# TOOLS OF MONTE CARLO SIMULATION IN INVENTORY MANAGEMENT PROBLEMS

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3 =IF(AND(H4=1;A4>=L3); \$E\$32- INT(RAND()*\$E\$32);0) Planned arriving day: =IF(IF(\$K4>0;\$A4+\$K4+1;\$L3) >=\$A4;IF(\$K4>0;\$A4+\$K4+1;\$L3);0) Fourth row of Figure (3) in columns O, Q, S contains formula = B26 and other rows in column O, Q, S contain formula =TABLE(;P2). RUNNING MONTE CARLO SIMULATIONS MODEL IN EXTEND Figures 2: Second Part of Our MS Excel Spreadsheet Figures 3: Tabularization of Simulation Outcomes of 60 Runs. Simulated lead time: =IF(L3<=A4+1;IF(I4=1;INDEX(B47:B50;MATCH(J 4;sG47:G50;1));0);0) Introduction to Modeling with Extend software The equivalent model was built in graphical environment of Extend software. Then, two models were compared and validated by confronting the outcomes. Modelling in Extend (Krahl 2002) consists in using pre-built modelling components to build and analyse system. This approach is also applied in other software like Arena, Flexim and others. As we see on Figure (4), results from this model implementation is similar (average and standard deviation 5.95) to MS Excel spreadsheet outcomes, Figure (3). It is worth mentioning that it was necessary to make two corrections into object s way in model. First, we have to secure to the arriving demand object a very small amount of time after the arriving of order object (it is beginning of the day), second we have to add 1 day for all lead times shown in Figure (1) before placing this information in Input Random Number (the block with histogram icon). After introductory validation of our Extend model, we think that discrete event model built in Extend is more flexible, because it is possible to easily prolong simulated time and the number of replications (runs), to see the animation of objects during the run and to optimise model variables (minimization of total cost). We will try to prove it in the next section. Guidelines of the Inventory Management Business Game with Cost Accounting We prepared the equivalent model to the previous one using the Extend software, but we extended it by cost coefficient taken from the example of inventory system simulation given in (Jensen and Bard 2003). Next, we validated it by comparing the optimal values found in our simulations with these presented in the book. The set of assumptions are as follows: the daily demand oscillates between 6 and 16 units, lead time oscillates between 1 and 5 day, initial inventory is 50 units, cost per day of unit holding is 10 cents, cost of lost sale (stockout) is \$5, ordering cost is \$20, reorder point is 35 and order quantity is 70 units. Note: in this situation, lead time equal to 1 day means that the order will arrive next morning.

4 Figures 4: Monte Carlo Method in Inventory Management Model Built in Extend Software. Equivalent of a Spreadsheet Simulation Model

5 Figures 5: Inventory Management Model with Cost Calculations, Ready for Optimisation.

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