## Description

Solve questions 1(a), 2(a) and 3(a) by hand (you can submit a scanned copy of your solution, or

you can just turn in a paper copy in class) and then, for questions 1(b), 2(b), 3(b)–6, create a

script in Matlab that performs the calculations needed to answer each question, one cell for each

part of each question. Please submit your script and diary/published output file via Moodle.

1. (a) Given the initial location sequence 1, 5, 2, 6, 4, 3, 1 with a total distance of 22, use the

table below to determine the final location sequence determined after applying the twoopt

improvement procedure by hand to the sequence. The total distance (TD) of each possible

of 120 possible sequences is listed in the table. Include the order in which each sequence

is considered by the procedure.

(b) Use the distance data in the following table and tsp2opt to solve the same problem.

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dij 1 2 3 4 5 6

1 0 8 6 9 1 5

2 3 0 1 5 4 2

3 9 2 0 3 1 1

4 8 2 1 0 10 6

5 6 7 10 1 0 10

6 6 2 5 2 1 0

2. (a) The two tables below list the travel times between six nodes and a time window for

each node. Given a delivery vehicle route that starts from the depot located at node 1 and

then visits each customer (i.e., node) in the sequence 4, 2, 5, 3, and 6 and then returns to

the depot, determine the minimum total time span (in hours) needed to complete all

deliveries and return to the depot. Loading/unloading time and vehicle capacity can be

ignored. The time window for each node indicates the earliest and latest times at which

the delivery can be made; for example, the earliest time at which the vehicle can depart

the depot (node 1) is 6:00, and the latest time at which it can return is midnight (24:00).

Travel Time (hrs)

Node 1 2 3 4 5 6

1 0 2 2 2 1 2

2 2 0 3 2 3 3

3 2 3 0 3 2 2

4 2 2 3 0 3 1

5 1 3 2 3 0 3

6 2 3 2 1 3 0

Time Window

Node Earliest Latest

1 6:00 24:00

2 9:00 12:00

3 18:00 21:00

4 9:00 18:00

5 15:00 18:00

6 21:00 24:00

(b) Use the same data and rteTC to solve the problem.

3. (a) Determine the minimum total logistics cost returned by minTLC for three shipments if

the following route is used: 2, 3, 2, 1, 3, 1. The two tables below list the distances

between each location and data for each shipment. A truck’s cubic and weight capacities

are 2,750 ft3

and 25 tons, respectively, and the PPI for TL is 125. The inventory carrying

rate for each shipment is 0.3, and each product is batch produced and consumed at a

constant rate.

Inter-Location Distances (mi)

Location 1 2 3 4 5 6

1 0 180 320 100 100 40

2 180 0 140 80 240 140

3 320 140 0 220 300 280

4 100 80 220 0 240 60

5 180 240 300 240 0 220

6 40 140 280 60 220 0

Shipment Data

Shipment 1 2 3

Demand (ton/yr) 200 300 100

Density (lb/ft3

) 20 5 10

Begin Location 6 3 2

End Location 5 1 4

Value ($/ton) 20,000 5,000 10,000

(b) Use the same data and minTLC to solve the problem.

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4. Consolidated Package Systems has hub in Knoxville, TN. The location of the hub is

provided in the worksheet Q4-DC of spreadsheet HW8data.xlsx, while the worksheet Q4-

Customers contains, for 180 customers that are to be served tomorrow, their location,

number of packages, and whether packages are to be delivered in the morning (M)

between 8–12, the afternoon (A) between 12–5, or evening (E) between 5–9 pm. The

maximum number of packages on board each identical van cannot exceed 35, and each

driver can work a maximum of seven hours per day. Each delivery to a customer takes

two minutes irrespective of the number of packages delivered. Most of the customers are

at residential locations and any differences in the physical weight and cube of the

packages can be ignored. Each vehicle travels at 70 mph on rural Interstate highways, 50

mph on urban Interstate highways, 20 mph on non-Interstate urban roads, 45 mph on the

remaining rural roads, and 15 mph on the connector links and residential roads. Your

routes should use all of the roads that are in a 12% expanded rectangle that encloses the

depot and customers. Determine the number of vans needed for tomorrow’s deliveries

along with the route of each van.

5. A 3PL would like to establish a set of regular routes (or “milk runs”) that they can use to

supply customers in the Carolinas with a variety of different products. The worksheet Q5-

Data of the spreadsheet HW8data.xlsx lists the origin (orig) and destination (dest) zip

codes and the volume (cu, ft3

), weight (wt, lb), annual demand (ud), and cost (uc, $) of

each unit of 64 products. The 3PL pays each supplier when the product is picked up and

is not paid by the customer for the product until it is used (i.e., a vendor managed

inventory scenario). Assuming that the demand of each customer is fairly constant

throughout the year, the inventory carrying rate is 0.3, and that there is space to store up

to a full truckload at each customer’s location, determine the best set of routes to use. P2P

TL or LTL can be used for transport for some of the shipments, in addition to the use of

consolidated loads.

6. Using Shipments 1, 3, 26, and 5 of the 30 shipments in shmtNC30.mat (see link on

schedule) with a transport rate for TL of $2 per mile and capacities of 2,750 ft3

and 25

tons, determine the transport charge for each shipment would be under equal charge,

equal savings, and exact and approximate Shapley allocation.