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Planning Techniques for Logistics and Transport Operations Name of the University Author

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Added on  2020-05-16

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Glasgow to Edinburgh, q1 be the number of units of product A transported to Edinburgh, r1 be the number of units of product A transported to Sheffield, r3 be the distribution cost of one unit of product A transported to London and s3 be the number of units of product A transported to Cardiff from Glasgow. Therefore, Glasgow to Edinburgh, q2 be the number of units of product A transported to Sheffield, r3 be the distribution cost of one unit of product A transported

Planning Techniques for Logistics and Transport Operations Name of the University Author

   Added on 2020-05-16

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Running Head: PLANNING TECHNIQUES FOR LOGISTICS AND TRANSPORTOPERATIONSPlanning Techniques for Logistics and Transport OperationsName of the StudentName of the UniversityAuthor Note
Planning Techniques for Logistics and Transport Operations Name of the University Author_1
1PLANNING TECHNIQUES FOR LOGISTICS AND TRANSPORT OPERATIONSTable of ContentsPart A.........................................................................................................................................2Part B..........................................................................................................................................5Answer 1................................................................................................................................5Answer 2................................................................................................................................7Answer 3................................................................................................................................9Part C........................................................................................................................................10Answer 1..............................................................................................................................10Answer 2..............................................................................................................................11References................................................................................................................................14
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2PLANNING TECHNIQUES FOR LOGISTICS AND TRANSPORT OPERATIONSPart ALet p1 be the number of units of product A transported to Edinburgh, q1 be the numberof units of product A transported to Sheffield, r1 be the number of units of product Atransported to London and s1 be the number of units of product A transported to Cardiff fromSouthampton.Let p2be the number of units of product A transported to Edinburgh, q2 be the numberof units of product A transported to Sheffield, r2 be the number of units of product Atransported to London and s2 be the number of units of product A transported to Cardiff fromLiverpool.Let p3 be the number of units of product A transported to Edinburgh, q3 be the numberof units of product A transported to Sheffield, r3 be the number of units of product Atransported to London and s3 be the number of units of product A transported to Cardiff fromGlasgow.Let Z1 be the cost of distribution from Southampton, Z2 be the cost of distribution fromLiverpool and Z3 be the cost of distribution from Glasgow.The objective of this problem is to minimize the total distribution cost. Thus,according to Dantzig (2016),the objective function is given by:Minimize Z = Z1 + Z2 + Z3Now, for Southampton, the distribution cost of one unit of product A is to Edinburgh is £5,the distribution cost of one unit of product A is to Sheffield is £1.5, the distribution cost ofone unit of product A is to London is £1 and the distribution cost of one unit of product A isto Cardiff is £2.Thus, the objective function in this case can be framed as:
Planning Techniques for Logistics and Transport Operations Name of the University Author_3
3PLANNING TECHNIQUES FOR LOGISTICS AND TRANSPORT OPERATIONSZ1 = 5 p1 + 2 q1 + r1 + 2s1The production capacity for Southampton is 4000 units. Therefore, p1 + q1 + r1 + s1 ≤ 4000.The demand for the product A in Edinburgh is 2000 units. Therefore, p1 + p2 + p3≥ 2000The demand for the product A in Sheffield is 3000 units. Therefore, q1 + q2 + q3≥ 2000The demand for the product A in London is 1000 units. Therefore, r1 + r2 + r3≥ 1000The demand for the product A in Edinburgh is 3000 units. Therefore, s1 + s2 + s3≥ 3000Now, for Liverpool, the distribution cost of one unit of product A is to Edinburgh is£1.5, the distribution cost of one unit of product A is to Sheffield is £1.2, the distribution costof one unit of product A is to London is £2.5 and the distribution cost of one unit of productA is to Cardiff is £3.Thus, the objective function in this case can be framed as: Z2 = 1.5 p2 + 1.2 q2 + 2.5 r2 + 3 s2The production capacity for Liverpool is 2000 units. Therefore, p2 + q2 + r2 + s2 ≤ 2000.The demand for the product A in Edinburgh is 2000 units. Therefore,
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