 | 100 | |||||
Regular time 1 | 800 | |||||
Over time 1 | 40 | 100 | 20 | |||
Subcontract 1 | 100 | |||||
Regular time 1 | 400 | |||||
Over time 1 | 50 | 30 | ||||
Subcontract 1 | 100 | |||||
Demand | 500 | 750 | 900 | 450 |
The given demand and supply should be splitted and the remaining supply and demand should be used as a dummy value.
Calculate the total optimal cost:
It is calculated by adding the multiple of values in the optimal plan table and the value in the cost matrix to the respective value.
Hence, the total optimal cost is $2,641.
c)
To determine: The number of units remained unused in regular time capacity.
Introduction: Aggregate planning using transportation method helps to attain minimum cost using the optimal plan. The major advantage of transportation method is to achieve the optimal solution using optimal plans.
c)

Answer to Problem 17P
No, the regular time capacity remains unused.
Explanation of Solution
Given information:
The following information has been given:
Quarter | Forecast (units) | Regular time | Overtime | Subcontract |
1 | 500 | 400 | 80 | 100 |
2 | 750 | 400 | 80 | 100 |
3 | 900 | 800 | 160 | 100 |
4 | 450 | 400 | 80 | 100 |
Initial inventory is given as 250 units, regular time cost is $1 per unit, overtime cost is $1.50 per unit, and subcontract cost is $2 per unit. Carrying cost is given as $0.5 per unit per quarter and backorder cost is $0.5 per unit per quarter. Initial inventory would incur $0.2 per unit.
Develop optimal plan:
Optimal plan | Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | Ending inventory | Dummy |
Beginning inventory | 100 | 150 | ||||
Regular time 1 | 400 | |||||
Over time 1 | 80 | |||||
Subcontract 1 | 100 | |||||
Regular time 1 | 400 | |||||
Over time 1 | 80 | |||||
Subcontract 1 | 100 | |||||
Regular time 1 | 800 | |||||
Over time 1 | 40 | 100 | 20 | |||
Subcontract 1 | 100 | |||||
Regular time 1 | 400 | |||||
Over time 1 | 50 | 30 | ||||
Subcontract 1 | 100 | |||||
Demand | 500 | 750 | 900 | 450 |
The given demand and supply should be separated and the remaining supply and demand should be used as a dummy value.
Determine whether the regular time capacity remain unused:
From the above table, it is clear that no regular time capacity remains unused. All the regular time capacity has been used in respective quarters.
d)
To determine: The extent of backordering in units and dollars.
Introduction: Aggregate planning using transportation method helps to attain minimum cost using the optimal plan. The major advantage of transportation method is to achieve the optimal solution using optimal plans.
d)

Answer to Problem 17P
The total unit of the backordered is 40 units and the total cost of producing the backorders are $20.
Explanation of Solution
Given information:
The following information has been given:
Quarter | Forecast (units) | Regular time | Overtime | Subcontract |
1 | 500 | 400 | 80 | 100 |
2 | 750 | 400 | 80 | 100 |
3 | 900 | 800 | 160 | 100 |
4 | 450 | 400 | 80 | 100 |
Initial inventory is given as 250 units, regular time cost is $1 per unit, overtime cost is $1.50 per unit, and subcontract cost is $2 per unit. Carrying cost is given as $0.5 per unit per quarter and backorder cost is $0.5 per unit per quarter. Initial inventory would incur $0.2 per unit.
Develop optimal plan:
Optimal plan | Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | Ending inventory | Dummy |
Beginning inventory | 100 | 150 | ||||
Regular time 1 | 400 | |||||
Over time 1 | 80 | |||||
Subcontract 1 | 100 | |||||
Regular time 1 | 400 | |||||
Over time 1 | 80 | |||||
Subcontract 1 | 100 | |||||
Regular time 1 | 800 | |||||
Over time 1 | 40 | 100 | 20 | |||
Subcontract 1 | 100 | |||||
Regular time 1 | 400 | |||||
Over time 1 | 50 | 30 | ||||
Subcontract 1 | 100 | |||||
Demand | 500 | 750 | 900 | 450 |
The given demand and supply should be separated and the remaining supply and demand should be used as a dummy value.
Determine the extent backordering in units and dollars:
The colored cell is the only cell in the optimal plan, which is used for backordering. Hence, the backordering in units is 40 units. It is given that backorder cost is $0.50 per unit per quarter.
Hence, the total unit backordered is 40 units and the total costs of producing the backorders are $20.
Want to see more full solutions like this?
Chapter 13 Solutions
EBK PRINCIPLES OF OPERATIONS MANAGEMENT
- How can HR proactively help ensure that other departments are operating in a legally acceptable manner? Answers Deliver interdepartmental training on legal compliance and requirements. Discuss potential sources of risk with an attorney and create a plan to respond to lawsuits. Ensure that all HR members are watching the conduct of other departments and report infractions to the head of HR. Record improper conduct from various employees throughout the organization and pursue disciplinary measures.arrow_forwardCan you guys help me with this? Thank you! Project is Terminal 1 at JFK International Airport Question: Risk management content: Discuss a major risk management event that affected the project (Keep this content about 2 minute talking and please provide actual sources that you have the information to go over this)arrow_forwarduse the screenshot to find the anwser to this If the project finishes within 27 weeks of its start, the project manager receives a $500 bonus. What is the probability of a $500 bonus? Note: Round z-value to 2 decimal places, and probability to 4 decimal places.arrow_forward
- Scan To Pay Log into your own Lightning UPI account of supporting app and scan QR code below to pay! ✰ BINANCEarrow_forwardTo help with preparations, a couple has devised a project network to describe the activities that must be completed by their wedding date. Start A Ꭰ F B E The following table lists the activity time estimates (in weeks) for each activity. Optimistic Most Probable Activity Pessimistic A 4 5 6 B 2.5 3 3.5 C 5 6 7 D 5 5.5 9 E 5 7 9 F 2 3 4 G 7 9 11 H 5 6 13 H Finish Based only on the critical path, what is the estimated probability that the project will be completed within the given time frame? (Round your answers to four decimal places.) (a) Within 19 weeks? (b) Within 21 weeks? (c) Within 25 weeks?arrow_forwardYou may need to use the appropriate technology to answer this question. Mueller Associates is a urban planning firm that is designing a new public park in an Omaha suburb. Coordination of the architect and subcontractors will require a major effort to meet the 46-week completion date requested by the owner. The Mueller project manager prepared the following project network. B H Start A C G Finish E Estimates of the optimistic, most probable, and pessimistic times (in weeks) for the activities are as follows. Activity Optimistic Most Probable Pessimistic A 4 12 B 6 7 8 C 6 18 D 3 5 7 E 6 9 18 F 5 8 17 G 10 15 20 H 5 13 (a) Find the critical path. (Enter your answers as a comma-separated list.) (b) What is the expected project completion time (in weeks)? weeks i (c) Based only on the critical path, what is the estimated probability the project can be completed in 46 weeks as requested by the owner? (Round your answer to four decimal places.) (d) Based only on the critical path, what is…arrow_forward
- Bridge City Developers is coordinating the construction of an office complex. As part of the planning process, the company generated the following activity list. Draw a project network that can be used to assist in the scheduling of the project activities. Activity Immediate Predecessor ABC E FGH ] A, B A, B D E с с F, G, H, I A E Start B D A E Start B D H H E A E Finish Start D F J Finish Start B D F Finish Finish C H I Harrow_forwardHow can mindfulness be combined with cognitive reframing to build emotional regulation and mental flexibility? What is the strategy for maintaining mental well-being to improve through deliberate practice? How to engage in practices that help regulate emotions and build resilience?arrow_forward• We Are HIRING Salesforce Developer (2 - 4 Years) @ Cloudodyssey It Solutions Requirement : Appropriate knowledge on Salesforce standard objects Leads, Account, Contacts, Opportunity, Products, Lead process, Sales process, is required. • Hands-on experience in Salesforce Experience Cloud, Sales Cloud and Lightning. • • Hands experience with Salesforce development, administration, system integrations, Lightning Design System, and bug fixes. Experience in configuration, integration, APIs creation, testing and deployment of Salesforce.com functionality. Eloquent verbal and written communication skills. • Familiar with Agile framework. Work Location: Bangalore SUBMIT YOUR CV hello@cloudodyssey.coarrow_forward
- Agree or disagree with post On the surface, the numbers in financial statements do present a snapshot of a company's financial position and performance. However, just looking at the raw numbers often doesn't tell the whole story or reveal underlying trends and relationships that are crucial for making informed decisions. Think of it like looking at individual pieces of a puzzle. Each number is a piece, providing some information. But to see the complete picture – the company's overall financial health, its performance over time, how it compares to its peers, and its potential future – you need to assemble those pieces using different analytical tools. For example: Horizontal analysis helps us understand how specific financial statement items have changed over multiple periods. Is revenue growing? Are expenses increasing at a faster rate than sales? This reveals trends that a single year's numbers wouldn't show. Vertical analysis allows us to see the relative size of each item within…arrow_forwardWhat can you do in response to an insulting offer?arrow_forwardAgree or disagree with post If someone hits you with an insulting offer, the first thing to do is not take it personally. It’s normal to feel a little offended, but blowing up or shutting down won’t help your case. Better move is to stay calm and treat it like a misunderstanding or just the first step in the conversation. That way, you keep things respectful but still let them know the offer doesn’t sit right with you. It also helps to back up your response with facts. Bring in things like your experience, numbers, or any specific results you delivered. That can shift the conversation away from feelings and toward the value you bring. Agree or disagree with postarrow_forward
- Purchasing and Supply Chain ManagementOperations ManagementISBN:9781285869681Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. PattersonPublisher:Cengage LearningPractical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
- MarketingMarketingISBN:9780357033791Author:Pride, William MPublisher:South Western Educational Publishing

