Question

A Kathmandu based solar panel manufacturing company that operates 250 days per year requires
50,000 solar cells on an annual basis to assemble their panels. The annual holding cost per solar cell is
Rs. 50. They are currently manufacturing the solar cells and have a production rate of 1000 cells per day.
The cost to setup the machinery to begin a production batch costs the company Rs. 10,000 per setup.
The company has discovered another solar cell manufacturer in China that can supply the cells at a
cheaper cost, but ordering the product from them costs Rs. 50,000 per order with an average lead time
of 50 days and a standard deviation of lead time of 15 days. The company will decide to purchase the
cells instead of manufacturing it only if it lowers their total cost (product, setup and holding costs). If the
company wants to maintain a 95% service level what is the maximum price per cell that the company
would be willing to pay to the subcontractor? (95% p value has a Z-score of 1.65)

Answer 1

Annual demand, D = 50000 cells

Daily demand rate, d = 50000/250 = 200 cells per day

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Option 1: In-house production

Daily production rate , p = 1000 cells per day

Setup cost, S = Rs 10000 per setup

Holding cost , H = Rs 50

Economic Production Quantity, EPQ = sqrt(2DS/(H*(1-d/p)))

= sqrt(2*50000*10000/(50*(1-200/1000)))

= 5000 cells

Average inventory level = Q*(1-d/p)/2 = 5000*(1-200/1000)/2 = 2000 cells

Total annual cost = Product cost + Setup cost + Holding cost

= D*c1+S*D/Q+H*Q*(1-d/p)/2

= 50000c1+50000*0+10000*50000/5000+2000*50

= Rs 50000c1+200000   (where c1 is the manufacturing cost)

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Option 1: Subcontractor

Setup cost, S = Rs 50000

EOQ = sqrt(2DS/H)

= sqrt(2*50000*50000/50)

= 10000 cells

Safety stock = Z√(L*σ_D² + d²*σ_L² ) (standard deviation of demand (σ_D) is not given, so we consider that to be 0)

= 1.65*sqrt(50*0+200²*15²)

= 4950 cells

Total annual cost = Product cost + Setup cost + Holding cost (of cycle stock and safety stock)

= 50000*c2+50000*50000/10000+50*10000/2+4950*50

= 50000c2+747500 (where c2 is the unit price charged by the subcontractor)

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In order to determine the price (c2) that should be charged by the subcontractor, we need to compare by equating the total cost of manufacturing and the total cost of subcontracting  

50000c1+200000  = 50000c2+747500 (where c1 is the in-house manufacturing cost per unit and c2 is the unit price charged by the subcontractor)

Solving for c2, we get,

c2 = c1-(747500-200000)/50000

c2 = c1-10.95

Therefore, the maximum price per cell that the company would be willing to pay to the subcontractor should be Rs 10.95 cheaper than the in-house manufacturing cost.