4 SOLUTION STRATEGIES AND SIMULATIONS 4.1 Strategy definition

In all seven strategies for all stages in the warehouse are defined. They are numbered from S1 to S7. The first three strategies are used for storage location assignment. The next two strategies S4 and S5 are related to the pre-marshaling operation and the last two are for block retrieval operations.

For each stage, one strategy is used.

 Strategy S1: experienced assignment. No location assignment optimization is conducted. The blocks are stacked just randomly or according to the experience of the operator in some stacks with free spaces. And the initial situation is not changed.

 Strategy S2: vertical spread. The initial configuration should be at first through pre-marshaling prepared to a configuration, in which the blocks with the same or close departure data are located in the same stack. After that, the new arriving blocks are also stacked in the stack with the same departure date. Figure 4 shows an example configuration of blocks by using this strategy at the beginning of the second of July. The boxes with question marks inside are those blocks without given departure date. They are stacked in the same stacks.

Figure 4: Block configuration with strategy S2.

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 Strategy S3: horizontal spread. The blocks with the later dates are stored lower in different stacks. The blocks with the same or similar date spread over the whole stacks. That means, in the same stack, the retrieval priorities of the blocks from bottom to top increase. To ensure this, it is quite often to do relocations.

 Strategy S4: experienced pre-marshaling. The preparation of the several blocks on the day for the next day is done according to operator’s experience.

Because the exact retrieval time is not yet known, all the requested blocks are relocated on the tops of different stacks. That means, above them, there are no other blocks and they are all directly accessible at the beginning of the second day.

 Strategy S5: optimized spread pre-marshaling. The requested blocks are prepared in the same way as strategy 4. That means the final configuration of the requested blocks is the same as the one with strategy 4. The difference is that the relocations are minimized for reaching the same aim of block preparation.

 Strategy S6: experienced retrieval. The same as stacking and pre-marshaling, the operator does the retrieval operations according to experience or randomly.

 Strategy S7: optimized retrieval. For the retrieval operations, the number of blocks relocation for reaching the target block is concerned and minimized.

4.2 Simulations

Data in a time period of four weeks are collected and used as the basis for simulations of the strategy combinations. As shown in Table 1, there are in all twelve strategy combinations, which are numbered from SC1 to SC12.

Table 1: Scenarios of strategy combinations.

Strategy

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With respect to stochastic departure date of the blocks during stacking and pre-marshaling, three scenarios are considered. Scenario 1 means that the departure dates of all blocks are known and fixed. There is no uncertainty and incompleteness in the information. Scenario 2 corresponds to the situation with some unknown, delayed and preponed departure dates. Scenario 3 shows an even higher uncertainty in the departure date. The data used for scenario 2 are the historical data being collected. For scenario 1 and scenario 3, data are randomly changed based on the basic data.

A manual analytic approach is used for simulation. That means the relocations during stacking, pre-marshaling, and retrieval are just calculated manually for different scenarios. The simulation results with regard to relocation percentage are shown in Figure 5. The strategy combination SC1 under the scenario 2 corresponds to the current operation situation in the warehouse. We consider the relocation percentage as 100 % for this situation and use this as a benchmark for other strategy combinations. From the results, it is to see that the strategy combination SC8 with Strategies S2, S5 and S7 exhibits the most saving for relocations under three scenarios. The strategy S3 “horizontal spread” for location assignment is in each case not recommended. If the uncertainty of departure dates is higher, the optimization contribution is not any more so obvious.

Figure 5: Simulation results.

5 CONCLUSION

In this paper, strategies are defined to reduce the operations, especially the relocation operations for the practical block storage warehouse proper strategy for each stage of block operations is determined based on simulations. The strategies with optimizations contribute in each case to the

60%

reduction of relocation operations when there is more known information on the departure date and the uncertainty of the information is low.

A big limitation of the simulations is the limited time period. Another limitation is that the uncertainty or stochastics of departure dates is only considered in very limited scenarios instead of being generally formulated. The consequence is that the result may be not general enough for other periods anymore. Future work is to develop a software which may adopt the optimization methods from the literature for the blocks operations and enables the automated place assignment.

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