Q2. What future works have the authors mentioned in the paper "An improved lagrangian relaxation-based heuristic for a joint location-inventory problem" ?
The following are some recommendations for future work and research directions for enhancing the model: ( 1 ) The model can be naturally extended to consider multiple products. ( 2 ) the authors have assumed that there is no capacity restriction on the amount of product that can be stored or processed by a facility. The authors can replace the uncapacitated fixed charge location problem by the capacitated fixed charge location problem and then integrate this with the proposed inventory model. ( 3 ) the authors can relax the single-sourcing restriction to allow a single retailer to be supplied by more than one distribution center.
Q3. What is the only reason for calling such problems location-inventory problems?
The existence of the location-type decision variables, in addition to the inventory decision variables, is the only reason for calling such problems location-inventory problems.
Q4. What is the structure of the model?
The structure of the model considered in this paper is such that new constraints or cost components can be added easily to the model.
Q5. What are the main issues in the efficient design of a supply chain network?
Inventory management and facility location are two major issues in the efficient design of a supply chain network; see Gunasekaran et al. [16,17] and Stevens [34].
Q6. What is the main factor to consider when calculating the inventory cost of platelets?
the expiration of the blood platelets a few days after they are collected is another important factor to be considered.
Q7. Why did the authors choose to address the MJIL with a Lagrangian relaxation he?
Due to the success that Lagrangian relaxation has exhibited in tackling several NP-hard supply chain combinatorial optimization problems, the authors chose to address the MJIL with a Lagrangian relaxation-based heuristic.
Q8. What is the solution to the MJIL problem?
when the Lagrangian procedure terminates, the best known lower bound is equal to the best known upper bound (within some pre-specified tolerance), the authors have found the optimal solution to the MJIL problem.
Q9. What is the reason why gi; j is recalcul?
The reason why Δgði; jÞ is recalculated for tuples ði; j;Δgði; jÞÞ with j¼ jmin in Step 3 is that the objective function (10) depends on all entries in the jth column of Y via the term βinvZ nj ðY ;jÞ, and hence when an entry in this column changes, all tuples that would add a “1” to this column must be recalculated.
Q10. How many randomly generated instances did the authors test?
The authors tested their heuristic for the MJIL problem on a total 1750 randomly generated instances against the Lagrangian relaxation based algorithm used by Diabat et al. [10].
Q11. What was the main reason for re-addressing this problem as location-inventory?
Each hospital stored its own platelet inventory and this independent inventory and location policy led to platelets going to waste after expiration in certain hospitals, while others ran out very soon.
Q12. What is the need for a cargo cost modelling?
Çetinkaya et al. [4] further consider that transportation costs are subject to truck and cargo capacity, leading to a need for explicit cargo cost modelling.
Q13. What is the reason why tuples i; j;g?
The reason that tuples ði; j;Δgði; jÞÞ with i¼ imin are removed in Step 3 is that once Yimin ;jmin has been set to one, the authors already have one “1” in row imin, so the authors remove any tuples that would place another “1” in this row.(ii)