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∑ =

∀ , ∀

(6)













=1
Constraints (6) state that the number of products requested from storage locations during period t is equal to the demand of that product during period t.











∑ =

∀ , ∀

(7)










=1
Constraints (7) ensure that then number of products moved from production area to the warehouse in a period is the same as what produced in the period.














∑ =

∀ , ∀

(8)













=1
Constraints (8) state that all the locations that items remain in at the end of time period t are consistent with the inventory at the end of time period t.

≤ +

∀ , ∀ , ∀

(9)







−1






Constraints in (9) state that items could only be retrieved from locations which they have previously been moved in from production area or inventoried.



+

≤ ∀ , ∀ , ∀

(10)




−1






Constraints in (10) state that when moving an item from production area to the warehouse, the item is only can be placed at an available storage location. Therefore, no item could be assigned to a location where an item has already been inventoried in the previous period.



= − +

∀ , ∀ , ∀

(11)







−1






Constraints (11) are the flow balance of an item from the production area to a storage location, and from the storage location to the output point.





∀ , ∀ , ∀

(12)









Constraints (12) ensure that items are only retrieved from locations that had been reserved for them.





∀ , ∀ , ∀

(13)










Constraints (13) ensure that items are only placed in locations that had been reserved for them.






∀ , ∀ , ∀

(14)

Constraints (14) ensure that items are only inventoried in locations that have been reserved for them.



11


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