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Erratum to “A modified two objective model for decision making in a supply chain” [International Journal of Production Economics 111 (2008) 378–388]
ARTICLE IN PRESS Int. J. Production Economics 119 (2009) 217–218
Contents lists available at ScienceDirect
Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe
Erratum
Erratum to ‘‘A modified two objective model for decision making in a supply chain’’ [International Journal of Production Economics 111 (2008) 378–388] Govindan Kannan Operations & Supply Chain Management, Department of Business and Economics, University of Southern Denmark, Odense, Denmark
a r t i c l e in fo
abstract
Article history: Received 9 October 2008 Accepted 19 November 2008 Available online 3 December 2008
Pokharel [2008. A two objective model for decision making in a supply chain. International Journal of Production Economics 111, 378–388] proposed a two-objective decision-making model for the choice of suppliers and warehouses for a SCN design. This is one of the first works in using multiple objectives in the design of supply chain networks. In this work, comments and suggestions are given to the recently published work (Pokharel, 2008). & 2009 Elsevier B.V. All rights reserved.
Keywords: Supply chain Modeling Multiple objectives Strategic decision making
1. Comments 1.1. Based on objective function 1 (f1) given in [1] 1.1.1. The capacity constraint given in [1] as Eq. (4) is the following: X rip xip pCAP ip ; 8p. (4) i
Comment: Each supplier’s annual allocated capacity for product ‘p’ (CAPip) is checked individually with processing time (rip) and number of quantity to be allocated (xip). However, the author [1] has used summation sign (S) in the left hand side of Eq. (4) which lead to an infeasible solution.
DOI of original article: 10.1016/j.ijpe.2007.01.006
So Eq. (4) in [1] should be rewritten as shown below:
rip xip pCAPip .
(4new)
1.1.2. The capacity constraint of assembler represented as Eq. (5) in [1] is given as the following The data for the capacity constraint of assembler represented as Eq. (5) in [1] is given as assembler allocated hours (CAPA):
ry ypCAPA .
(5)
Comment: Constraint 5 in [1] should be checked with unit processing time at assembler (rA), but the constraint 5 in [1] is checked with respect to unit volume of assembled product ‘Y’ (ry) which is not correct. Therefore, the equation has to be modified as
Tel.: +45 65 50 3188; fax: +45 65 50 3237.
E-mail addresses: [email protected], [email protected] (G. Kannan). 0925-5273/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2008.11.004
rA ypCAPA .
(5new)
ARTICLE IN PRESS 218
G. Kannan / Int. J. Production Economics 119 (2009) 217–218
Table 1 Optimum values and network allocation (f2). Payoff table Variables Reliability composite Cost Choice and allocation for the solutions in Payoff table xi1, i ¼ 1–4 xi2, i ¼ 5–8 xi3, i ¼ 9–12 xi4, i ¼ 13–17 W1m, m ¼ 1–4 W2m, m ¼ 1–4 W3m, m ¼ 1–4 W4m, m ¼ 1–4 W5m, m ¼ 1–4 W6m, m ¼ 1–4
74,454.2 (optimum) $378,047
(2878,3846,2800,4230) ¼ 13,754 (2570,3225,4166,3793) ¼ 13,754 (3793,3333,3870,2758) ¼ 13,754 (0,4482,747,3870,4655) ¼ 13,754 (0,250,2250,0) (0,1750,0,0) (0,0,0,750) (1000,0,0,0) (2000,0,0,0) (0,0,750,2250)
1.2. Based on objective function 1 (f2) given in [1] Eqs. (7), (8) and (9) given in [1] are valid only if inventory is not considered, which seems to be the case in the paper. That means, these equations have to be equated during the implementation part. This gives the result presented in [1], that is, there are no losses in the supply chain due to reliability objective. However, if reliability is considered by including inventory, then direct implementation of Eqs. (7), (8) and (9) will give an increased quantity of 11,000 instead of 9200 as mentioned [1]. This will increase the composite value of reliability to 74,454 but it will also increase the minimum cost. That is, if reliability is to be increased, the cost would have to be increased further. Quantity 11,000 refers to the product. However, if we investigate the individual parts or modules, then it will require more parts (13,754) instead of 11,000. The details on the output of this analysis are given in Table 1. Two insights from the results are as follows: (1) If we substitute the decision variables found in objective function (f2) in f1 then the cost goes up to $378,047.
(2) The actual demand is 9200 units only, but based on the objective function 2, the optimal incoming of quantities at assembler is 13,754 and the optimal allocation of quantities from the assembler is 11,000. That means, there would be an excess of 3554 quantities of parts at assembler and 1800 quantities at retailer end. These excess quantities will incur some extra inventory or holding cost in the assembler and warehouse apart from the regular holding cost (he) in the warehouse.
1.2.1. Discussion 1. As per the author [1] if inventory is not considered then we can retain the model proposed by Pokharel [1] by changing the constraints 4 and 5 by the proposed new constrains 4new and 5new. Therefore, [1] shows that when inventory is not considered in the supply chain, it will sacrifice a bit in terms of reliability but it will provide a minimum cost option. 2. But in the real scenario, neglecting inventory is the major disadvantage. If maximum reliability is the concern disregarding the increase in cost, then supply chain partners can allow an increase in the inventory.
2. Conclusion From the above discussions, it can be concluded that capacity equation (4) for each supplier should be modified as suggested in (4new), capacity constraint Eq. (5) for assembler should be modified as suggested in (5new). Then with respect to the objective function (f2) of [1] if inventory is to be considered in the supply chain then it might increase the reliability to a higher level but the tradeoff is on the substantial increase in cost of supply chain operation. Reference Pokharel, Shaligram, 2008. A two objective model for decision making in a supply chain. International Journal of Production Economics 111, 378–388.
Contents lists available at ScienceDirect
Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe
Erratum
Erratum to ‘‘A modified two objective model for decision making in a supply chain’’ [International Journal of Production Economics 111 (2008) 378–388] Govindan Kannan Operations & Supply Chain Management, Department of Business and Economics, University of Southern Denmark, Odense, Denmark
a r t i c l e in fo
abstract
Article history: Received 9 October 2008 Accepted 19 November 2008 Available online 3 December 2008
Pokharel [2008. A two objective model for decision making in a supply chain. International Journal of Production Economics 111, 378–388] proposed a two-objective decision-making model for the choice of suppliers and warehouses for a SCN design. This is one of the first works in using multiple objectives in the design of supply chain networks. In this work, comments and suggestions are given to the recently published work (Pokharel, 2008). & 2009 Elsevier B.V. All rights reserved.
Keywords: Supply chain Modeling Multiple objectives Strategic decision making
1. Comments 1.1. Based on objective function 1 (f1) given in [1] 1.1.1. The capacity constraint given in [1] as Eq. (4) is the following: X rip xip pCAP ip ; 8p. (4) i
Comment: Each supplier’s annual allocated capacity for product ‘p’ (CAPip) is checked individually with processing time (rip) and number of quantity to be allocated (xip). However, the author [1] has used summation sign (S) in the left hand side of Eq. (4) which lead to an infeasible solution.
DOI of original article: 10.1016/j.ijpe.2007.01.006
So Eq. (4) in [1] should be rewritten as shown below:
rip xip pCAPip .
(4new)
1.1.2. The capacity constraint of assembler represented as Eq. (5) in [1] is given as the following The data for the capacity constraint of assembler represented as Eq. (5) in [1] is given as assembler allocated hours (CAPA):
ry ypCAPA .
(5)
Comment: Constraint 5 in [1] should be checked with unit processing time at assembler (rA), but the constraint 5 in [1] is checked with respect to unit volume of assembled product ‘Y’ (ry) which is not correct. Therefore, the equation has to be modified as
Tel.: +45 65 50 3188; fax: +45 65 50 3237.
E-mail addresses: [email protected], [email protected] (G. Kannan). 0925-5273/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2008.11.004
rA ypCAPA .
(5new)
ARTICLE IN PRESS 218
G. Kannan / Int. J. Production Economics 119 (2009) 217–218
Table 1 Optimum values and network allocation (f2). Payoff table Variables Reliability composite Cost Choice and allocation for the solutions in Payoff table xi1, i ¼ 1–4 xi2, i ¼ 5–8 xi3, i ¼ 9–12 xi4, i ¼ 13–17 W1m, m ¼ 1–4 W2m, m ¼ 1–4 W3m, m ¼ 1–4 W4m, m ¼ 1–4 W5m, m ¼ 1–4 W6m, m ¼ 1–4
74,454.2 (optimum) $378,047
(2878,3846,2800,4230) ¼ 13,754 (2570,3225,4166,3793) ¼ 13,754 (3793,3333,3870,2758) ¼ 13,754 (0,4482,747,3870,4655) ¼ 13,754 (0,250,2250,0) (0,1750,0,0) (0,0,0,750) (1000,0,0,0) (2000,0,0,0) (0,0,750,2250)
1.2. Based on objective function 1 (f2) given in [1] Eqs. (7), (8) and (9) given in [1] are valid only if inventory is not considered, which seems to be the case in the paper. That means, these equations have to be equated during the implementation part. This gives the result presented in [1], that is, there are no losses in the supply chain due to reliability objective. However, if reliability is considered by including inventory, then direct implementation of Eqs. (7), (8) and (9) will give an increased quantity of 11,000 instead of 9200 as mentioned [1]. This will increase the composite value of reliability to 74,454 but it will also increase the minimum cost. That is, if reliability is to be increased, the cost would have to be increased further. Quantity 11,000 refers to the product. However, if we investigate the individual parts or modules, then it will require more parts (13,754) instead of 11,000. The details on the output of this analysis are given in Table 1. Two insights from the results are as follows: (1) If we substitute the decision variables found in objective function (f2) in f1 then the cost goes up to $378,047.
(2) The actual demand is 9200 units only, but based on the objective function 2, the optimal incoming of quantities at assembler is 13,754 and the optimal allocation of quantities from the assembler is 11,000. That means, there would be an excess of 3554 quantities of parts at assembler and 1800 quantities at retailer end. These excess quantities will incur some extra inventory or holding cost in the assembler and warehouse apart from the regular holding cost (he) in the warehouse.
1.2.1. Discussion 1. As per the author [1] if inventory is not considered then we can retain the model proposed by Pokharel [1] by changing the constraints 4 and 5 by the proposed new constrains 4new and 5new. Therefore, [1] shows that when inventory is not considered in the supply chain, it will sacrifice a bit in terms of reliability but it will provide a minimum cost option. 2. But in the real scenario, neglecting inventory is the major disadvantage. If maximum reliability is the concern disregarding the increase in cost, then supply chain partners can allow an increase in the inventory.
2. Conclusion From the above discussions, it can be concluded that capacity equation (4) for each supplier should be modified as suggested in (4new), capacity constraint Eq. (5) for assembler should be modified as suggested in (5new). Then with respect to the objective function (f2) of [1] if inventory is to be considered in the supply chain then it might increase the reliability to a higher level but the tradeoff is on the substantial increase in cost of supply chain operation. Reference Pokharel, Shaligram, 2008. A two objective model for decision making in a supply chain. International Journal of Production Economics 111, 378–388.