The Manitoba Liquor & Lotteries (MLL) currently purchases a product at a rate of

Question

The Manitoba Liquor & Lotteries (MLL) currently purchases a product at a rate of $ 11 per unit from the a supplier. Recently, the supplier decided to offer discounted prices as a special case to MLL to encourage it to continue to purchase from them. The annual demand forecast for this product is 15578 units. Ordering costs are estimated to be pegged at $45.50 per order. Annual holding rates are 37%. The price schedule offered is us under: Calculate the optimal order size so that total annual inventory cost can be minimized? What is the total annual inventory cost?

Explanation / Answer

Total Inventory Cost=Demand*Ordering cost/Order size +order size*holding cost per unit/2

EOQ=sqrt(2*annual demand*ordering cost/holding cost)

Annual Demand(D)=15578 Price of Product(P)=11 Ordering Cost(O)=45.5 Holding Cost per unit=37%=37%*11= 4.07 a) EOQ=sqrt(2*15578*45.5/4.07) 590.173 Total Inventory cost at order size of 590=15578*45.5/590+590*4.07/2= 2402.004 at order size of 1101=15578*45.5/1101+(1101/2)*(11*0.95*0.37)= 2772.286 At order size of 2101=15578*45.5/2101+(2101/2)*(11*0.9*0.37)= 4185.344 at order size of 3101=15578*45.5/3101+(3101/2)*(11*0.88*0.37)= 5781.842 at order size of 5101=15578*45.5/5101+(5101/2)*(11*0.80*0.37)= 8443.381 hence least Total inventory cost is achieved at EOQ of 590 units though I assume the question also must have been about minimizing total cost Total cost=Total Inventory Cost+Price*demand Total cost at various order sizes Order size Total cost Total cost 590 2402+11*15578= 173760 1101 2772.29+15578*0.95*11= 165562.4 2101 4185.34+15578*11*0.9= 158407.5 3101 5781.84+15578*11*0.88= 156576.9 5101 8443.38+15578*11*0.8= 145529.8 the minimum total cost is achieved if order size is 5101

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