The demand for a perishable item over the next four months is 400, 300, 420, and...

70.2K

Verified Solution

Question

General Management

The demand for a perishable item over the next four months is400, 300, 420, and 380 tons, respectively. The supply capacitiesfor the same months are 500,600, 200, and 300 tons The purchaseprice per ton varies from month to month and is estimated at $100,$140, $120, and $150, respectively. Because the item is perishable,a current month's supply must be consumed within 3 months (startingwith current month). The storage cost per ton per month is $3. Thenature of the item does not allow back-ordering. Solve the problemas a transportation model, and determine the optimum deliveryschedule for the item over the next 4 months.
A) Formulate the problem as a transportation problem byhand
B) Using the initial solution with the lowest cost usethe method of multiplier to fond the optimal solution

Answer & Explanation Solved by verified expert

4.1 Ratings (616 Votes)

a The transportation table is as follows TOTAL number of supply constraints 4 TOTAL number of demand constraints 4 Problem Table is Month1 Month2 Month3 Month4 Supply S1 150 120 140 100 500 S2 150 120 140 100 600 S3 150 120 140 100 200 S4 150 120 140 100 300 Demand 380 420 300 400 b Solution with the lowest cost method is as follows Here Total Demand 1500 is less than Total Supply 1600 So We add a dummy demand constraint with 0 unit cost and with allocation 100 Now The modified table is Month1 Month2 Month3 Month4 Ddummy Supply S1 150 120 140 100 0 500 S2 150 120 140 100 0 600 S3 150 120 140 100 0 200 S4 150 120 140 100 0 300 Demand 380 420 300 400 100 The smallest transportation cost is 0 in cell S1Ddummy The allocation to this cell See Answer

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member