6 Managing freight transport - Wiley Managing freight transport Questions and problems Problem 6.7 (1/8) Rinaldi is an Italian fast carrier located in Parma, whose core business is

6 Managing freight transport6.1 Introduction6.2 Freight traffic assignment problems6.3 Service network design problems6.4 Vehicle allocation problems6.5 A dynamic driver assignment problem6.6 Fleet composition6.7 Shipment consolidation6.8 Vehicle routing problems6.9 Real-time vehicle routing problems

6.10 Integrated location and routing problems6.11 Vendor-managed inventory routing6.12 Case study: Air network design at Intexpress6.13 Case study: Meter reader routing and scheduling at Socal6.14 Case study: Dynamic vehicle-dispatching problem with pickups

and deliveries at eCourier6.15 Questions and problems

G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management © John Wiley & Sons, Ltd 1 / 55

6 Managing freight transport Questions and problems

Problem 6.1 (1/2)

JKL is a national carrier operating in Australia. The transportrates for class 25 LTL palletized freight from Melbourne toDarwin are reported in Table 1. Determine the break weightformula (the break weight is the weight over which it isconvenient to apply the rate of the subsequent range to reducethe overall transport cost). Compute the break weight for eachweight range of Table 1.



Problem 6.1 (1/2)




Problem 6.1 (1/2)




Problem 6.1 (1/2)




Problem 6.1 (2/2)

Weight range (W , kg) Rate (A$/kg)

0≤W < 0.1 137.130.1≤W < 0.2 112.460.2≤W < 0.5 98.230.5≤W < 1 72.381≤W < 10 60.6910≤W < 20 54.2120≤W < 50 47.7150≤W < 100 46.14100≤W < 250 41.23W ≥ 250 39.77

Table 1: JKL transport rates for class 25 LTL palletized freight fromMelbourne to Darwin.



Problem 6.2

Camberra Freight is in charge of transporting auto parts for anUS car manufacturer in Australia. Every week a tractor and oneor two trailers move from the port of Melbourne to a warehouselocated 430 km away. A tractor costs A$ 75 per day, a trailer A$30 and a driver A$ 7.5/h, while running costs are A$ 0.75/km. Atrailer can contain 36 pallets. Derive the transport cost per palletas a function of shipment size for the case where one or twotrailers are used.



Problem 6.2




Problem 6.2




Problem 6.2




Problem 6.2




Problem 6.3

TL trucking rates from Boston, Massachusetts, to Miami, Florida(both in the United States) are usually higher than those fromMiami to Boston. Why?



Problem 6.4

Freight transport costs of Class 55 are cheaper than those ofClass 70. Why?



Problem 6.5

In international freight transport, a key role is played by thefree-trade zones. In such areas, freight may be entered withoutthe intervention of the customs authorities and customs dutiesare due only when the goods are moved outside. Get moremore information on the free-trade zones through the Internet.



Problem 6.5




Problem 6.5




Problem 6.6

Formulate the minimum-cost flow problem for the Swiss NTN(see Section 6.2.2) intermodal carrier by knowing that thedemand of containers in Milan and Madrid is 70 and 25,respectively. What is the optimal solution?



Problem 6.6

Formulate the minimum-cost flow problem for the Swiss NTN(see Section 6.2.2) intermodal carrier by knowing that thedemand of containers in Milan and Madrid is 70 and 25,respectively. What is the optimal solution?



Problem 6.7 (1/8)

Rinaldi is an Italian fast carrier located in Parma, whose corebusiness is the transport of small-sized and high-valuedrefrigerated goods (such as chemical reagents used by hospitalsand laboratories). Goods are picked up from manufacturers’warehouses by small vans and carried to the nearest transportterminal operated by the carrier. These goods are packed ontopallets and transported to destination terminals by means oflarge trucks. The merchandise is then unloaded and delivered tocustomers by small vans (usually the same vans employed forpickup). In order to make capital investment in equipment as lowas possible, Rinaldi makes use of one-way rentals of trucks.



Problem 6.7 (1/8)




Problem 6.7 (1/8)




Problem 6.7 (1/8)




Problem 6.7 (2/8)

Recently, the company has decided to enter the fast parceltransport market by opening four terminals in the cities ofBologna, Genoa, Padua and Milan. This choice madenecessary a complete revision of the service network. Thedecision was complicated by the need to transport therefrigerated goods by special vehicles equipped withrefrigerators, while parcels can be transported by any vehicle.The forecasted daily average demand of the two kinds ofproducts in the next semester is reported in Tables 2 and 3.



Problem 6.7 (2/8)




Problem 6.7 (2/8)




Problem 6.7 (2/8)




Problem 6.7 (3/8)

Bologna Genoa Milan Padua

Bologna – 3 8 2Genoa – – 1 2Milan 4 2 – 1Padua 3 1 1 –

Table 2: Forecasted transport demand of refrigerated goods (palletsper day) in the Rinaldi problem.



Problem 6.7 (4/8)


Bologna – 3 4 2Genoa 1 – 1 –Milan 6 2 – 2Padua 1 1 1 –

Table 3: Forecasted transport demand of goods at room temperature(pallets per day) in the Rinaldi problem.



Problem 6.7 (5/8)

Between each pair of terminals, the company can operate oneor more lines. Vehicles are of two types:

- trucks with refrigerated compartments, having a capacity of12 pallets and a cost (inclusive of all charges) of e 0.4/km;

- trucks with room temperature compartments, having acapacity of 18 pallets and a cost (inclusive of all charges) ofe 0.5/km.

In addition, the company considers the possibility of transportinggoods at room temperature through another carrier, by paying e0.1/km for each pallet. A directed graph representation of theproblem is given in Figure 1.



Problem 6.7 (5/8)







Problem 6.7 (5/8)







Problem 6.7 (5/8)







Problem 6.7 (5/8)







Problem 6.7 (5/8)







Problem 6.7 (6/8)3

2 1

4

Milan Padua

BolognaGenoa

Figure 1: Multigraph representation of the service network design ofthe Rinaldi problem. In order to simplify the multigraph, a single edgefor each pair of opposite arcs is represented. The dotted edgesrepresent the connections served by truck lines of 12-pallet capacity,dashed edges represent the connections served by truck lines of18-pallet capacity and solid lines represent connections served by theexternal service.G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management © John Wiley & Sons, Ltd 14 / 55


Problem 6.7 (7/8)

Distances between terminals are reported in Table 4. Formulatethe LFCND problem of finding the least-cost service network(hint: |K | = 22 commodities, one for each combination of anorigin-destination pair with positive demand and a kind ofproduct). Apply the drop heuristic to find a feasible solution ofthe problem. By using a solver, determine the optimal solution ofthe problem and the costs corresponding to the weak and thestrong continuous relaxations. What is the quality of the feasiblesolution provided by the drop heuristic and the two lowerbounds?



Problem 6.7 (7/8)




Problem 6.7 (7/8)




Problem 6.7 (7/8)




Problem 6.7 (7/8)




Problem 6.7 (8/8)


Bologna 0 225 115 292Genoa 225 0 226 166Milan 115 226 0 362Padua 292 166 362 0

Table 4: Distances (in km) between terminals in the Rinaldi problem.



Problem 6.8

Devise a local search heuristic for the service network designproblem in which an individual move is to remove an existing arcor to add a new arc to the current solution.



Problem 6.9

Show that the deterministic VAP with multiple vehicle types canbe modelled as an LMMCF problem on a time-expandeddirected graph.



Problem 6.10

Examine how the optimal solution of the Murthy problem (seeSection 6.4) changes whenever:

- on July 11, there is an empty vehicle in Skrikakulam;- d533 = 1, d531 = 0;- d533 = 1, d531 = 0, and m31 = 1.



Problem 6.10





Problem 6.10





Problem 6.10





Problem 6.11

Show that, in the DDAP, costs ci0, i ∈D, can be set equal,equivalently, to ∞.



Problem 6.12 (1/3)

The travel agency Gare, located in Lausanne, organizes toursby bus in several European capitals. In April there are still sevendifferent tours to organize whose dates of departure andduration are reported in Table 5. The agency has to assign adriver to each tour on the basis of the driver’s experience. Tothis end, a different value is assigned to each driver-tour pair, asreported in Table 6: value 3 means that driver usually makesthat trip, value 1 means that driver has made that trip in the pastand value 0 means that driver never made that trip in the past.



Problem 6.12 (1/3)




Problem 6.12 (1/3)




Problem 6.12 (1/3)




Problem 6.12 (2/3)

City︷︸︸︷

Tour Madrid Paris Rome London Vienna Budapest Berlin

Date of departure 2 8 7 9 9 12 13Trip duration 7 4 4 4 5 4 3

Table 5: Date of departure and duration (in days) of the bus toursorganized by the travel agency Gare.



Problem 6.12 (3/3)

City︷︸︸︷

Driver Madrid Paris Rome London Vienna Budapest Berlin

1 3 3 0 0 1 3 12 1 3 1 0 1 3 13 1 3 0 0 1 3 14 3 1 1 0 1 3 15 1 0 3 0 1 3 16 1 0 0 3 1 3 1

Table 6: Ranking driver-tour value of the travel agency Gare problem.



Problem 6.13

In the Fast Courier transport problem (see Section 6.6), assumethat the unit cost cH per time period of hiring a vehicle changeson the basis of the number of hired vehicles (a 10% discount isapplied for any additional hired vehicle, up to a total discount of$ 300). Determine how the original solution changes.



Problem 6.13

In the Fast Courier transport problem (see Section 6.6), assumethat the unit cost cH per time period of hiring a vehicle changeson the basis of the number of hired vehicles (a 10% discount isapplied for any additional hired vehicle, up to a total discount of$ 300). Determine how the original solution changes.



Problem 6.14

In which case is the problem formulated in Section 6.7infeasible?



Problem 6.15 (1/4)

Estimate the travel time on a 8.5 km segment of the Dungannonroad, between Cookston and Dungannon in Ireland, on thebasis of the experimental measures obtained by using a smallvan and reported in Tables 7–9.



Problem 6.15 (2/4)Traffic Weather Time Travel Traffic Weather Time Travelvolume conditions slot time volume conditions slot time

1 1 1 5.85 2 2 3 6.231 1 1 6.23 2 2 3 6.421 1 2 6.25 2 2 4 6.611 1 2 4.50 2 2 4 6.851 1 3 6.18 2 3 1 7.591 1 3 5.95 2 3 1 6.741 1 4 5.84 2 3 2 6.941 1 4 5.84 2 3 2 6.111 2 1 5.41 2 3 3 7.801 2 1 5.93 2 3 3 7.751 2 2 6.06 2 3 4 6.321 2 2 4.96 2 3 4 6.85

Table 7: Part I - travel time measures (in minutes) on the Dungannonroad (traffic volume: 1= low, 2=medium, 3= high; weather conditions:1= dry, 2= light rain, 3= heavy rain; time slot: 1= 10:00 PM–6:00 AM,2= 6:00 AM–9:00 AM, 3= 9:00 AM–3:00 PM, 4= 3:00 PM–10:00 PM).




1 2 3 6.78 2 1 1 7.121 2 3 6.80 2 1 1 6.961 2 4 6.52 2 1 2 7.551 2 4 6.05 2 1 2 7.201 3 1 6.04 2 1 3 6.771 3 1 7.03 2 1 3 7.881 3 2 6.33 2 1 4 6.081 3 2 6.82 2 1 4 6.851 3 3 6.38 2 2 1 7.911 3 3 7.33 2 2 1 7.451 3 4 6.70 2 2 2 7.951 3 4 7.02 2 2 2 6.56

Table 8: Part II - travel time measures (in minutes) on the Dungannonroad (traffic volume: 1= low, 2=medium, 3= high; weather conditions:1= dry, 2= light rain, 3= heavy rain; time slot: 1= 10:00 PM–6:00 AM,2= 6:00 AM–9:00 AM, 3= 9:00 AM–3:00 PM, 4= 3:00 PM–10:00 PM).




2 1 1 6.20 2 2 3 7.212 1 1 6.07 2 2 3 7.692 1 2 5.49 2 2 4 7.372 1 2 5.28 2 2 4 7.822 1 3 6.96 2 3 1 7.322 1 3 5.87 2 3 1 8.672 1 4 5.81 2 3 2 8.642 1 4 6.55 2 3 2 8.352 2 1 5.76 2 3 3 7.802 2 1 5.17 2 3 3 8.032 2 2 6.58 2 3 4 8.662 2 2 5.50 2 3 4 9.07

Table 9: Part III - travel time measures (in minutes) on the Dungannonroad (traffic volume: 1= low, 2=medium, 3= high; weather conditions:1= dry, 2= light rain, 3= heavy rain; time slot: 1= 10:00 PM–6:00 AM,2= 6:00 AM–9:00 AM, 3= 9:00 AM–3:00 PM, 4= 3:00 PM–10:00 PM).



Problem 6.16

You have an algorithm capable of solving the capacitated NRPwith no fixed vehicle costs, and you would like to solve aproblem where a fixed cost is attached to each vehicle. Showhow such a problem can be solved using the algorithm at hand.



Problem 6.16

You have an algorithm capable of solving the capacitated NRPwith no fixed vehicle costs, and you would like to solve aproblem where a fixed cost is attached to each vehicle. Showhow such a problem can be solved using the algorithm at hand.



Problem 6.17

Show that, if there are no operational constraints, there alwaysexists an optimal NRP solution in which a single vehicle is used(hint: least-cost path costs satisfy the triangle inequality).



Problem 6.18

Show that if the costs associated to the arcs of a completedirected graph G satisfy the triangle inequality property, thenthere exists in G′ an ATSP optimal solution which is aHamiltonian tour.



Problem 6.19

Show that, in the ATSP formulation, the connectivity constraintsand the subtour elimination constraints are equivalent.



Problem 6.20

Show that the number of vertices of odd degree in a graph iseven.



Problem 6.21 (1/2)

Let G = (V ,A) be a complete directed graph such that |V | = 10and the costs associated to the arcs belong to A , as reported inTable 10:

- check if the triangle inequality property holds for each arccost;

- formulate the corresponding ATSP;- solve the relaxed AP;- determine a feasible ATSP solution and evaluate its quality;- apply a 2-exchange procedure for finding a better feasible

solution.



Problem 6.21 (1/2)




solution.



Problem 6.21 (1/2)




solution.



Problem 6.21 (1/2)




solution.



Problem 6.21 (1/2)




solution.



Problem 6.21 (1/2)




solution.



Problem 6.21 (2/2)

0 1 2 3 4 5 6 7 8 9

0 – 28.55 12.10 43.15 66.10 38.35 79.70 17.00 77.60 55.201 15.80 – 23.10 28.85 52.55 53.65 66.90 4.15 71.70 61.902 54.95 48.90 – 52.95 88.55 54.75 77.80 42.55 91.45 76.403 39.80 27.95 37.85 – 79.00 41.40 79.05 19.15 44.95 35.354 49.80 63.95 46.15 43.50 – 71.30 41.60 35.55 67.30 78.605 46.50 55.70 28.10 72.30 93.65 – 55.30 54.20 93.70 94.406 99.55 84.25 86.15 60.40 63.70 99.85 – 72.30 88.35 81.907 31.00 28.80 21.35 34.55 69.55 67.65 67.95 – 77.40 68.308 60.35 75.35 46.85 68.15 39.05 75.05 48.90 52.60 – 80.359 66.00 61.10 60.75 83.50 87.30 92.50 86.40 62.00 64.00 –

Table 10: Costs associated to the arcs of graph G′ of Problem 6.21.



Problem 6.22

Demonstrate that the optimal solution value of MSrTP is a lowerbound on the optimal solution value of STSP.



Problem 6.23 (1/2)Show that an optimal solution of the least-cost perfect-matchingproblem (see Section 6.8) can be obtained by solving thefollowing LP problem:

Minimize∑

(i,j)∈E ′

M

cijxij

subject to∑

i∈V ′

M :(i,j)∈E ′

M

xij +∑

i∈V ′

M :(j,i)∈E ′

M

xji = 1, j ∈V ′

M

∑

(i,j)∈E ′

M ,i∈W ,j∉Wxij+

∑

(j,i)∈E ′

M ,i∈W ,j∉Wxji ≥ 1, W ⊂V ′

M ,

∣∣V ′

M∣∣> 1, |V ′

M | oddxij ≥ 0, (i, j) ∈E ′

M .



Problem 6.23 (1/2)Show that an optimal solution of the least-cost perfect-matchingproblem (see Section 6.8) can be obtained by solving thefollowing LP problem:

Minimize∑

(i,j)∈E ′

M

cijxij

subject to∑

i∈V ′

M :(i,j)∈E ′

M

xij +∑

i∈V ′

M :(j,i)∈E ′

M

xji = 1, j ∈V ′

M

∑

(i,j)∈E ′

M ,i∈W ,j∉Wxij+

∑

(j,i)∈E ′

M ,i∈W ,j∉Wxji ≥ 1, W ⊂V ′

M ,

∣∣V ′

M∣∣> 1, |V ′

M | oddxij ≥ 0, (i, j) ∈E ′

M .



Problem 6.23 (2/2)

(Hint: observe that, given any subset W of V ′

M having oddcardinality, each perfect matching must contain at least oneincident edge into the nodes of W .)



Problem 6.24

Demonstrate that the cost of the STSP solution produced by theChristofides heuristic is within 3/2 of the optimum.



Problem 6.25 (1/3)

The GermanExpress transport company, based in Cologne, hasto schedule a pickup service to five customers located in thecities of Bonn, Düsseldorf, Essen, Hennef and Koblenz,respectively. The distance (calculated with respect to the fastestroute) between each pair of cities is reported in Table 11. Thedaily average amount of goods to pick up by each customer isprovided in Table 12. The transport vans have a capacity of 15quintals. Determine the number of vehicles to be used and, foreach of them, the daily service route starting from the depotlocated in Cologne.



Problem 6.25 (1/3)




Problem 6.25 (1/3)




Problem 6.25 (1/3)




Problem 6.25 (1/3)




Problem 6.25 (2/3)

Bonn Düsseldorf Essen Hennef Koblenz

Cologne 40 50 85 52 123Bonn 85 114 30 65Düsseldorf 45 76 134Essen 107 167Hennef 87Koblenz 0

Table 11: Distances (in km) between the depot and the five cities inthe GermanExpress transport problem.



Problem 6.25 (3/3)

Bonn Düsseldorf Essen Hennef Koblenz

4 12 7 5 8

Table 12: Daily average amount of goods (in quintals) to pickup at thefive customers of the GermanExpress.



Problem 6.26

Show that the NRPSC formulation is correct.



Problem 6.27 (1/2)

The Bioenergy is a wood pellet factory located in Austria; itsupplies a chain of supermarkets located in Italy and Germany.The orders have to be met by minimizing the transport cost. Thedistances among the supermarkets, the distances between thesupermarkets and the depot and the quantity ordered (in pallets)are reported in Table 13. Formulate the problem as a NRPCLassuming that:

the average unloading time for a pallet is 1.5 minutes;the average speed is 90 km/h;the shift time is 8 h;two type of trucks can be used: those with 22-palletcapacity and those with 32-pallet capacity.



Problem 6.27 (1/2)





Problem 6.27 (1/2)





Problem 6.27 (1/2)





Problem 6.27 (1/2)





Problem 6.27 (1/2)





Problem 6.27 (1/2)





Problem 6.27 (1/2)





Problem 6.27 (2/2)

Supermarket︷︸︸︷

1 2 3 4

Depot 140.0 250.0 185.0 92.0Supermarket 1 12.0 34.0 24.0Supermarket 2 14.5 19.3Supermarket 3 17.0Supermarket 4 0.0

Order 15 32 30 18

Table 13: Distances (in km) among the Bioenergy pellet factory andthe supermarkets; in last row, the next-day orders (in pallets) arereported.



Problem 6.28

Explain why distances in Tables reporting the kilometricdistances between cities computed on the fastest route in theMcNish problem (see Section 6.8.3.1) do not necessarily satisfythe triangle inequality.



Problem 6.29

How do you solve the McNish problem if the time windows of thesales point with ID= 5 and ID= 10 were 9:00 AM – 10:00 AMand each vehicle had a capacity of 25 pallets?



Problem 6.30

Devise a local search for the capacitated ARP.



Problem 6.31

Illustrate how the Christofides and Frederickson heuristics canbe adapted to the undirected general routing problem, whichconsists of determining a least-cost tour including a set ofrequired vertices and edges.



Problem 6.32

Solve Problem 6.27 by imposing that a work shift has a durationof six hours.



Problem 6.33

Analyse the dynamism of an airport bus service.



Problem 6.34 (1/2)

Recall the GermanExpress transport problem (Problem 6.25)and assume that the depot in Cologne has a yearly facility costof e 155000. Furthermore, we assume that the transportservice is realized 230 times in a year, according to the dailyaverage requests reported in Table 12. The van travel cost isabout e 1.15/km. The shipper has the possibility to rent a depotin Dortmund, with a yearly cost of e 130000, from which thetransport service can alternatively start. Establish which solutionis preferable, in terms of yearly cost, by considering thedistances between Dortmund and the five customers reported inTable 14.



Problem 6.34 (1/2)




Problem 6.34 (1/2)




Problem 6.34 (1/2)




Problem 6.34 (1/2)




Problem 6.34 (2/2)

City Distance

Bonn 122Düsseldorf 70Essen 39Hennef 119Koblenz 197

Table 14: Distances (in km) between Dortmund and the five cities inthe GermanExpress transport problem.



Problem 6.35

Modify the mathematical model formulation of IRP to take intoaccount the following constraints:

- the supplier’s production is unbounded;- the inventory level of the commodity at the supplier is It0 =∞

for all t ∈T ;- the initial inventory level of the commodity at the supplier

I00 = 0 and the quantity of commodity available in time periodt ∈T is pt =∞.

In which case you can suppose that the commodityconsumption rate µ is constant during a given planning horizon?



Problem 6.35








Problem 6.35








Problem 6.35








Problem 6.35







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6 Managing freight transport - Wiley Managing freight transport Questions and problems Problem 6.7 (1/8) Rinaldi is an Italian fast carrier located in Parma, whose core business is