MGT Exam 2 Formulas. Item $ Usage % of $ usage Cumulative % of $ Cumulative % of no. of items Class

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1 Chapter 12 Inventory Management MGT Exam 2 Formulas ABC Classification rule: Class A: ~15% of items, 70-80% annual $ usage Class B: ~30% of items, 15-25% annual $ usage Class C: ~55% of items, 5% annual $ usage Item $ Usage % of $ usage Cumulative % of $ Cumulative % of no. of items Class Basic EOQ Model Q * = H H = Holding (carrying) cost per unit per year Expected number of orders (N) = D/Q Expected time between orders (T) = (Q/D) No. of days per year = Q/d Annual ordering cost = NS = (D/Q)S Annual carrying cost = (Q/2)H Total annual cost (TC) = (D/Q)S + (Q/2)H POQ Model * Q p = H (1 d / p) H = Holding (carrying) cost per unit per year p = Daily production rate d = Daily demand rate = D/No. of working days Length of production run (t) = Q/p Rate of increase of inventory during production = (p - d) Maximum inventory = I max = (Q/p)(p-d) Average inventory = I max /2 Expected number of batches (N) = D/Q Expected time between orders (T) = (Q/D) or No. of days per year = Q/d Annual setup cost = NS = (D/ Q)S Annual carrying cost = (I max /2)H Total annual cost (TC) = (D/Q)S + (I max /2)H Quantity discount model Q = IP IP = H = Holding (carrying) cost per unit per year I = Holding cost as a % of item cost P = Item cost per unit

2 Step 1: Determine Candidate Q a. Compute Formula-Q for each price break price. b. If Formula Q < Lower limit for price, then Candidate Q = Lower limit If Formula Q is within the limits for the price, then Candidate Q = Formula Q If Formula Q > Upper limit for price, then no candidate Q, ignore the Formula Q Q-Range Price Holding cost/unit = % x P Formula Q Adjusted Q Step 2: Compute total annual cost (TC) for each valid candidate Q and select the candidate Q with least cost as EOQ. Total annual cost = Annual holding cost + Annual ordering cost + Annual item cost i.e. = (Q/2)H + (D/Q)S + PD, where P = cost of the item per unit ROP Models Discrete Probability model Total cost = Annual Holding cost + Annual stock out cost Annual Holding cost = Safety stock x H Annual stock-out cost = Expected stock out per cycle x N x C s Where, Expected stock out = Σ (Stock out x Probability) N = No. of orders per year = D/Q C s = Cost of stock out per unit Reorder point model with Normal distribution: Reorder point (ROP) = Average demand during lead time + Safety stock i.e. ROP = d x L + Z σ dlt where, d = Demand rate per period L = Lead time Z = Normal table value for the given service level σ dlt = Standard deviation of demand during lead time (as give in table below) Lead time is constant Lead time is variable Demand is constant dlt = 0 dlt = d Demand is variable dlt = σ d dlt = Single-Period model Service level =, where C s = Cost of shortage, C o = cost of overage C s = Lost profit = Selling price per unit Cost per unit C o = Cost/unit salvage value/unit Order quantity = µ + Zσ, where µ = mean demand, σ = standard deviation of demand Stock-out risk= 1 - service level

3 Chapter 13 Aggregate Planning Production rate/day/worker = Hours per day/ Labor hours per unit Production rate/period/worker = Production rate/day/worker x No. of days per period Wage/worker/day = Wage rate/hour x hours/day Wage/worker/period = Wage rate/worker/day x days per period OT cost/unit = Standard hours x OT wage per hour No. of workers needed = Production Required Production per worker (Rounded up) Cost summary for aggregate planning: Cost summary Regular wages No. of workers x no. of periods x wage rate per period per worker OT cost OT quantity x OT rate/unit (Only for mixed strategy) SC cost SC quantity x SC rate/unit (Only for mixed strategy) Hiring cost Workers hired x hiring cost per worker Firing cost Workers fired x firing cost per worker Carrying cost Sum of ending inventory x inventory carrying cost/unit/period Total cost Chase: Production 1 st period = Forecasted Demand - (Initial inventory - Safety stock) Production for all other periods = Forecasted demand Period Demand Production Workers Hire Fire Hire/fire cost may be based on production rate changes or number of workers hired/fired. Level: Initial estimate of production rate = ( ( ) Number of workers = Production rate/production rate per worker Period Demand Production Ending inventory Mixed: Production Capacity = number of workers * production rate/worker/period Regular time production = Minimum{Requirement, Capacity} Shortage = Requirement Regular time production Over time capacity = OT Limit % x Regular time capacity Over time production = Minimum{Shortage, Over time Capacity} Subcontracting production = Shortage Over time production Period Demand Requirement Capacity RT Production Shortage OT Capacity OT SC

4 Chapter 14 Material Requirements Planning Gross requirement: = Number of units required per unit of Parent (from BOM) x MPS quantity if parent is at Level zero of BOM or = Number of units required per unit of Parent (from BOM) x Planned Order Release (PORL, the last row) if parent is at an intermediate Level of BOM Projected on-hand for week t+1 POH t+1 = POH t + SR t GR t POH is always > Safety stock, if not there is net requirement Net requirement If POH t+1 < Safety stock, then NR t = GR t (POH t + SR t ) POH t = Projected on hand for week t POH t+1 = Projected on hand for week t+1 SR t = Scheduled Receipt for week t GR t = Gross requirement for week t NR t = Net requirement for week t Lot sizing: Lot-for-lot: Total cost = No. of setups x Setup cost + Total ending inventory x Holding cost/week EOQ: Q = 2dS H / week d = Average demand per week S = Setup cost H = Holding cost per week Total cost/week = (d/q)s + (Q/2)*Holding cost per week Total cost for n weeks = Total cost/week x n Periodic Order Quantity POQ interval = EOQ/Average weekly demand rounded to whole number Chapter 15 Short-term Scheduling Input Output Control Chart Cumulative deviation of input = Previous cumulative deviation + actual input planned input Cumulative deviation of output = Previous cumulative deviation + actual output planned output Cumulative backlog = Previous backlog + Actual input Actual output Job due date = Days till due date = Due date Today s date Completion time (Flowtime) of a job = Completion time of the previous job + processing time Average completion (flowtime) time = Number of jobs

5 Average job lateness = Average number of jobs in the system = Utilization = Critical Ratio = =