LSA_12_chp5_terminal_transshipment.pdf

# One to many distribution with transshipments section

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One-to-many distribution with transshipments • section 5.2: introduce transshipments: design principles LSA: Chapter 5 One-to-many distribution with transshipments Near-optimality of non-redundant systems O B C A D E F G H Example: Redundant paths to demand point F: Nodes C, A and D visited on multiple routes of the same echelon level O-A-O , A-B-C-D-A , C-F-G-H-C or O-A-D-O , D-A-C-E-D , C-F-G-H-C Benefit from operating perspective: With economies of scale in vehicle size, always want largest delivery (lot) size Choose smallest vehicle for a route that can carry the load Exceptions: items with different characteristics – need multiple paths Benefit from a modeling perspective: Problem can decompose by echelon level; influence area and routing at each level Routes serve either terminals or endpoints; not both Assumptions: • Terminals can be located anywhere • Transportation cost is concave and increasing with link flow – economies of scale • Holding cost is linear with link flow • Hence logistics cost is concave with link flow Then, when route choice exists for an O/D pair, all flow should go to one most efficient route. (No demand split.) One-to-many distribution with transshipments • section 5.2: introduce transshipments: design principles

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4 LSA: Chapter 5 One-to-many distribution with transshipments Near-optimality operations • Minimize route length – construct routes using VRP principles from Chapter 4 • Vehicle routes stop at only one level of terminals • Each level can be modeled as a VRP • Flow through a terminal is lower than the flow through the terminal feeding it • Locate terminals centrally within influence area • Influence areas should be round; not elongated --- VRP routes within area will be elongated I j (x): influence area of terminal j 2 I 2 1 I 1 3 I 3 D H i outbound H o H t terminal ( λ,δ, r ) inbound outbound terminal \$ ? ? ? One-to-many distribution with transshipments • section 5.2: introduce transshipments: design principles Question: Density of terminals = ? Assume further that in the time-space continuum, system parameters are slow-varying. Considers the area around point (t, x): D’(t) D’ δ (x) δ r(x) r Define three decision variables/functions load per stop stop per tour n s (t, x) RECAP: Chapter 4 One-to-many without transshipment headway H(t, x) ( ) ( ) ( ) x t H t D x t v , ' , = t t max (t,x) 0 x ' ' 1 ' 1 ' 1 ' 1 2 2 1 s s s s d s d m c H n D c H D c H D k c H n D r c z + + + + = δ s s i i s i i p n t c s k c t c s r c z + + + = 2 2 2 2 1 δ ( ) z s i r h c c H c H = + = motion pipeline inventory
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• Fall '16
• Trigraph, Transshipments

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