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Operation and Supply Management

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Submitted By rich55
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Homework 3
Product A We want to minimize the overall cost that is given by the sum of two factors: a fixed cost and a variable cost. If we increase the number of orders, we increase setup costs while decreasing holding costs. On the other hand, if we decrease the number of orders, we increase holding costs while reducing setup costs. Hence, there’s a trade off between these two expenses that reaches equilibrium when the setup costs meet the holding costs, as shown in the figure below.

In order to find the optimal quantity that minimizes costs, we need to derive the following formula that represents the overall cost as a function of Q (c = 0): G(Q) = k* λ/Q + h*Q/2 If we derive this equation and we set it equal to zero we easily find that the optimal quantity is: Q*= (2*k* λ/h)1/2 Therefore plugging numbers into the formula we obtain: Q* = (2*400*2769/4)1/2 = 744,17. In this case the overall cost would be ! G(740,17) = (2*k* λ*h)1/2 = (2*400*2769*4)1/2 = 2976,7 ₪ However, we have a constraint that obliges us to order product A at batches of 50 units. Thus, we need to decide wether to order 750 units or 700 units, taking into consideration different increasing rates when moving towards the right or left side of the graph, which represents the total cost. The

right side of the total cost graph has a lower slope than the left side so it can be presumably argued that a surplus in the optimal quantity would be preferred to a deficit. Additionally, the decrease in the optimal quantity is more than three times greater than the deficit in the optimal quantity when we increase it. A quantitative analysis can compare the two costs and evaluate the best one: G(700) = 400*2769/700 + 4*700/2 = 2982,3 ₪ G(750) = 400*2769/750 + 4*750/2 = 2976,8 ₪ In conclusion, the optimal solution is Q = 750, which is given by a binding constraint that doesn’t allow the supplier to order

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...San Jose State University SJSU ScholarWorks Faculty Publications Management School 1-1-2009 Commonalities and differences between service and manufacturing supply chains: Combining operations management studies with supply chain management Ming Zhou San Jose State University, ming.zhou@sjsu.edu J. Yi. Saint Joseph's University, Philadelphia, PA T. Park San Jose State University Follow this and additional works at: http://scholarworks.sjsu.edu/org_mgmt_pub Part of the Business Administration, Management, and Operations Commons, and the Organizational Behavior and Theory Commons Recommended Citation Ming Zhou, J. Yi., and T. Park. "Commonalities and differences between service and manufacturing supply chains: Combining operations management studies with supply chain management" California Journal of Operations Management (2009): 136-143. This Article is brought to you for free and open access by the Management School at SJSU ScholarWorks. It has been accepted for inclusion in Faculty Publications by an authorized administrator of SJSU ScholarWorks. For more information, please contact scholarworks@sjsu.edu. Commonalities and Differences between Service and Manufacturing Supply Chains: Combining Operations Management Studies with Supply Chain Management Ming Zhou • Taeho Park San Jose State University, San Jose, CA John Yi Saint Joseph's University, Philadelphia, PA The service sector of the US economy has been gaining importance...

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