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In this research a three-stage supply chain is studied that includes retailers, several manufacturers and a single supplier. Each retailer has a constant demand rate for a single product. This product is provided by a single manufacturer that produces multiple unique products for a set of retailers. The manufacturers all receive a common processed raw material from the supplier. The objective is to minimize holding, setup, and ordering costs across all stages by defining the common production cycle length and production sequence for each product at the manufacturers and the delivery sequence to retailers. This study extends the work by Khouja [9], Lee[11], and Kim [10]. An analytical model and heuristic solution is proposed, in which the heuristic finds optimal solutions for small and medium sized problems in reasonable time.
What is good about the paper
This is a well written paper that offers an extension of previous research that analyzes supply chain wide costs for an integrated supply chain, incorporating many of the relevant costs observed in practice. The research provides a thorough review of the literature and a clear explanation of the model under study. The solution approaches are clearly defined and they are explored in an empirical study. I have recommended the paper requires major revisions (discussed below), however, this is not because the paper is poor in many areas - rather, it just needs more then the "minor" improvement rating allows. I believe the paper is worthy of publication with the improvements suggested below.
What main improvements should be considered in the paper
There are three main improvements I would recommend for the paper. Two are related to the numerical experiments. The final improvements relates to the length of the paper - as it exceeds the 25 page limit for submissions - this should be relatively easy to address.
1. I would suggest that the parameter sets (Pg. 19, line 32-42) are more thoroughly described and evaluated. Using the uniform distributions to generate the problem data it is not easy for the reader to interpret how this range of values impacts the final solution. Specifically, the parameter description should provide information on the following questions. Does this range of data capture situations in which each of the supply chain costs becomes significant or immaterial to the solution (i.e. Is the setup cost very important to the end solution?, How does changing the holding cost effect the solution?). This can be stated in another way - It may be beneficial to look at a low, medium, and high value for each of the costs and then test many of these combinations, providing some insight into the solutions. Also, the insight gained from this analysis may allow for removal of one or more of these costs (i.e. set the cost to zero) in certain problem tests, thus allowing
for the analytical solution to solve larger problems.
2. More experiments should be conducted to clarify the efficiency of the heuristic. Since the heuristic finds the optimal solution for every problem tested it can not be determined if the heuristic is efficient due to its methodology or if the problems are relatively simple to solve. This can be addressed in several ways. Has another solution technique been proposed for this problem - if so can it be tested as a solution technique. OR, is there a solution technique for a simpler problem that can be adapted and tested on these problems - the focus being on comparing how the solutions compare with the proposed heuristic. Also, can the range of experiments be expanded to allow for the analytical solution to solve larger problems providing for additional comparisons for the heuristic. For example, can the number of retailers be increased while keeping the number of manufacturers fixed. AND/OR as described above, can some of the costs be removed (set to zero) so that the
analytical method can solve larger problems. Along these lines, I would suggest for Figure 9 and 10 that the cumulative solution time for the heuristic be shown for both smaller and larger problems, even if the analytical solution is not available, to provide more data points. For example, in Figure 9 show the results for problems with retailer values of (3,3), (4,4) and (5,5). Also, is it possible to combine the setup cost at the manufacturer with the retailer ordering cost (as these appear to always be linked together in a 1 to 1 relationship such that they can be combined to a single parameter). If so, this simplification should allow the analytical solution to solve larger problems.
3. Suggestions for shortening the manuscript:
1. combine Figure 1 and 2. Can show the EPQ and EOQ information at the bottom of Figure 2.
2. Eliminate Figure 3. This inventory level cyclic behavior should be understand by the audience.
3. Eliminate Figure 9 or 10. This data can be highlighted in Table 1.
4. Eliminate most of the pseudo code (Pg. 16,17,18) by referring to Clausen reference and only showing the changes/additions to their pseudo code.
5. In Table 1, eliminate the "manufacturer index" column and display the "No. of retailers" column as a list in a single row (ex: 4,3,3). Also, eliminate the "No. of instances" column - this is not needed (you have described this information in the text.)
Minor Problems -
Suggestions for grammatical improvements
Pg. 1, Abstract, shorten to 150 word limit. Suggest something like the following:
In this research, we investigate a three-stage supply chain with one supplier, several manufacturers and multiple retailers where the supplier provides a common raw material to each manufacturer, who in turn uses a single stage production facility to convert it into final products that are delivered at fixed lot sizes to retailers. An integrated economic procurement, production and delivery model is developed whose objective is to find the common production cycle length, production sequences of final products at manufacturers and delivery frequencies of final products to retailers minimizing the total costs of considered supply chain. We propose an analytical solution procedure and an efficient heuristic solution method. The proposed heuristic solution algorithm is able to find the optimal solutions for the small and medium problem instances and consequently it is very promising for solving the large-sized instances in a reasonable time.
Pg. 2, line 11: have the minimum -> minimize
Pg. 2, line 48: a three mathematical were presented -> a mathematical model was presented
Pg. 3, line 25: [7] -> [10]
Pg. 4, line 26: Fig. 2 shows a scheme of the considered supply chain -> Figure 2 depicts the supply chain configuration.
Pg. 4, line 39: The first sentence is not clear. There are no cost elements shown in Figure 2.
Pg. 4, line 55: is facing with demand of just one final product. -> fulfills demand for a single final product.
Pg. 5, line 31: Moreover, the following notations are used for the model formulation-> The following notations are used for the model formulation
Pg. 5, line 34: Supplier level's parameters -> Supplier level parameter
Pg. 6, line 16: Retailer's level's parameters -> Retailer level parameter
Pg. 6, line 13: Why not define TCMi as was done for Retailers
Pg. 6, line 13: Retailer's level's parameters -> Retailer level parameter
Pg. 13, line 46: use of the word "nominator" is not clear
Pg. 14, line 13: As it mentioned -> As mentioned
Pg. 18, line 59: set of -> sets of
Pg. 18, line 59: using some uniform -> using uniform
Pg. 19, line 12: Consequently, makes the frequent occurrence -> Consequently, this increases the occurrence
Pg. 19, line 29: must be hold -> must hold
Pg. 19, line 33, consider putting the cost parameters into a table showing costs by level
Pg. 19, line 50: Surprisingly, in all -> In all
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