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Calculate EOQ Q eoq = 2DS H = 2(Annual Demand)(Order or set-up cost) Annual Holding Cost Reorder point R=DL D = Avg daily demand (constant) L = Lead time (constant) when to place an order. Exercise EOQ and reorder point? Annual demand = 2,000 units Days/year in average daily demand = 365 Cost to place an order = £10 Holding cost /unit p.a. = £2.50 Lead time = 7 days Cost per unit = £15

EOQ Solution Q = 2DS H = 2(1,000 )(10) 2.50 = units or 90 units eoq d = 1,000 units p.a. 365 days p.a. = 2.74 units/day Reorder point D L = 2.74 units/day = or 20 for 7 day lead time EOQ order = 90 units. When only 20 units left, place next order for 90 units.

EOQ and ROQ example 2 Annual Demand = 10,000 units Days per year considered in average daily demand = 365 Cost to place an order = £10 Holding cost per unit per year = 10% of cost per unit Lead time = 10 days Cost per unit = £ (366 units)= (10,000)(10) = H 2DS =Q eoq D = 10,000 units/year 365 days = units/day If lead time = 10 days, ROL= = 274 units Place order for 366 units. When 274 left, place next order for 366.

Total variable cost Demand 2 x unit cost x Hc% + Oc x £3 x 25% = £450 + £10 Once per year = £ /52 2 x £3 x 25% = £9 + £510 Once per week = £519 approx Find point of minimum TVc Avg.stock

EOQ Table – minimum TVc Avg.stock x item £ x hc % Oc + Hc

Minimum point of Total Inventory Costs EOQ = minimum TVc point Total variable costs Total Hc Total Oc EOQ*Order Size (Q) £ Costs

EOQ Example Cheapo Bags wants to calculate the EOQ for tapestry cloth used to produce hand bags.  Last year demand = 10,000 metres (constant rate).  Value per metre of tapestry = £6.40  Oc – each order = £250.  Hc = £1.20 per metre = 18.75% What is the EOQ? 2 x 10,000 x £250 = 2042 metres £6.40 x 18.75%

Price-Break Model Holding cost per annum 2(Demand p.a.)(Order or Setup-cost) = iC 2DS = Q OPT Assumptions similar to as EOQ model i = % of unit cost as carrying cost C = cost per unit “C” varies for each price-break so apply the formula to each price-break cost value.

Price-Break Example Brunel University can reduce ordering costs for photocopy paper by placing larger quantity orders. What is the optimal order quantity? order cost = £4 carrying cost % = 2% Demand p.a. = 10,000 units? Order Quantity(unit s) Price/un it(£) 0 to 2,499£1.20 2,500 to 3, ,000 or more0.98 Quantity price breaks iC 2DS

Solution = 1,826 units 0.02(1.20) = iC 2DS D = 10,000 units Order cost (S) = £4 Put data into formula for each price-break of “C”. =2,000= =2,020 4)2(10,000)( = Carrying cost % (i) = 2% Cost per unit (C) = £1.20, £1.00, £0.98 Q opt Feasible and Not feasible Are Q opt values feasible for the price breaks? 2(10,000)(4) 0.02(1.00) 0.02(0.98) 2(10,000)(4)

U-shaped function True Q opt values occur at the start of each price-break interval.The total annual cost function is a “u” shaped function Order Quantity Total annual costs Price-breaks

Price-Break Solution Now apply the Q opt values to total annual cost & identify the total cost for each price-break. TC(0-2499)= (10000x1.20)+(10000/1826)x4+(1826/2)(0.02x1.20) = £12, TC( ) = £10,041 TC(4000+) = £9, Least cost Q opt = 4000