Delft University of Technology
Faculty Mechanical, Maritime and Materials Engineering
Transport Technology

M.R. Martens A modelling approach towards more responsive supply chain designs
Masters thesis, 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 defined as:
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: 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.

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:
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 innovation.

Physical distribution

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.

Materials management

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: 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.

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.

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: 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 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 multipliers alternatively.

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)
Modified: 2005.11.10; , TU Delft / 3mE / TT / LT.