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copper and brass tubes. The company™s production processes take place in a factory
located in London (Ontario, Canada) with highly automated systems operating with
a very low work-in-process. The raw materials originate from mines located close
to the factory. Consequently, the ¬rm does not need to stock a large amount of raw
materials (as a rule, no more than a two-week demand). As far as the ¬nished product
inventories are concerned, Wolferine makes use of EOQ models (see Section 4.4.2).
In the autumn of 1980, the ¬rm operated with a production level close to the plant™s
capacity. At that time the interest rate was around 10%. Using this value in the EOQ
model, the company set the ¬nished goods inventory level equal to 833 tons. During
the subsequent two years, an economic recession hit the industrialized countries. The
interest rate underwent continuous and quick variations (up to 20% in August 1981),
the demand of ¬nished products went down by 20%, and the price level increased
sharply. According to the EOQ model, the ¬nished goods inventory level should
have been lower under those conditions. In order to illustrate this result, let n be the
number of products; k an order ¬xed cost (assumed independent from the product);
di , i = 1, . . . , n, the annual demand of the product i; p the interest rate (increased to
¯
take into account warehousing costs); ci , i = 1, . . . , n, the price of product i; I the
average stock level at time period t0 (January 1981). On the basis of Equation (4.28),
n
1 2kdi
¯
I (t0 ) = .
pci
2
i=1
We can express parameter p as the sum of a bank interest rate p1 and of a rate p2
associated with warehousing costs:
p = p1 + p2 .
Moreover, let δ1 , δ2 and δ3 be the variation rates (assumed equal for all products) of
price, demand and interest rate at time period t, respectively. The average stock level
is equal to
n
2[k(1 + δ1 )][di (1 + δ2 )]
1
¯
I (t) =
[p1 (1 + δ3 ) + p2 ][ci (1 + δ1 )]
2
i=1

(1 + δ2 )p
¯
= I (t0 ) . (8.18)
p1 (1 + δ3 ) + p2
According to Equation (8.18), if demand decreases (δ2 < 0) and the interest rate
increases (δ3 > 0), the stock level should be lower. However, the managers of Wolfer-
ine continued to operate as in 1981. As a result, the ITR (see Section 4.1) suddenly
decreased. Moreover, to protect the manufacturing process against strikes at the mines,
the ¬rm also decided to hold an inventory of raw materials. Consequently, when the
recession ended in 1983, the ¬rm had an exceedingly large stock of both raw materials
and ¬nished products.




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322 LINKING THEORY TO PRACTICE
% container
loading success

100

90

80

70

60

50

40

30

20

% of used
10
capacity


73 78 83 87 92 94 100


Figure 8.15 Percentage of success in loading an aircraft as a function of
the percentage of load capacity (simulation made by FedEx).

8.11 Airplane Loading at FedEx
FedEx is one of the leading express carriers in the world, with a freight traf¬c estimated
at about 2 million parcels per day. Its sales of¬ces are located in 187 countries and
the company uses a ¬‚eet of 437 airplanes and about 30 000 trucks and vans.
In the USA, parcels whose origin and destination exceed a given distance are
consolidated in containers and sent by air. An airplane may ¬‚y between a pair of
destinations or may follow a multi-stop route where containers are loaded or unloaded
at intermediate stops.
In order to use airplane capacity ef¬ciently, a key issue is to devise good loading
plans, taking into account a number of aspects: the load must be balanced around the
centre of gravity of the aircraft, the total weight in the various areas of the aircraft
must not exceed given thresholds in order to limit the cutting forces on the plane,
etc. These aspects are critical, especially for some planes, such as the Airbus A300,
a low fuel consumption aircraft. In addition, when loading an airplane assigned to a
multi-stop route, containers to be unloaded at intermediate stops must be positioned
close to the exit.
In order to allow airplanes to take off on time, allocating containers on-board must
be done in real time, i.e. containers must be loaded on the aircraft as soon as they arrive
at the airport. As a matter of fact, 30% to 50% of the containers are already on board
when the ground staff has a complete knowledge of the features of the containers
to be loaded. Of course, once some containers have been loaded, it may become
impossible to load the subsequent containers. As a result, when new containers arrive
at the airport, it is sometimes necessary to de¬ne a new loading plan in which some
containers previously loaded are unloaded. This situation arises frequently when the
total load is close to the capacity of the aircraft, as shown in Figure 8.15, where the
percentage of success in loading an airplane is reported as a function of the percentage
of the load capacity used.




TLFeBOOK
LINKING THEORY TO PRACTICE 323

The objective pursued by FedEx consists of loading the largest number of con-
tainers as possible. If no container is yet loaded, the following solution procedure is
implemented.
Step 1. Let m be the number of containers to be loaded, n the number of positions
in the loading area, q the number of areas into which the plane is divided, pi , i =
1, . . . , m, the weight of container i; Pj , j = 1, . . . , n, the maximum weight that
can be loaded in position j ; dj , j = 1, . . . , n, the distance from position j to the
centre of gravity O, M min and M max the minimum and maximum moments of the
loads with respect to O, Lk , k = 1, . . . , q, the total maximum weight that can
be placed in area k; fj k , j = 1, . . . , n, k = 1, . . . , q, the fraction of position
j contained in area k. Also let xij , i = 1, . . . , m, j = 1, . . . , n, be a binary
decision variable equal to 1 if container i is placed in position j , and 0 otherwise,
uj , j = 1, . . . , n, a binary decision variable equal to 1 if position j is used, and 0
otherwise. A feasible solution is de¬ned by the following set of constraints:
n
xij = 1, i = 1, . . . , m, (8.19)
j =1
m
j = 1, . . . , n,
xij muj , (8.20)
i=1
m
j = 1, . . . , n,
pi xij P j uj , (8.21)
i=1


m n
M max ,
dj pi xij (8.22)
i=1 j =1
mn
M min ,
dj pi xij (8.23)
i=1 j =1

m n
k = 1, . . . , q,
pi fj k xij Lk , (8.24)
i=1 j =1


xij ∈ {0, 1}, i = 1, . . . , m, j = 1, . . . , n, (8.25)
uj ∈ {0, 1}, j = 1, . . . , n. (8.26)

Constraints (8.19) guarantee that each container is allocated to a position. Con-
straints (8.20) state that if a position j, j = 1, . . . , n, accommodates a container,
then its uj variable must be equal to 1. Constraints (8.21) ensure that the total
weight loaded in any position does not exceed a pre-established upper bound. Con-
straints (8.22) and (8.23) impose that the total moment, with respect to point O,




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324 LINKING THEORY TO PRACTICE

is within the pre-established interval. Constraints (8.24) ensure the respect of the
weight bounds in each section.
¯
Step 2. If problem (8.19)“(8.26) is infeasible, a container i is eliminated from the
loading list and the problem is solved again (where, of course, xij = 0, j =
¯
1, . . . , n). Step 2 is repeated until a feasible solution is found.
If some containers have already been loaded, the previous procedure is modi¬ed
¯ ¯
as follows. Let I be the set of the containers already loaded and let ji , i ∈ I , be the
position assigned to container i. Then, additional constraints,
¯
xiji = 1, i ∈ I, (8.27)
are added to (8.19)“(8.26). If this problem is feasible, the procedure stops since
the partly executed loading plan can be completed. Otherwise, the constraint (8.27)
¯
associated with container i ∈ I allocated to the position closest to the entrance/exit
is removed (this corresponds to unloading the container from the aircraft). This step
is repeated until a feasible solution is obtained.


8.12 Container Loading at Waterworld
Like other commodities derived from wood, paper is typically produced a long way
from the main points of consumption and then often transported by sea in containers.
As a rule, the transportation cost accounts for a signi¬cant part of the selling price.
Moreover, competition among manufacturers is ¬erce so that pro¬ts are very low. In
this context, it is crucial to reduce transportation costs as much as possible. To this
purpose, a key issue is to consolidate loads ef¬ciently.
Paper is usually transported in rolls having a diameter ranging between 0.5 m and
1.5 m, or in large size sheets. In the ¬rst case, rolls are loaded directly into containers,
while in the second case, the sheets are loaded onto pallets which are put in containers.
Generally, an order is composed of a set of different products of varying size, thickness
and density. A typical order can ¬ll several tens of containers.
Waterworld determines its own loading plans through an ad hoc heuristic procedure
outlined below.


8.12.1 Packing rolls into containers
Rolls vary in diameter and height. Roll packing amounts to loading rolls into con-
tainers with the circular base parallel to the bottom surface. The packing procedure
is divided into two steps.
Step 1. In the ¬rst step, each roll is characterized by its circular section and the aim
is to determine the least number of rectangles (representing bottom surfaces) that
can accommodate such sections (referred to as objects in the following). Let (X, Y )
be a Cartesian reference system with origin in the bottom left corner of a container.




TLFeBOOK
LINKING THEORY TO PRACTICE 325




L




W W

Figure 8.16 Two ways circular objects can be loaded in the Waterworld problem.

The objects are introduced in the container one at a time, the position of each
object being de¬ned in such a way that »1 x + »2 y is minimized ((x, y) are the
coordinates of the centre of the object, »1 and »2 are two positive constants). The
choice of (x, y) must result in a feasible solution, i.e. the object must be entirely
kept in the container and must not be overlapping the objects already inserted (see
Figure 8.16). The following combinations of parameters »1 and »2 were used:
(a) »1 = 1 and »2 = 0; (b) »1 = 0 and »2 = 1; (c) »1 = »2 = 0.5.
Step 2. With each cluster of rolls formed in the ¬rst step is associated a weight equal to
the height of the tallest roll of the cluster. Then, a classical 1-BP (see Section 5.4.3)
is solved heuristically in order to determine the least number of containers (each
characterized by a capacity equal to container height) that can accommodate all
clusters (see Figure 8.17).


8.12.2 Packing pallets into containers
Paper sheets are mounted on pallets in such a way that the total height of two stacked
pallets is equal to the container height. These pallet pairs are then packed through a
2-BP heuristic (see Section 5.4.3). The procedure followed by Waterworld is a slight
variant of the BL method (see Section 5.4.3).


8.13 Air Network Design at Intexpress
Intexpress is a ¬rm whose core business is express freight delivery all over North
America. The services provided to customers are (a) delivery within 24 hours (next
day service); (b) delivery within 48 hours (second day service); (c) delivery within 3“5
days (deferred service). In order to provide quick deliveries, long-haul transportation
is made by plane.




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326 LINKING THEORY TO PRACTICE




H




L

Figure 8.17 Roll packing in the Waterworld example.

The Intexpress logistics system comprises a set of shipment centres (SCs), of a
single hub, of a ¬‚eet of airplanes and of a ¬‚eet of trucks. Loads are consolidated
both in the SCs and in the hub. In particular, goods originating from the same SC are
transported as a single load to the hub while all the goods assigned to the same SC are
sent jointly from the hub. Freight is ¬rst transported to an originating SC, where it is
consolidated; it is then transported to a ¬nal SC by air, by truck (ground service), or
by using a combination of the two modes. Finally, freight is moved from the ¬nal SC
to the destination by truck. Of course, an SC to SC transfer by truck is feasible only
if distance does not exceed a given threshold. Air transportation is performed by a
company-owned ¬‚eet (dedicated air service) or by commercial airlines (commercial
air service). The outgoing freight is collected in the evening and delivered the morning
after. Every day a company-owned aircraft leaves the hub, makes a set of deliveries,
then travels empty from the last delivery point to the ¬rst pick-up point, where it
makes a set of pick-ups and ¬nally goes back to the hub. Each SC is characterized by
an ˜earliest pick-up time™ and by a ˜latest delivery time™. Moreover, all arrivals in the
hub must take place before a pre-established arrival ˜latest delivery time™ (cut-off time,
COT) in such a way that incoming airplanes can be unloaded, sorted by destination,
and quickly reloaded on to outgoing aircraft.
Since it is not economically desirable nor technically feasible that airplanes visit
all SCs, a subset of SCs must be selected as aircraft loading and unloading points (air-
stops, ASs). An SC that is not an AS is connected to an AS by truck (ground feeder
route). Figure 8.18 depicts a possible freight route between an origin“destination pair.
Commercial air services are less reliable than dedicated air services and their costs
are charged depending on freight weight. These are used when either the origin and
its closest SC are so far apart that no quick truck service is possible, or when the
overall transportation demand exceeds the capacity of company-owned aircraft.
Planning the Intexpress service network consists of determining
• the set of ASs served by each aircraft of the ¬rm;




TLFeBOOK
LINKING THEORY TO PRACTICE 327
Shift with a dedicated aircraft
Origin
Consolidate land shift
Local pick-up/delivery
SC




AS
AS
AS

Hub
AS




SC
Destination

AS


Figure 8.18 A possible freight route between an origin“destination pair at Intexpress.

• truck routes linking SCs (which are not ASs) to ASs;
• the transportation tasks performed by commercial airlines.
The objective pursued is the minimization of the operational cost subject to ˜earliest
pick-up time™ and ˜latest delivery time™ constraints at SCs, to the COT restriction, etc.
The solution methodology used by Intexpress is made up of two stages: in the
¬rst stage, the size of the problem is reduced (preprocessing phase) on the basis of a
qualitative analysis; in the second stage, the reduced problem is modelled and solved
as an IP program. In the ¬rst stage,
• origin“destination pairs that can be serviced by truck (in such a way that all
operational constraints are satis¬ed) are allocated to this mode and are not
considered afterwards;
• origin“destination pairs that cannot be served feasibly by dedicated aircraft or
by truck are assigned to the commercial ¬‚ights;
• low-priority services (deliveries within 48 hours or within 3“5 days) are made
by truck or by using the residual capacity of a company-owned aircraft;
• the demands of origin/destination sites are concentrated in the associated SC.
A route is a partial solution characterized by
• a sequence of stops of a company-owned aircraft ending or beginning in the
hub (depending on whether it is a collection or a delivery route, respectively).
• a set of SCs (not ASs) allocated to each aircraft AS.
Therefore, two routes visiting the same AS in the same order can differ because
of the set of SCs (which are not ASs), or because of the allocation of these SCs
to the ASs. If the demand of a route exceeds the capacity of the allocated aircraft,




TLFeBOOK
328 LINKING THEORY TO PRACTICE

the exceeding demand is transported by commercial ¬‚ights. The cost of a route is
therefore the sum of costs associated with air transportation, land transportation, and
possibly a commercial ¬‚ight if demand exceeds dedicated aircraft capacity.
The IP model solved in the second stage is de¬ned as follows. Let K be the set of
available airplane types; U k , k ∈ K, the set of the pick-up routes that can be assigned
to an airplane of type k; V k , k ∈ K, the set of the delivery routes that can be assigned
to an airplane of type k; R the set of all routes (R = k∈K (U k ∪ V k )); nk , k ∈ K,
the number of company-owned airplanes of type k; S the set of SCs, oi , i ∈ S, the
demand originating at the ith SC; di , i ∈ S, the demand whose destination is the ith
SC; cr , r ∈ R, the cost of route r; qi , i ∈ S, the cost paid if the whole demand oi
is transported by a commercial ¬‚ight; si , i ∈ S, the cost paid if the whole demand
di is transported by a commercial ¬‚ight; ±ir , i ∈ S, r ∈ R, a binary constant equal
to 1 if route r includes picking up traf¬c at the ith SC, and 0 otherwise; δir , i ∈ S,
r ∈ R, a binary constant equal to 1 if route r includes delivering traf¬c to the ith SC,
and 0 otherwise; γir , i ∈ S, r ∈ R, a binary constant equal to 1 if the ¬rst (last) AS
of pick-up (delivery) route r is the ith SC, and 0 otherwise. The decision variables of
binary type are vi , i ∈ S, equal to 1 if demand oi is transported by commercial ¬‚ight,
and 0 otherwise; wi , i ∈ S, equal to 1 if demand di is transported by commercial
¬‚ight, and 0 otherwise; xr , r ∈ R, equal to 1 if (pick-up or delivery) route r is selected,
and 0 otherwise.
The integer program is as follows.
Minimize
cr xr + (qi vi + si wi ) (8.28)
k∈K r∈U k ∪V k i∈S
subject to

xr ±ir + vi = 1, i ∈ S, (8.29)
k∈K r∈U k

xr δir + wi = 1, i ∈ S, (8.30)
k∈K r∈V k

xr γir ’ xr γir = 0, i ∈ S, k ∈ K, (8.31)
r∈U k r∈V k

nk , k ∈ K,
xr (8.32)
r∈U k


∈ F, r ∈ R,
xr (8.33)
∈ {0, 1}, r ∈ R,
xr (8.34)
∈ {0, 1}, i ∈ S,
vi (8.35)
∈ {0, 1}, i ∈ S.
wi (8.36)
The objective function (8.28) is the total transportation and handling cost. Con-
straints (8.29) and (8.30) state that each SC is served by a dedicated route or by a




TLFeBOOK
LINKING THEORY TO PRACTICE 329

commercial route; constraints (8.31) guarantee that if a delivery route of type k ∈ K
ends in SC i ∈ S, then there is a pick-up route of the same kind beginning in i. Con-
straints (8.32) set upper bounds on the number of routes which can be selected for
each dedicated aircraft type. Finally, constraints (8.33) express the following further
restrictions. The arrivals of the airplanes at the hub must be staggered in the period
before the COT because of the available personnel and of the runway capacity. Simi-
larly, departures from the hub must be scheduled in order to avoid congestion on the
runways. Let na be the number of time intervals in which the arrivals should be allo-
cated; np the number of time intervals in which the departures should be allocated;
fr , r ∈ R, the demand along route r; at the maximum demand which can arrive to
the hub in interval t, . . . , na ; At the set of routes with arrival time from t on; Pt the
set of routes with departure time before t; pt the maximum number of airplanes able
to leave before t. Hence, constraints (8.33) are
t = 1, . . . , na ,
fr xr at , (8.37)
k∈K r∈U k ©At

pt , t = 1, . . . , np .
xr (8.38)
r∈V k ©Pt
k∈K

Constraints (8.37) ensure that the total demand arriving at the hub is less than or
equal to the capacity of the hub in each time interval t = 1, . . . , na , while constraints
(8.38) impose that the total number of airplanes leaving the hub is less than or equal
to the maximum number allowed by runaway capacity in each time interval t =
1, . . . , np .
Other constraints may be imposed. For instance, if goods are stored in containers
one must ensure that once a container becomes empty it is brought back to the orig-
inating SC. To this end, it is necessary that the aircraft arriving at and leaving from
each SC be compatible. In the Intexpress problem, there are four types of airplanes,
indicated by 1, 2, 3 and 4. Aircraft of type 1 are compatible with type 1 or 2 planes,
while aircraft of type 2 are compatible with those of type 1, 2 and 3. Therefore, the
following constraints hold:

xr ±ir + xr δir i ∈ S,
’ 0, (8.39)
r∈V 1 ∪V 2
r∈U 1

xr ±ir ’ xr δir i ∈ S,
0, (8.40)
r∈U 1 ∪U 2 r∈V 1

xr ±ir + xr δir
’ i ∈ S,
0, (8.41)
r∈V 1 ∪V 2 ∪V 3
r∈U 2

xr ±ir ’ xr δir i ∈ S.
0, (8.42)
r∈U 1 ∪U 2 ∪U 3 r∈V 2

Moreover, some airplanes cannot land in certain SCs because of noise restrictions
or insuf¬cient runaway length. In such cases, the previous model can easily be adapted
by removing the routes r ∈ R including a stop at an incompatible SC.




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330 LINKING THEORY TO PRACTICE

The variables in the model (8.28)“(8.32), (8.34)“(8.42) are numerous even if the
problem is of small size. For example, in the case of four ASs (a, b, c and d), there
are 24 pick-up routes (abcd, acbd, adbc, etc.) each of which has a different cost and
arrival time at the hub. If, in addition, two SCs (e and f ) are connected by truck to one
of the ASs a, b, c and d, then the number of possible routes becomes 16—24 = 384 (as
a matter of fact, for each AS sequence, each of the two SCs e and f can be connected
independently by land to a, b, c or d). Finally, for each delivery route making its last
stop at an AS d, one must consider the route making its last stop in a different SC
g ∈ S \ {d}. Of course, some of the routes can be infeasible and are not considered
in the model (in the case under consideration the number of feasible routes is about
800 000).
The solution methodology is a classical branch-and-bound algorithm in which at
each branching node a continuous relaxation of (8.28)“(8.32), (8.34)“(8.42) is solved.
The main disadvantage of this approach is the large number of variables. Since the
number of constraints is much less than the number of variables, only a few variables
take a nonzero value in the optimal basic solution of the continuous relaxation. For
this reason, the following modi¬cation of the method is introduced. At each iteration,
in place of the continuous relaxation of (8.28)“(8.32), (8.34)“(8.42), a reduced LP
problem is solved (in which there are just 45 000 ˜good™ variables, chosen by means of
a heuristic criterion); then, using the dual solution of the problem built in this manner,
the procedure determines some or all of the variables with negative reduced costs,
introducing the corresponding columns in the reduced problem (pricing out columns).
Various additional devices are also used to quicken the execution of the algorithm.
For example, in the preliminary stages only routes with an utilization factor between
30% and 185% are considered. This criterion rests on two observations: (a) because
of the reduced number of company aircraft, it is unlikely that an optimal solution
will contain a route with a used capacity less than 30%; (b) the cost structure of the
air transportation makes it unlikely that along a route more than 85% of the traf¬c is
transported by commercial airlines.
The above method was ¬rst used to generate the optimal service network using
the current dedicated air ¬‚eet. The cost reduction obtained was more than 7%, cor-
responding to a yearly saving of several million dollars. Afterwards, the procedure
was used to de¬ne the optimal composition of the company™s ¬‚eet (¬‚eet planning).
For this purpose, in formulation (8.28)“(8.32), (8.34)“(8.42), it was assumed that nk
was in¬nite for each k ∈ K. The associated solution shows that ¬ve aircraft of type 1,
three of type 2 and ¬ve of type 3 should be used. This solution yielded a 35% saving
(about 10 million dollars) with respect to the current solution.


8.14 Bulk-Cargo Ship Scheduling Problem at the
US Navy
The Tanker Division of the US Navy is in charge of planning the fuel replenishment
of the US naval bases in the world. This task is accomplished by a ¬‚eet of 17 tankers




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LINKING THEORY TO PRACTICE 331

owned by the US Navy and, if needed, of specialized companies (spot carriers). Every
three months a team of the Tanker Division works out a replenishment plan including
both a scheduling of the military tanks and a possible list of tasks for the spot carriers.
The objective is to minimize the operational expenses of the military tanks plus the
hiring costs of additional tankers provided by spot carriers. The main operational
constraints are related to delivery times, which must be included in pre-established
time windows, and the impossibility for some ships to moor in certain ports. The
replenishment plans must also consider the current position and initial status of the
¬‚eet. Plans are revised daily in order to consider new demands, or delays due to
unfavourable weather conditions.
Each fuel request consists of a type of product, a demand, a delivery point and a
delivery time. On the basis of fuel availability at the depots, the team establishes how
each request must be satis¬ed.After this preliminary analysis, the demand is expressed
by a set of elementary fuel transfers. An elementary transfer is composed of two or
three pick-ups in a same port or in adjacent ports, and of two or three deliveries to
adjacent demand points. Typically, a tank is able to make two elementary transfers
in a month. The formulation of the model takes into account the fact that because of
the operational constraints, a tank can only complete a limited number of elementary
transfers (generally, no more than 10) in the planning period.
Let n be the number of elementary transfers; m the number of ports, K (= 17) the
number of military tanks; Sk , k = 1, . . . , K, the set of the feasible working plans
for tank k; aij k , i = 1, . . . , n, j ∈ Sk , k = 1, . . . , K, a binary constant equal
to 1 if working plan j for tank k includes elementary transfer i, and 0 otherwise;
fi , i = 1, . . . , n, the cost paid if transfer i is committed to a spot carrier; gj k ,
j ∈ Sk , k = 1, . . . , K, the variation of cost incurred if tank k executes working plan
j , as opposed to the situation in which the tank lies idle for all the planning period.
Further, let xj k , j ∈ Sk , k = 1, . . . , K, be a binary decision variable equal to 1 if
working plan j is selected for tank k, and 0 otherwise; yi , i = 1, . . . , n, a binary
decision variable equal to 1 if transfer i is made by a spot carrier, and 0 otherwise.
The problem was formulated as follows.
Minimize
K n
gj k xj k + fi yi (8.43)
k=1 j ∈Sk i=1

subject to
K
aij k xj k + yi = 1, i = 1, . . . , n, (8.44)
k=1 j ∈Sk

k = 1, . . . , K,
xj k 1, (8.45)
j ∈Sk

xj k ∈ {0, 1}, j ∈ Sk , k = 1, . . . , K, (8.46)
yi ∈ {0, 1}, i = 1, . . . , n. (8.47)




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332 LINKING THEORY TO PRACTICE

The objective function (8.43) is equal to the total transportation cost. Constraints
(8.44) impose that each transfer is realized by a military tank or by a spot carrier.
Constraints (8.45) establish that, for each tank, at most one working plan must be
selected. Model (8.43)“(8.47) is therefore a set partitioning problem with some addi-
tional constraints (relations (8.45)). The US Navy has almost 30 elementary transfers
in each planning period, to which correspond various thousands of feasible work-
ing plans. Using a general-purpose IP solver it is generally possible to solve these
instances exactly.
The optimal solution yielded an average monthly cost of $341 900, inferior by
$467 000 to the manual scheduling. The yearly saving was about 1.5 million dollars.
Further cost reductions were obtained by simulating various compositions of the
military ¬‚eet. This analysis suggested a reduction of the current ¬‚eet, no longer using
¬ve tanks and using mainly the spot carriers. This solution generated a cost reduction
of 3.2 million dollars per year.


8.15 Meter Reader Routing and Scheduling at Socal
Socal (Southern California Gas Company) distributes, with its own pipe network,
domestic and industrial gas in an area including all of southern California (USA).
The task of surveying user consumption is accomplished by motorized operators.
Every day a meter reader makes an initial car trip from the of¬ces of the company up
to a parking point; afterwards, he walks along several streets (or segments of streets)
where he does some surveying; ¬nally, he reaches the parking point from which he
returns to the company by car. According to the working contract, if the duration of
a shift exceeds a pre-established maximum value T max , a meter reader receives an
additional remuneration, proportional to the overtime. For reasons of equity, Socal
prefers solutions in which all service routes have a similar duration. The planning
of the meter-reading activities then consists of partitioning the set of street segments
into subsets yielding service routes with a duration close to T max .
In 1988 Socal mandated a consulting ¬rm, Distinct Management Consultants, Inc.
(DMC) to evaluate the costs and the potential bene¬ts resulting from the use of an
optimization software for the planning of meter-reading activities. A pilot study was
conducted in a sample region including the townships of Culver City, Century City,
Westwood, West Hollywood and Beverly Hills. This area corresponds to about 2.5%
of the entire service territory and to 242.5 working days per month. The interest of
Socal in this project was prompted by the sizeable expense (about 15 million dollars
per year) resulting from meter-reading activities.
DMC built a model of the problem integrating the data contained in the Socal
archives with those derived from a GIS. In the case of streets having users on both sides,
it was assumed that the meter reader would cover both sides separately. Therefore, the
problem was represented by a multigraph G(V , E) in which the road intersections
are described by vertices in V and street segments are associated with single edges or
to pair of parallel edges. The street sides containing some consumers formed a subset




TLFeBOOK
LINKING THEORY TO PRACTICE 333

1 2 3 4




5 6 7 8




9 10 11 12




13 14 15 16



Figure 8.19 An example of a multigraph used for modelling the Socal problem
(bold edges are required, while those with a dotted line are not required).

R ⊆ E (see Figure 8.19). With each edge (i, j ) ∈ E was associated a traversing time
tij , and with each edge (i, j ) ∈ R, was associated a service time sij (> tij ).
The duration t (R ) of a work shift corresponding to a subset of the service edges
R ⊆ R has a cost equal to the sum of three terms: (a) the time spent to deal with
administrative issues at the company headquarter (generally 15 min); (b) the travel
time by car from the headquarter to a parking site; (c) the duration T (R ) of the
solution of the RPP (see Section 7.6.2) associated with the service on foot of all edges
of R . Socal prefers work shifts associated with subsets R ⊆ R whose duration is
included between T min = 7.9 hours and T max = 8 hours (balanced work shifts).
A partition {R1 , . . . , Rn } of R is feasible if each pair of parallel service arcs belongs
to the same subset Ri , i = 1, . . . , n (feasible partition). The search for a feasible bal-
anced partition (or, at least, ˜almost™balanced) of R can be viewed as the minimization
of a penalty associated with a violation of the desired length [T min , T max ] of each
work shift (edge partitioning problem).
Denoting by U and L the penalties associated with the two types of violation, the
objective function to minimize is
n n
max{t (Ri ) ’ T , 0} + L max{T min ’ t (Ri ), 0}.
max
U
i=1 i=1

DMC solved the problem by means of the following procedure.
Step 0. The workloads associated with T (R ), R ⊆ R, are approximated as W (R ) =
(i,j )∈R tij . This approach is justi¬ed by the presence of consumers on both sides
¯
of most of the street segments. An evaluation of the average useful time T of a route
(the time a meter reader will take on average to travel on foot) was calculated as
the difference between T max and the average time required for the administrative
tasks and for driving.




TLFeBOOK
334 LINKING THEORY TO PRACTICE

Table 8.10 Comparison between the results provided by DMC procedure and
the manual solution used by Socal.

Socal DMC Savings
routes routes (%)

Number of routes 242,5 236 2.7
Average shift duration (hours) 7.82 7.95
Shift interval duration [7.03; 8.56] [7.77; 8.11]
Overtime (minutes) 293.4 110.4 62.3
Total deadheading time 693.4 63.1 90.9
(without service)
Total travel time by car 545.5 133.2 75.6


Step 1. The number n of shifts was evaluated by rounding down the ratio between
¯
the total workload W (R ) of the service area and T .
Step 2. The load of remaining workload (W (R )’nT max ) was assigned to an ˜incom-
plete™ auxiliary route, built with a heuristic criterion along the border of the service
area.
Step 3. The n ˜complete™ shifts were de¬ned by means of a local search procedure
(see Section 7.3.2). The algorithm ¬rst selected n seed vertices appropriately spaced
out and then progressively generated the routes by adding to each of them couples
of parallel edges in order to constantly have balanced work shifts. The solution
obtained in this manner was improved, where possible, with some exchanges of
couples of edges (or of groups of couples of edges) among the work shifts.
The solution generated by this procedure for the sample district was characterized,
compared to the one obtained manually by Socal, by a reduced number of meter
readers, by a remarkable reduction of overtime and by an increase in the average
useful time of an operator (see Table 8.10). Extrapolating the savings associated with
these improvements, DMC estimated at about $870 000 the saving expected after the
use of the optimization method for the entire area served by Socal.
The previous analysis convinced the Socal management to order from DMC a
decision support system with a user-friendly interface, based on the optimization
method just described. The system development required one year and was installed
at the beginning of 1991.


8.16 Annotated Bibliography
The ExxonMobil case (see Section 8.2) is derived from:
1. Ferrarese G 2003 Un sistema di supporto alle decisioni per la piani¬cazione
delle spedizioni in un™azienda manifatturiera. Bachelor thesis, University of
Lecce, Lecce (Italy).




TLFeBOOK
LINKING THEORY TO PRACTICE 335

The P¬zer case (see Section 8.3) is derived from documents courtesly provided by
the company.
The Railion case (see Section 8.4) is derived from the company™s website: www.
railion.nl
The Gioia Tauro case (see Section 8.5) is derived from:
2. Chiodo A 2000 Modelli di ottimizzazione nella gestione dei terminali marittimi.
Master thesis, University of Calabria, Rende (CS), Italy.
The Hamilton-Wentworth case (see Section 8.6) is derived from:
3. Huang G H, Baetz B W, Patry G C and Terluk V 1996 Capacity planning for
an integrated waste management system under uncertainty: a North American
case study. Waste Management 15, 523“546.
The Adriatica Accumulatori case (see Section 8.7) is inspired by:
4. Stampacchia P 1988 Le tecniche di estrapolazione e di correlazione per la
previsione delle vendite. In Il sistema d™impresa (ed. S Sciarelli), pp. 359“367.
Cedam, Milan.
The case of DowBrands (see Section 8.8) is taken from:
5. Powell RE, Gao L and Muggenborg SD 1993 Designing an integrated distri-
bution system at DowBrands. Interfaces 23(3), 107“117.
The case of Hardcastle (see Section 8.9) is taken from:
6. Crainic TG, Dejax P and Delorme L 1989 Models for multimode multicom-
modity location problems with interdepot balancing requirements. Annals of
Operations Research 18, 279“302.
The case of Wolferine (see Section 8.10) is taken from:
7. Bell PC and Noori H 1985 Managing inventories through dif¬cult economic
times: a simple model. Interfaces 15(5), 39“45.
The case of FedEx (see Section 8.11) is taken from:
8. Thomas C, Campbell K, Hines G and Racer M 1998 Airbus packing at Federal
Express. Interfaces 28(1), 21“30.
The case of Waterworld (see Section 8.12) is taken from:
9. Fraser HJ and George JA 1994 Integrated container loading software for pulp
and paper industry. European Journal of Operational Research 77, 466“474.
The case of Intexpress (see Section 8.13) is taken from:
10. Barnhart C and Schneur RR 1996 Air network design for express shipment
service. Operations Research 44, 852“863.




TLFeBOOK
336 LINKING THEORY TO PRACTICE

The case of the US Navy (see Section 8.14) is taken from:
11. Fisher ML and Rosenwein MB 1989 An interactive optimization system for
bulk-cargo ship scheduling. Naval Research Logistics 36, 27“42.
The case of Socal (see Section 8.15) is taken from:
12. Wunderlich J, Collette M, Levy L and Bodin L 1992 Scheduling meter readers
for Southern California gas company. Interfaces 22(3), 22“30.


8.17 Further Case Studies
A large number of logistics case studies can be found in operations research and
management science journals, such as Operations Research, the European Journal of
Operational Research, the Journal of the Operational Research Society, Omega and
Interfaces. In what follows, a few remarkable articles are introduced and summarized.
Various options are examined for shipping tomato paste from Heinz™s processing
facilities on the west coast of the USA to factories in the Midwest in:
Kekre S, Purushottaman N, Powell TA and Rajagopalan S 1990 A logistics
analysis at Heinz. Interfaces 20(5), 1“13.
An MILP model is solved to determine a worldwide manufacturing and distribution
strategy at Digital Equipment Corporation in:
Arntzen BC, Brown GG, Harrison TP and Trafton LL 1995 Global supply chain
management at Digital Equipment Corporation. Interfaces 25(1), 69“93.
A continuous approximation method is used for designing a service network for the
US Postal Service in:
Rosen¬eld DB, Engelstein I and Feigenbaum D 1992 An application of sizing
service territories. European Journal of Operational Research 63, 164“172.
A decision support system is developed to reduce the cost of transporting materials,
parts and components from 20 000 supplier plants to over 160 General Motors plants
in:
Blumenfeld DE, Burns LD, Daganzo CF and Hall RH 1987 Reducing logistics
costs at General Motors. Interfaces 17(1), 26“47.
A system for dispatching and processing customer orders for gasoline and distillates
at ExxonMobil Corporation is illustrated in:
Brown GG, Ellis CJ, Graves GW and Ronen D 1987 Real time, wide area
dispatch of Mobil Tank Trucks. Interfaces 17(1), 107“120.
A combined location-routing problem is illustrated in:




TLFeBOOK
LINKING THEORY TO PRACTICE 337

Rosen¬eld DB, Engelstein I and Feigenbaum D 1992 Plant location and vehicle
routing in the Malaysian smallholder sector: a case study. European Journal of
Operational Research 38, 14“26.
A routing problem associated with the collection and delivery of skips is described
in:
De Meulemeester L, Laporte G, Louveaux FV and Semet F 1997 Optimal
sequencing of skip collection and deliveries. Journal of the Operational Re-
search Society 48, 57“64.
A complex vehicle routing problem occurring in a major Swiss company is analysed
in:
Rochat Y and Semet F 1994 A tabu search approach for delivering pet food and
¬‚our in Switzerland. Journal of the Operational Research Society 45, 1233“
1246.




TLFeBOOK
TLFeBOOK
Index

3-BP-L algorithm, 194, 195 automated storage and retrieval
system (AS/RS), 4, 161“165
ABC auxiliary graph, 155, 252, 281, 285,
classi¬cation, 151 290
technique, 149
back order, 122
accuracy, 64
backhaul customer, 250, 251
add“drop, 231
balance-and-connect heuristic, 287
Adriatica, 312, 313
balanced graph, 282
after-sales service, 1
bar code, 6, 166, 167
agent, 10
basic solution, 210, 220, 223, 330
aggregate demand, 28
batch, 164, 171, 172, 181“183
air
formation, 158, 181
¬‚eet, 330
picking, 164, 181, 183
network design, 325
sizing, 182
transportation, 11, 12, 13, 203,
belt conveyor, 4, 162, 164, 182, 183
326, 328, 330
benchmarking, 19
air“truck (birdyback) transportation,
Benders decomposition, 99, 102, 105
13
berth, 310, 311
air-stops, 326
best ¬t (BF), 188, 189, 196
aisle, 160, 161, 163, 165, 169“174,
best ¬t decreasing (BFD), 189, 190,
183“185, 196
195, 196
alternating heuristic, 237, 238
big M method, 212
arc routing problem (ARP), 249, 281,
bin, 147, 185“192, 194, 196, 201, 267
297
bipartite complete directed graph, 77
assembly, 1, 4, 5, 18, 157, 180, 216 bipartite directed graph, 283, 284
assignment problem (AP), 253“255 bottom left (BL), 192, 195, 324, 325
asymmetric travelling salesman bottom“up, 27
problem (ATSP), 252, 256 Box“Jenkins method, 29, 62
branch-and-bound, 76, 79, 99, 188,
Introduction to Logistics Systems Planning
226, 231, 330
and Control
breakbulk terminal, 200
G. Ghiani, G. Laporte and R. Musmanno
broker, 10, 199
© 2004 John Wiley & Sons, Ltd
ISBN: 0-470-84916-9 (HB) Brown method, 48, 49
0-470-84917-7 (PB)
budget constraint, 1, 136, 138, 226




TLFeBOOK
340 INDEX

bullwhip effect, 22 complementary slackness conditions,
220
bundle constraints, 209, 225
computational complexity, 184, 189,
business
192, 271
cycle, 34
concave, 77, 79, 90, 92, 96, 132, 141,
logistics, 73
155
business-to-business (B2B), 17
conjugate gradient method, 137
business-to-consumers (B2C), 17
connectivity constraints, 253, 258
consolidation, 10
capacitated plant location (CPL), 80,
consolidation-type transportation,
84, 85, 88, 94, 98, 116, 118
200
capacity constraint, 83, 91, 97, 98,
consumer, 3, 5, 7, 10, 28, 87, 332, 333
136, 137, 210, 265, 267, 280, 316
consumer goods, 10
capital cost, 122, 124
container, 2, 3, 5, 11, 13, 14, 17, 67,
car, 2, 196, 243, 308, 312“314, 332,
185, 192, 193, 200, 201, 204, 212,
333
224, 239, 307, 308, 310, 311,
carrier, 3, 9, 11, 14, 18, 67, 81, 194,
317“320, 322“325, 329
196, 199“201, 204, 224, 229“231,
on ¬‚atcar, 14
234, 235, 239, 241, 242, 248, 307,
transshipment hub, 3, 308
315, 322
continuous approximation method,
causal
20, 336
method, 29, 30, 61, 313
contract transportation, 9
variable, 30
control chart, 65“67
central distribution centre (CDC), 4,
conveyor, 4, 162
14, 18, 22, 73, 74, 118, 157, 304,
convoy, 3, 12, 310, 311, 318
306, 314“316 corner, 237, 324
centrality of a terminal, 236 cost versus level of service, 15
centralized warehousing, 9 crane, 163, 311
Chebychev metric, 163 crew, 2, 9, 88, 200, 201, 203, 204, 302
Chinese postman problem (CPP), crossdock, 4, 8
249, 281, 282, 284 crossdocking, 8
circuit, 249, 252“254, 274, 291, 296 cumulative error, 65
class-based storage policy, 167 customer, 4“6, 8, 14, 15, 17, 19,
clothing industry, 10 25“28, 62, 74“78, 85, 111, 113,
cluster ¬rst, route second, 269, 270, 114, 116, 117, 122, 123, 149, 157,
281 199, 200, 203, 224, 229, 234, 235,
coal, 3, 12, 77, 300, 307 242, 247“250, 254, 265, 267“269,
coef¬cient of variation, 11, 12 271“273, 280, 293, 294, 296, 302,
commodity, 26, 61, 73, 97, 98, 104, 308, 315, 317, 318, 325
119, 123, 137, 138, 141, 149, 199, degree constraints, 267
200, 204, 207, 225, 226, 228, 324 demand, 7, 25, 78, 97, 121
common transportation, 9 order, 5, 25, 122, 157, 159, 160,
company-owned warehouse, 157 164, 165, 181, 235, 247, 248,
competitive location model, 76 336




TLFeBOOK
INDEX 341

service, 7, 9, 17, 73, 123, 241 history, 29, 48, 67
pattern, 25“29, 33“35, 37, 41, 43,
zone, 9, 18, 116
47, 51, 54“56, 60, 61, 73, 306,
customized transportation, 200, 201
314
cycle, 211, 215, 252, 291
point, 73, 77, 97, 98, 103, 104,
cyclical variation, 34
115, 117, 315, 318, 331
data aggregation, 115, 119 rate, 123, 127, 130, 136, 144, 292,
decentralized warehousing, 9 293, 296
decision, 4, 5, 10, 18, 25“27, 73“75, volume, 4, 27, 74
111, 141, 171, 197, 200, 201, 203, destination, 11, 12, 81, 200, 201, 206,
204, 206, 224, 229, 236, 237, 247, 207, 212, 221, 229, 234, 236, 240,
292, 294, 295, 318 291, 292, 307, 308, 317, 322, 326,
maker, 29, 115, 165 328
-making, 18“20, 29 deterministic model, 123
support, 18, 165, 186, 194, 334 dial-a-ride, 247
variable, 77, 78, 82, 88, 94, 98, diameter of a terminal, 236
104, 105, 112, 114, 131, 165, direct shipment, 8
169, 172, 176, 182, 205, 225, directed
234, 240, 250, 252, 257, 267, Chinese postman problem, 283,
274, 283, 316, 319, 323, 328, 287
331 graph, 108, 131, 196, 207, 208,
decomposition, 29, 33“35, 37, 40, 71, 210, 212, 221, 230, 232, 233,
72, 270 252, 254, 265, 282“284, 288,
principle, 294 290, 291, 296
dedicated rural postman problem, 287, 299
air service, 326 disposal, 3, 5, 22, 312
storage policy, 167 distribution
defective, 17 centre, 1, 2, 7, 8, 22, 76, 97, 98,
deferred service, 292, 325 103“105, 157, 160, 302
degree, 5, 258, 262, 263, 281“283, channel, 9, 10, 306, 307
285 company, 7, 22, 77, 247, 248
constraints, 253, 258, 267 cost, 88, 117
of dynamism, 292, 293 decision, 4
Delphi method, 28, 29 function, 141
demand logistics, 314
aggregation, 116 management, 17, 184, 302
allocation, 83, 85, 89, 95, 98, network, 21, 104, 118, 151, 314,
101“103, 106, 206 315
divisibility, 75 pattern, 116
entry, 30 plan, 26, 216, 248
forecast, 26, 27, 35, 40, 42, 48, 49, problem, 255, 256, 261, 262
64, 67, 147, 313 strategy, 8, 336
forecasting, 28, 46, 59, 60, 144, system, 3, 74, 303, 305, 314, 315
312 distributor, 5, 9, 17, 21, 43




TLFeBOOK
342 INDEX

elementary technique, 29, 30, 33,
dock, 160, 166, 196, 236, 304, 310
42“44, 50, 55
door, 204, 236“238
emergency service, 247, 292
door-to-door, 10“12, 206, 290
end-of-line
double moving average method, 52,
port, 3, 310
53
terminal, 200
DowBrands, 314, 315
end-pairing procedure, 282, 285, 287,
dual, 99, 100, 106, 211
291
cycle, 163
end-user, 2, 5“7, 10, 17, 22, 302
Lagrangian multiplier, 219
µ-optimal solution, 86, 102, 107
Lagrangian relaxation, 218
equipment, 10
problem, 101, 211
error, 30, 49, 63“67, 117, 118, 153,
simplex, 220
212, 272, 313
solution, 100“103, 106, 330
pattern, 66, 67
variable, 99, 219
Eulerian
dummy
graph, 281, 282
arc, 212
multigraph, 262, 264, 284“286,
customer, 299
288
directed graph, 213
subgraph, 262
driver, 241
tour, 281, 282, 287
facility, 94, 95
European Union (EU), 1
load, 241, 243
even graph, 282
problem, 212
event, 14
vertex, 213
expected
dump site, 1
demand, 141, 144
dynamic
revenue, 76, 141, 142
driver assignment problem
value, 28, 34, 37, 40, 47, 66, 67,
(DDAP), 241, 243, 244
144, 146, 153, 316
network, 208
exponential smoothing method, 48
programming, 131, 184, 196
ExxonMobil Chemical, 2, 300, 301
e-commerce, 16, 17 facility, 1“4, 7“9, 17, 22, 25, 73“80,
e-logistics, 17 83“85, 90“97, 108, 109, 111“119,
earliest 123, 149, 151, 157, 170, 199, 207,
pick-up time, 326, 327 236, 294, 308, 312, 318, 336
time, 273 consolidation, 11
econometric model, 29, 61 location, 17, 18, 25, 73, 74, 76,
economic order quantity (EOQ), 129, 107, 108, 119, 294
132, 136, 137, 143, 145, 149, 151, operating cost, 77“79, 90
153“155, 321 typology, 74
economies of scale, 5 fast-moving
edge partitioning problem, 333 goods, 69
electronic data interchange (EDI), 6, item, 123
product, 152
17




TLFeBOOK
INDEX 343

FedEx, 236, 322, 323 Frederickson, 290“292, 297
feeder, 310 freight
few-to-many transportation system, consolidation, 9
200 rail transportation, 3, 307
¬nished route, 315, 326, 327
goods, 1, 3, 7, 18, 27, 62, 121, terminal design, 236
305, 321 transportation, 3, 5“7, 9, 67, 199,
item, 27 200, 203, 304, 315, 317, 318
product, 3“5, 7, 12, 77, 88, 321
gap, 102, 184
¬nite
garbage
best ¬t (FBF), 191“193
collection, 1, 3, 247
¬rst ¬t (FFF), 191
incinerator, 1
¬rst
gate, 236, 237
come ¬rst served (FCFS) policy,
geographic information system
182, 292
(GIS), 17, 248, 332
¬t (FF), 188, 189, 196
Gioia Tauro, 3, 308, 310, 311
¬t decreasing (FFD), 189
global positioning system (GPS), 17,
¬xed
22, 248
cost, 7, 75, 79, 80, 93, 94, 97, 104,
globalization, 16, 17
112“114, 118, 121, 123, 138,
government, 1, 199, 303, 308
147, 148, 155, 172, 205, 227,
232, 234, 235, 251, 296, 315, graph, 71, 111, 184, 252, 281, 286
316, 319“321 Gross Domestic Product (GDP), 1, 30
order quantity policy, 143 ground
¬xed-charge network design (FCND) feeder route, 326
problem, 225, 226 service, 326
¬‚eet
Hamilton-Wentworth, 3, 312
composition, 204
Hamiltonian
planning, 330
cycle, 257, 261, 263“265, 267,
sizing, 18
270, 271
food industry, 10
path, 261
forecast, 4, 5, 18, 25, 28, 33, 37,
tour, 252
41“44, 46“50, 55, 56, 61, 62, 64,
handling cost, 167, 200, 201, 328
147, 149, 167, 251, 313
Hardcastle, 317, 318
control, 65
hazardous waste depot, 3, 312
error, 30, 48, 64
heuristic, 19, 20, 76, 84, 85, 89, 98,
forecasting
137, 138, 184, 187“189, 191, 192,
accuracy, 64, 65, 67
194, 226, 231, 237, 252, 261,
method, 25, 28“30, 49, 50, 54, 61,
268“270, 274, 278, 287, 290, 294,
63“66
296, 299, 324, 325, 330, 334
forklift, 4, 160, 165, 236, 237, 305
historical data, 21, 29, 48, 49, 56, 58,
forward
93
area, 171
holding cost, 8, 122
zone, 160




TLFeBOOK
344 INDEX

inventory-routing problem (IRP),
Holt method, 53
295, 296
hub, 81, 310
item aggregation, 116
and spoke system, 310

I/O port, 165, 174“178, 180, 185 joint
in-transit inventory, 7 cost, 123, 138
inbound order, 140
¬‚ow, 8, 77 just-in-time distribution, 8
transportation cost, 9
k-exchange, 264
incremental quantity discount, 132,
kerbside garbage collection, 3, 312
134, 135
key performance indicator (KPI), 19
industrial
cargo shipping, 200
labour cost, 8, 25, 73, 163, 166
goods, 6, 9, 10
Lagrangian
user, 7
heuristic, 84, 89, 98, 118
information
multiplier, 84“87, 98, 217, 218,
¬‚ow, 5, 6
259, 260
system, 8, 305
procedure, 80, 84, 217
technology, 6, 16, 17
relaxation, 84“86, 217, 259, 260
input“output model, 29, 61
land¬ll, 3, 312
insertion heuristic, 274, 275
laptop computer, 6
instantaneous resupply, 123, 128
largest gap heuristic, 184“186
integer programming (IP), 19, 315,
latest time, 273
327, 328, 332
lead time, 4, 7“9, 25, 121, 123, 124,
integrated location and routing, 294
130, 141, 144“147, 306
interest rate, 122, 124, 127, 129, 132,
least squares method, 31
134, 136, 137, 144, 147, 321
least-cost perfect matching, 262
intermodal
Leibnitz rule, 141
carrier, 11, 212
less-than-truckload (LTL), 11, 12,
train, 308
200, 201, 203, 234, 236, 243, 315,
transportation, 13, 317
316
Intexpress, 325“327, 329
life-cycle, 29, 62
inventory
linear
level, 6, 22, 25, 27, 124“126,
¬xed-charge network design
128“131, 138, 139, 143,
(LFCND) problem, 226, 228,
145“147, 149“151, 167, 168,
230, 232, 233
248, 296, 321
multicommodity minimum-cost
management, 6, 7, 25, 26, 64, 121,
¬‚ow (LMMCF) problem, 217,
123, 136, 152, 321
218, 220, 221, 232, 233, 244
policy, 62, 121, 123, 128, 132,
network ¬‚ow problem, 19
136, 141, 145, 146, 148, 149,
programming (LP), 19, 83, 98, 99,
153
174, 210, 217, 218, 228, 330
turnover ratio, 121, 321
regression method, 51
inventory-balance constraint, 131




TLFeBOOK
INDEX 345

make-to-
single-commodity minimum-cost
assembly (MTA) system, 5, 68
¬‚ow (LMCF) problem, 209,
order (MTO) system, 4, 5, 26
210, 216, 218
stock (MTS) system, 4, 5, 25, 68
linehaul customer, 250, 251
manufacturer, 4, 5, 7“10, 17, 71, 233,
liner cargo shipping, 200
324
local search, 19, 263
manufacturing
location
and assembly centre, 1, 4, 18
decision, 19, 74, 75, 78, 111, 294
centre, 3
model, 75“77, 95
cost, 16, 122, 141
problem, 73, 74, 76, 77, 84, 90,
plant, 2, 4, 9, 206, 300
95, 110, 115
process, 4, 77, 123, 132, 147, 302,
location“allocation, 74
321
location-covering, 108, 111, 112,
resource planning (MRP), 27
114, 115, 119
site, 2, 303, 304
location-routing, 75, 294
many-to-many transportation system,
logistician, 7, 9, 21, 26, 27, 29, 31
200
logistics
marginal cost, 79, 93, 94, 96, 97, 104
cost, 1, 2, 5, 7, 9, 73, 89, 108, 118,
market research, 28
121, 199, 315
master problem, 100
decision, 18, 19
material
management, 20, 299
¬‚ow, 1, 4, 74, 75, 77, 96, 237
network, 20, 26, 73
handling, 4, 157, 167, 236, 310,
service, 14, 15
311
system, 1“3, 6, 7, 9, 14, 15,
mean
17“20, 22, 25, 68, 74, 88, 93,
absolute deviation (MAD), 64, 65
149, 299, 303, 318, 326
absolute percentage deviation
long-haul
(MAPD), 64, 72
carrier, 247, 248
error, 67
freight transportation, 199
squared error (MSE), 64, 66, 69,
transportation, 17, 81, 200, 325
144, 147
long-term forecast, 26, 28
medium-term forecast, 26, 28
lost sales cost, 122
merchandise, 7, 11
lower bound (LB), 77, 80, 84, 85, 87,
meter reader routing and scheduling,
98, 99, 101, 102, 173, 188, 190,
332
194, 196, 197, 218“220, 228, 253,
minimum-cost
254, 258, 267, 296
¬‚ow, 207, 228, 239“241, 283
lumpy demand, 25
spanning r-tree problem
machine scheduling, 4, 181 (MSrTP), 258, 259, 296
mail spanning tree, 262“264
box, 294 mixed
delivery, 1, 247 Eulerian graph, 282
distribution, 76 graph, 108, 249, 254, 299
sorting centre, 1 rural postman problem, 299




TLFeBOOK
346 INDEX

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