Abstract
Consider a situation where a buyer has to procure an item from outside suppliers and is faced with the decision whether to procure the item from a single supplier or from multiple suppliers. Supply risk has become, in the recent years, a key consideration for a manager while taking such decisions and often mitigation of such risks is done either by building up inventory or having multiple suppliers. In this paper, we address the problem of determining the optimal number of suppliers to be engaged in order to minimize the effects of supply risks on the focal firm. In the literature, the events leading to supply risks have been classified into three categories viz. super events, semi-super events and unique events. However, none have considered all the three types of events together into a single model in order to determine the optimal size of the supply base. In the present work, we have considered all three types of events and calculated the probability of complete supply disruption. We formulate the problem as a cost minimization problem so as to find the optimal size of the supplier base that minimizes the effects of such supply disruptions. The mathematical formulation of the problem is combinatorial in nature. When a decision tree is used, a moderate size problem results in an unmanageable number of decision alternatives. In this paper, we propose mathematical theorems and rules that helps avoid considering many non-optimal decision alternatives for evaluation. The proposed solution procedure is very simple and reduces the number of decision alternatives to be evaluated significantly, thus saving time and effort in solving the problem.
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Abbreviations
- K :
-
Number of Locations
- J k :
-
Total number of suppliers available at location k
- y k :
-
Number of suppliers selected from location k
- y :
-
Total number of suppliers selected from all locations \( = \mathop \sum \limits_{{\varvec{k} = 1}}^{\varvec{K}} \varvec{y}_{\varvec{k}} \)
- P* :
-
Probability of occurrence of a super-event causing all suppliers to fail
- P k ** :
-
Probability of occurrence of a semi-super-event causing all suppliers at location k to fail where \( \varvec{k} = 1, 2, \ldots , \varvec{K} \)
- ρ jk :
-
Probability of occurrence of a unique-event causing supplier j at location k to fail where \( \varvec{j} = 1,\varvec{ }2,\varvec{ } \ldots .,\varvec{ J}_{\varvec{k}} \)
- Y k :
-
Set that contains all the suppliers selected from a location k
- C(y) :
-
Cost of operating y suppliers
- C T :
-
Cost of supply disruption
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Sarkar, A., Mohapatra, P.K.J., Chaudhary, A. et al. Single or Multiple Sourcing: A Method for Determining the Optimal Size of the Supply Base. Technol. Oper. Manag. 3, 17–31 (2012). https://doi.org/10.1007/s13727-013-0013-6
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DOI: https://doi.org/10.1007/s13727-013-0013-6