A modelling approach towards more responsive supply chain designs
Report 2005.TL.6944, Transport Engineering and Logistics.
More and more retailers and manufacturers are feeling the effect of
increasing demand uncertainty of consumers, in traditional retail stores
as well as on the internet. A way to stay ahead of the competition is to
introduce new products quickly, and maximize customization and availability.
To achieve this, the supply chain has to change from the supply chain
where lowering costs was the primary goal (the so called efficient supply
chain, including just-in-time supply chains) into a responsive supply
chain where stock-outs and lead times are reduced. Responsiveness is here
Responsiveness is the rate at which a supply chain can deal with certainty
and uncertainty in demand by fulfilling customer orders with the highest
service level and shortest order lead times.
The market characteristics that ask for responsiveness are:
Responsiveness can be increased by:
- high demand variation
- high stock-out costs
The general tactics to increase responsiveness in a supply chain usually
raise unit costs. Therefore, not all companies use this differentiation:
several companies have chosen to stay with price differentiation. However,
cases of Zara, Spadel, and Albert Heijn prove that responsiveness can be
fruitful in the long term.
- higher service level
- shorter order lead times
It is highly dependent on the type of products and the current state of
the market whether responsiveness is required. The products to which
responsiveness is related are physical products that are for sale in
retail stores, or on the internet. The typical products are:
- fast moving consumer goods, which must be available on the
shelves at all times
- products that must be delivered in a day or two when ordered, for
instance home appliances
- products that require some customization or configuration before they
are delivered to the customer, for example computers or cars.
Supply chain management tactics increase responsiveness
The four fields in supply chain management that have tactics to increase
responsiveness are physical distribution, materials management (including
inbound logistics), information technology, and the coordination between
parties in the supply chain. The adjustment of physical distribution is
considered the first and simplest level at which responsiveness can be
improved, the other fields are at the second level. The third level is
At the strategic (long term) level, responsiveness can be increased by
redesigning the physical distribution network. The distribution network in
this context is the physical layout that determines the location of
plants, distribution centres, etc. Typical actions to be more responsive
are to use faster transportation modes, to place strategic buffers at
distribution/consolidation centres, to place the facilities closer to
customers, and/or to deliver more frequently.
At the tactical level (mid term) collaboration with other shippers results
in economies of scale: at lower costs per participant, more distribution
centres (DC's) can be placed, and more frequent deliveries to the DC can
take place. At the operational level (short term) special deliveries (also
called emergency transhipments or express deliveries) between warehouses,
cross-docks, retailers and/or customers prevent stock-outs. Special
deliveries can also move planned delivery times forward to fulfil an
individual customer's wish. So, special deliveries can reduce order lead
time and increase service level, thus increasing responsiveness.
The higher the uncertainty of demand is, the more flexible the
manufacturer has to be. It has to deal with many product variants demanded
by the customer, as well as with peaks and steeps in the demand quantity.
Flexibility of the production is called agility: with small batches and
postponement (locating the customer order decoupling point downstream in
the production process) one can quickly respond to market demand.
Agility is not always recommendable or necessary to be responsive. For
companies that sell fast moving consumer goods, which must be available on
the shelves at all times, even flexible production cannot respond in time.
In this case, if the product variety is low, safety stock can easily be
built up at relative low costs. Otherwise, a very fast distribution network
is necessary, so the stock can be located at the suppliers to save costs.
Information technology and coordination between supply chain parties
In the field of information technology expensive automatic systems improve
the coordination among various members of a supply chain, resulting in
meeting customer demand more often. In coordination between parties in a
supply chain, it is easier for a dominant party to switch suppliers
rapidly and frequently, which increases responsiveness.
Redesign the physical distribution network to increase responsiveness
The layout of the physical distribution network is a trade-off between
costs and customer service. Service is primarily determined by lead time,
product variety, product availability, customer experience, and the
ability to return products. The costs of the network are primarily holding
costs, transportation costs, and facilities costs.
When placing more facilities in the network to increase customer service
the total logistic costs first tend to decrease due to more direct
shipment. Eventually, the total logistic costs rise due to lower
utilization. The objective is now to find the network, which minimizes
total logistic costs, while still providing required service components.
When designing responsive supply chains, costs for delivery times longer
than the desired lead time should be added to the costs of the physical
distribution network. This inclusion tends to increase the logistic costs.
To find the minimum, a model is necessary.
Models which assist the designer with the physical layout of the distribution network
are called facility location models. A literature review of available facility
location models points out that none of the models exactly matches the requirements
to design responsive physical distribution networks. Five candidate models which
match many, but not all, of the requirements are used to derive a new model.
Responsive physical distribution network model
The objective function of a new facility location model minimizing the total
logistic while ensuring a specified service level, and optimize both plant
and DC locations, under stochastic demand and with multiple products is:
The most important restrictions of this responsive physical distribution
model are that capacities of facilities may not be exceeded, and that
average demand for each customer for each product is fulfilled. The output
of the model determines which possible DC locations to open, which
possible plant locations to open, where to allocate safety stock, and what
quantities of goods flow between the facilities.
This model includes the logistic structures which are most suited for
responsive supply chains:
(1) Manufacturer ships directly to customers
The model presented is solved by Lagrange relaxation. There are many
examples found in the literature where this approach gives excellent
results. In this case, by relaxing the capacity restrictions of
facilities, an uncapacitated fixed charge facility location problem
remains. When the demand restriction is also relaxed, four subproblems
remain that can be solved independently from each other: the DC problem,
the plant problem, the safety stock problem, and the flow problem. These
problems can be solved quite easily by an algorithm.
(2) Manufacturer ships to DC, which ships to customer
(3) Manufacturer ships to DC, which ships to pick up sites. Pick up is
done by end customers.
The heuristic solving algorithm gives a lower bound (invalid solution) and
an upper bound (valid solution) to the optimal solution of the facility
location problem. The lower bound is calculated by solving the problem
with the demand restriction relaxed. The upper bound solution is found by
repairing the lower bound solution so that capacity restrictions are no
longer violated. This process of finding lower and upper bound solutions
is repeated until they are close to each other. Then, it can be stated
that upper bound solution is close to the optimal solution.
The implementation of the responsive physical distribution model and the
heuristic algorithm to solve the model is programmed in the
object-oriented language Visual Basic .NET. The calculation time of the
model is mostly determined by the time that it takes to solve the flow
subproblem. The precision of the data type used to store floating point
values has no influence on the outcome of the calculations. When the lower
and upper bound come closer together, there comes a moment when no
improvement can be found. In this case the number which represents the
ratio at which the capacity Lagrange multipliers should be adjusted must
be halved. But initial tests show that halving this number has little to
no improvement in the solution.
The implementation of the model proved rather slow in large networks, and
the gap between the lower and upper bound solution is too high. Several
performance improvements have been implemented. The upper bound solution
procedure has been simplified, resulting in a speed increase. Updating the
Lagrange multipliers using the Kobyashi method instead of the sub-gradient
optimization method proved very fruitful in terms of quality. Replacing
the redirecting of violated flows in the upper bound algorithm by the
standard transhipment problem proved less successful, in terms of speed as
well as in terms of quality. If the capacities of facilities are infinite,
the model reduces immediately to an uncapacitated fixed charge facility
location model, resulting in an enormous performance increase.
Sensitivity analysis of service level, order lead time, penalty for
exceeding lead time, and demand uncertainty
European Fruit is a new player in the market that wishes to ship various
fruits from production areas all over the world to wholesalers in Western
Europe. The fruit from production areas located outside Europe is first
shipped to harbours in Europe, and then shipped by truck to distribution
centres located close the customers. The fruit from production areas
located in Europe is directly shipped to the distribution centres by truck.
The question of European Fruit is: what is the layout of the physical
distribution network when we wish to compete with an 18, 21, or 24 hours
service in Europe under different market circumstances?
To give insight in the costs the following parameters are varied:
Specific values for the parameters rule out other scenarios, leaving 100
scenarios to test with the implementation of the responsive physical
distribution network model. To answer the question of European Fruit, for
each of the four different values of the lead time a scenario without
demand variation, and a scenario with a high coefficient of variation
(0.90) and a high service level (99.9%) are selected.
- order lead time (infinite, 18, 21, and 24 hours)
- penalty for not delivering in time (€0.00, €5.00,
€10.00, and €20.00/box)
- coefficient of variation (0.00, 0.30, 0.60 and 0.90); the rate of
uncertainty in demand
- required service level (90%, 99%, and 99.9%)
When interest goes out to the best valid solutions found by the model, the
following remarks can be made specifically for European Fruit:
The general conclusions, important when designing responsive physical
distribution networks, are:
- without demand variation, a responsive network is 33% more expensive
than an efficient network
- with high demand variation and service level, a responsive network is
36% more expensive than an efficient network
When analysing the stability of the networks by varying transportation
costs and average demand, the influence is significant on the optimal
layout of the responsive network under market circumstances with high
demand variation. Thus responsive networks lose more efficiency when
transportation costs or average demand change.
- the lead time is the parameter which has the most influence on
the total logistic costs
- if the penalty for not delivering in time is high (for instance as
high as the value of the product), it is never an option to deliver
- when demand variation and service level increase not all products are
shipped by every DC anymore
- some outputs of the model are very close together when looking at the
total logistic costs, but can differ in for example the number of open DC's
The performance of the model in terms of finding good solutions can be
improved. In scenarios with increased responsiveness, it becomes more
difficult to tell whether the solution is close to the optimal solution,
due to the high duality gap (difference between lower and upper bound
solution) of sometimes 30%. This makes it difficult to compare these
scenarios with the efficient networks with a duality gap of less than
5.5%. The high duality gaps are primarily caused by the lower bound
solutions, which are too low when penalty costs are specified. In some
cases the upper bound solutions are too high. An improvement in the model
should have the goal to reduce the duality gap to 10%.
The total logistic costs of solutions of the model do not represent the
real costs of the physical distribution network, since the responsive
physical distribution network model uses a linear costs function. However,
the case results show that it is possible to compare scenarios with
different parameters. The model proved reliable enough to be able to
compare efficient and responsive networks at the strategic level.
To design the final physical distribution network one can follow the procedure of
performing a sensitivity analysis on the chosen scenarios, and observe what happens
if for instance a DC is added or removed. Also recommended is to perform what
if scenarios, and observe how the solution performs under different economic
circumstances. Next, an inventory model should be applied. The last step is to apply
a vehicle routing model to determine which scenario should be carried out.
To improve the solution, a branch-and-bound algorithm method could be
applied. It is also possible to relax more restrictions to independently
select the number of plants, distributions and safety stocks to be opened
or assigned. The last recommended improvement is to update the Lagrange
The model can be extended with more aspects of responsiveness, namely
shipment frequency, consolidation, long-term change in demand, delivery
uncertainty, and production.
Future research of responsive supply chains should mainly focus on the
second level of increasing responsiveness. For this, tactics to increase
responsiveness in production, information technology, and coordination
between parties in the supply chain are to be integrated with tactics
within the physical distribution network.
Reports on Transport Engineering and Logistics (in Dutch)
, TU Delft