METHODOLOGY AND EXPERIMENT

The research realized a three-stages modular framework to identify priorities and to take them into proper account in a step-optimization (Fig.3). Comparing these three basic problems we can face different strategic, tactic and operational levels: depending on the geographic context, infrastructures, products, company background and logistic network maturity, different cost issues can prevail. The first model optimizes transportation costs and immobilizations, depending on the number of the customer served by the distribution centre and on the procurement time to restore level of goods in stock. The second model evaluates the impact on the network configuration of a particular strategy, aggregating more product in a single delivery along the logistic chain and not in production sites. The third model determines logistic knots to activate and paths to cover, basing on the best routes for vectors.

As a first step of the methodology, the optimization analysis is effectuated on parallel branches to evaluate the impact levels of each perspectives of

optimization: this could be considered as the weight of not optimized configurations on the item in focus. In the second step, the methodology benchmarks the three different approaches by comparing the best and the worst cases investigated, calculating the difference between the two values and assigning a greater importance to the perspective of optimization with the higher spread or (as a second criterion of priority) to the one more significant in percentage. Characterizing the models with a degree of their relative impact allows to proceed with a stratified resolution of the problem, from the more relevant effect (Higher Impact Model – HIM) to the less one (Lower Impact Model – LIM). Therefore, in the third step, the optimization process considers the specific results obtained by the HIM, fixing results of the most important solution, and then running the middle impact model with more bounds and less degree of freedom. The new results create new added bounds, input for the last optimization problem (LIM), that completes the network configuration. Figure 3 shows the six possible combinations of priorities, explaining from each stage the bounds of the following optimization to the final logistics solution.

Figure 3 - Methodology framework

To avoid a classification priority where network characteristics do not permit to identify a sharp difference, a simple tool to measure the range of impact was developed, as shown in the example of Table 2. Every model is compared on cost results, considering the best and the worst solution, that means the biggest possible loss for a non appropriate configuration. Table inputs compares two perspective a time, by rows with percentage difference between two solutions, in

DESIGN / RE-DESIGN GATHER NETWORK INFORMATION RISK POOLING OPTIMIZATION MERGE IN TRANSIT OPTIMIZATION VEHICLE ROUTING OPTIMIZATION IMPACTS COMPARISON

FIRST PRIORITY LEVEL OPTIMIZATION

SECOND PRIORITY LEVEL OPTIMIZATION

THIRD PRIORITY LEVEL OPTIMIZATION BEST CONFIGURATION IMPROVEMENT PRIORITY LEVELS DEFINED? YES COMPARISON BETWEEN SIMILAR PRIORITY LEVEL

SOLUTIONS NO Highest Impact Model (HIM) Bounds from HIM solution Middle Impact Model (MIM) Added bounds from MIM solution Lowest Impact Model (LIM) Final bounds from LIM solution Bounds on assembly centers Bounds on DC clients assignment Routes Bounds on routes knots DC clients assignment MIT VRP VRP RP RP Bounds on DC clients assignment Bounds on

assembly centers Routes

Bounds on routes

knots Assembly centers

RP VRP VRP MIT MIT Bounds on routes knots Bounds on DC clients assignment Assembly centers Bounds on assembly centers DC clients assignment VRP MIT MIT RP RP

terms of absolute variation and relative variation, to consider the level of importance of the possible loss, related to total cost. The three combinations of the model can individuate balanced configurations when identifying the correct priority scale of strategies. When the result of the tool cannot identify a neat preference (values in table from 0,6 to 1) or gives a slight difference (from 0,3 to 0,6), the step-optimization has to be carried on completely for the two alternatives of path (in figure 3) to compare the final cost and define the better sequence.

To test this decision support system, a simple network was developed composed of two production plants with given capacity, three distribution centres (DC) and five points of aggregated demand, all placed around Italy as potential location points (as for Tab.1). Products are low value goods, with the possibility of aggregating different component in a single order: three input elements can constitute, according to appropriate assembly rates, two output products. A complete order is composed of two of input product A, one of input B and C while a partial order can be composed by just one input product A and C; in the test, Plant1 could supply input product A and C and Plant2 could supply input product A and B. The assembly process can be effectuated in just one knot, a production plant or a distribution centre or, in a Merge-in-Transit solution, every network point could merge components into order, with different cost of assembly. Every possible DC has a starting situation of activation or deactivation, with a fix switching cost. Two type of vectors can be chosen for shipping, with different fixed and variable costs, depending on their capacity. Avoiding the description of the mathematical models, in table 2 the final results are directly represented. Starting from the first issue, it’s to notice how Risk Pooling absolute variation is about 7% of Merge-in-Transit, while the ratio between percentage weights, 9% and 20%, gives a relative variation of 45%: the second model it’s strongly to prefer as HIM. Practically, the third model is recognised as LIM, due to its very limited impact both on maximum absolute and relative loss to the optimal value. At this point, once identified the issue that could cause the most significant effect, the architecture stars taking into account the HIM solution that returns bounds on assembly centres, finding out only one DC as the assembly point. With a new RP model solution where the assembly point is now forced, it is possible to find all the clients assignment to DC, that means who buys from who. The final step is a bounded network to solve with a simple VRP problem.

Table 1 – Distance table

LT VR GE FI NA MI TO RM BA BO LT 1 585 580 355 167 VR 585 1 290 231 716 GE 580 290 1 225 715 140 170 507 945 670 FI 355 231 225 1 490 295 400 280 720 101 NA 167 716 715 490 1 785 885 219 260 590 MI 140 295 785 1 140 575 880 210 TO 170 400 885 140 1 675 1000 330 RM 507 280 219 575 675 1 450 380 BA 945 720 260 880 1000 450 1 670 BO 670 101 590 210 330 380 670 1

Table 2 – Classification table

PERSPECTIVE BEST WORST DELTA ORDER

Risk Pooling 230000 € 250000 € 20000 € (9%) 2

MIT 1340000 € 1610000 € 270000 € (20%) 1

VRP 134000 € 138000 € 4000 € (3%) 3

COMPARISON DELTA VAR. % RELATIVE DELTA VAR. %

Risk Pooling vs. MIT (#1) 20000/270000=7% 45%

VRP vs. MIT (#2) 4000/270000=1% 15% VRP vs. Risk Pooling (#3) 4000/20000=20% 33% 80% - 100% 0,2 0,4 0,6 0,8 1 60% - 80% 0,16 0,32 0,48 0,64 0,8 40% - 60% 0,12 0,24 0,36 0,48 0,6 20% - 40% 0,08 0,16 (#3) 0,24 0,32 0,4 De lt a Var iatio n 0% - 20% 0,04 (#2) 0,08 0,12 (#1) 0,16 0,2 0% - 20% 20% - 40% 40% - 60% 60% - 80% 80% - 100%

Relative Delta Variation % CONCLUSIONS

The research allowed to test a methodology that can integrate different mathematical models and propose a parallel and critic vision on different logistics aspects. The study of the literature shows a general difficulty in considering and analysing various configuration choices as the real context, not always suggesting a particular criterion to follow, leaves many different possibilities of improvement to test. The most significant results of the project are in the identification of a logic scheme, applied to three classic problems, that can be easily extended for a general plurality of optimization functions. Finally, the modular methodology could be fed up with different mathematical models and solving algorithms to grant an higher speed of calculus and integrate new performance issues, both strictly logistics and multi-criteria analysis to evaluate different solutions and performance parameters.

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