Project and Production Management

module 9:Tactical Decisions and Review Back to main indexexit continue Project and Production Management Module 9 Tactical Decisions and Review Prof Arun Kanda & Prof S.G. Deshmukh, Department of Mechanical Engineering, Indian Institute of Technology, Delhi

module 9:Tactical Decisions and Review MODULE 9: Tactical Decisions and Review • 1.Basic Inventory Principles • 2.Inventory Modeling • 3.Material Requirements Planning • 4.Job shop scheduling • 5.Course Summary and Review • 6. Illustrative Examples • 7. Self Evaluation Quiz • 8. Problems for Practice • 9. Further exploration Back to main indexexit

module 9:Tactical Decisions and Review Back to main indexexitback to module contents 1. Basic Inventory Principles

module 9:Tactical Decisions and Review Back to main indexexitback to module contents FUNCTIONS OF INVENTORIES Inventories are Idle Resources maintained in various forms: • - Raw materials • Purchased & manufactured parts • Subassemblies • Finished products Since inventories represent a sizable investment in a logistic system, we must be aware of the functions they perform

module 9:Tactical Decisions and Review Back to main indexexitback to module contents FIVE CATEGORIES OF STOCKS • PIPELINE stock (in process stock, in transit stock) • CYCLE stocks (batch production owing to - economies of scale - technological requirements) • SEASONAL stocks ( time varying requirements of an item) • SAFETY stocks (supply and demand uncertainties, lead time uncertainties) • Stocks held for OTHER REASONS (- decoupling stages of production - price, quantity discounts, - speculation)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents INVENTORY RELATED COSTS • Procurement cost • Cost/order generally fixed • (not dependent on order qty) • Costs associated with existence of inventories • (supply exceeds demand) • Cost/unit/unit time • i C • (i = inventory carrying cost rate) • Costs associated with • stock outs • (demand exceeds supply) • (cost/unit) (cost/unit/unit time)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents PROCUREMENT COSTS • Procurement cost Cost of goods Cost/order generally fixed Ordering cost (not dependent on order qty) - Administrative component - Handling - Transportation - Inspection of arrivals

module 9:Tactical Decisions and Review Back to main indexexitback to module contents INVENTORY HOLDING COSTS • Costs associated with existence of inventories (supply exceeds demand) Cost/unit/unit time i C (i = inventory carrying cost rate) - Storage and handling - Interest on tied up capital - Property taxes - Insurance - Spoilage - Obsolescence - Pilferage

module 9:Tactical Decisions and Review Back to main indexexitback to module contents SHORTAGE COSTS • Costs associated with stock outs (demand exceeds supply) (cost/unit) (cost/unit/unit time) - Additional costs of special order - Backorder, if possible - Loss of customer goodwill - Lost sales

D E A B C V F S N module 9:Tactical Decisions and Review Back to main indexexitback to module contents SELECTIVE INVENTORY CONTROL In a large number there are PARETO’s Law significant few insignificant many Typical organisations deal with a large variety of stocked items (10,000 – 100,000 …is not uncommon) Depending on rankings of • VALUE ((Annual demand X unit price))  ABC Analysis • (Always Better Control) • CRITICALITY (Vital, Essential, Desirable)  VED Analysis • USAGE FREQUENCY  FSN Analysis • (Fast moving, Slow moving, Non moving) Based on product characteristics, suitable policies can be chosen USAGE FREQUENCY

module 9:Tactical Decisions and Review Back to main indexexitback to module contents 100 90 75 Percent of average inventory investment C 50 B 25 A 10 25 50 75 100 Percent of number of inventory items ABC ANALYSIS 5-10% items account for about 75% value 15-20% items account for about 15% value Balance items account for about 10% value (or A class ≥ 6 items average annual usage C class ≤ 0.5 items average annual usage B in between) Where, Average Annual usage=

Total cost Annual cost inventory carriage Q* = time ordering Q* OBJECTIVE OF ABC ANALYSIS: Rationalization of Ordering Policies EQUAL TREATMENT TO ALL The optimum no of orders can be arrived at by using models of inventory control eg. EOQ

module 9:Tactical Decisions and Review Back to main indexexitback to module contents Prob. of stockout kL + kL xL xL Total demand in lead time DETERMINATION OF REORDER POINT Reorder point = Max. reasonable demand during lead time = expected demand during lead time + safety stock (usually pre specified by management) K= 0; risk of shortage = 50% service level = 50% K= 0; risk of shortage = 15.87% service level = 84.13% K= 0; risk of shortage = 2.28% service level = 97.72% K= 0; risk of shortage = 0.13% service level = 99.87% Higher safety stock • A class items have relatively low service levels (0.8 or so) • Lower safety stocks • Tighter control & efficient expediting • B class items handled routinely with service levels of 0.95 or so • C class items should be present in ample supply, minimum records, controls, procedure very high service levels (0.95 to 0.98)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents (min) % risk Of shortage (max)  VED ABC POLICY IMPLICATIONS OF SELECTIVE INVENTORY CONTROL ABC analysis A class items need continuous rigourous control (use of mathematical models justified) B class items – relaxed control (periodic review) C class items – simple rules of thumb V class items call for a high level of service E class items call for medium level of service D class items call for tolerable level of service jointly determine service levels VED analysis FSN analysis Fast  most inventory models apply to this class Slow ( spare parts etc) Non – moving (dead stock) (optimal stock disposal rules)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents A SAMPLE SET OF SERVICE LEVELS FOR DIFFERENT CATEGORIES OF ITEMS High cost of stockout decreasing decreasing Low cost of stockout decreasing decreasing

module 9:Tactical Decisions and Review Back to main indexexitback to module contents OBJECTIVE OF INVENTORY MANAGEMENT SYSTEM An inventory system consists of a set of rules and procedures that allow for routine decisions on when & how much to order of each item needed in the manufacturing or procurement process, which call attention to the non-routine situations, the rules do not cover & which provide managers with the necessary information to make these decisions effectively. 1 2 3 The objective of a well designed procedure should be the minimization of the costs incurred in the inventory system, attaining at the same time the customer service level specified by the company policies.

module 9:Tactical Decisions and Review Back to main indexexitback to module contents STRUCTURE OF A TYPICAL COMPUTERISED INVENTORY MANAGEMENT SYSTEM • Basic sub systems or modules:- • Transactions and file maintenance module • Decision rules module • System integrative module • System-management interaction and evaluation module

module 9:Tactical Decisions and Review Back to main indexexitback to module contents TRANSACTIONS AND FILE MAINTENANCE MODULE • Book keeping of inventory control – • Entry, auditing, control and processing of inventory transactions • NECESSITY: Continuous updating to provide accurate information on • Available stock (on hand and on order) • Customer order status • Cost of items • Delivery lead times • Source of acquisition • Ordering restrictions • … DEVELOPMENT: mainly the area of data processing.

module 9:Tactical Decisions and Review Back to main indexexitback to module contents ITEM EOQ, q* = THE DECISION RULES MODULE This is concerned with the fundamental components of inventory planning and control procedures aimed at answering when and how much to order of each item to maintain inventories at the right level. A forward looking system should include forecasting capabilities safety stocks (to account for unavoidable in accuracies) decision rules are needed to guarantee some desired level of customer service. A-class C-class B-class Use EOQ and continuous monitoring Order in lots of 3 months demand if stock at hand is less than ROP Order in lots of 6 months demand if stock on hand is less than ROP

module 9:Tactical Decisions and Review Back to main indexexitback to module contents SYSTEM INTEGRATIVE MODULE Decision rules Distinct inventory policies The various items being controlled, depending on their inherent characteristics require specific degree of management attention and service levels that can be achieved by using some appropriate stock policy

module 9:Tactical Decisions and Review Back to main indexexitback to module contents SYSTEM MANAGEMENT INTERACTION AND EVALUATION MODULE • Intended to provide management with such information as to permit evaluation • Evaluation of operating performance • Identify problem areas • Allow for management selection of policy variables (system parameters)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents SUMMARY & CONCLUSIONS • Omnipresence of inventories (‘necessary evil’) • Nature of inventory related costs • Principles of selective inventory management • ABC analysis • VED analysis • FSN analysis • Ordering rules and reorder point determination • Policy implications of selective inventory management • Features of a computerized inventory management system • Relevance ? – independent vs. dependent demand systems • MRP vs. conventional inventory management

module 9:Tactical Decisions and Review Back to main indexexitback to module contents 2. Inventory Modelling

module 9:Tactical Decisions and Review Back to main indexexitback to module contents I PURCHASE Inv. Order qty., q Reorder point NO BACKLOGGING Lead time LOT SIZING • When to order ? • How much to order ? • Decision variables are • Order quantity, q per lot • Maximum backorder level, b (in class III, IV)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents II PRODUCTION Inv. q LOT SIZING • When to order ? • How much to order ? • Decision variables are • Order quantity, q per lot • Maximum backorder level, b (in class III, IV)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents III Inv. q BACKLOGGING b LOT SIZING • When to order ? • How much to order ? • Decision variables are • Order quantity, q per lot • Maximum backorder level, b (in class III, IV)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents IV Inv. b LOT SIZING • When to order ? • How much to order ? • Decision variables are • Order quantity, q per lot • Maximum backorder level, b (in class III, IV)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents • (1) Identify the cost components in each cycle (of length t) • (2) Express costs in terms of decisions variables • (order qty, q and backorder level, b) • (3) Develop annual cost by multiplying (1) by number of cycles/year • (4) Optimize to find q*, b* • Carrying cost • Shortage cost • Set up or order cost ANALYSIS BROAD APPRAOCH

module 9:Tactical Decisions and Review Back to main indexexitback to module contents WITHOUT BACKLOGGING VARIATIONS IN THE LOT-SIZE FORMULE C = unit cost (Rs/piece) C1 = i X C = carrying cost (Rs/unit/time) C2 = shortage/backlogging cost (Rs/unit/time) C3 = order cost (Rs/order)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents VARIATIONS IN THE LOT-SIZE FORMULE C = unit cost (Rs/piece) C1 = i X C = carrying cost (Rs/unit/time) C2 = shortage/backlogging cost (Rs/unit/time) C3 = order cost (Rs/order)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents VARIATIONS IN THE LOT-SIZE FORMULE WITH BACKLOGGING b C = unit cost (Rs/piece) C1 = i X C = carrying cost (Rs/unit/time) C2 = shortage/backlogging cost (Rs/unit/time) C3 = order cost (Rs/order)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents b VARIATIONS IN THE LOT-SIZE FORMULE C = unit cost (Rs/piece) C1 = i X C = carrying cost (Rs/unit/time) C2 = shortage/backlogging cost (Rs/unit/time) C3 = order cost (Rs/order)

module 9:Tactical Decisions and Review Back to main indexexitback to module contents ASSUMPTIONS in CLASSICAL LOT-SIZE SYSTEM • Demand fixed at constant rate of d units/unit time • Replenishments made when inventory reaches zero level so that no shortages occur. • Fixed lot size q. • Infinite replenishment rate • Lead time is known • The unit carrying cost, c, is constant Rs/unit/unit time. • The replenishment cost, C3 is constant Rs/Order.

module 9:Tactical Decisions and Review Back to main indexexitback to module contents LOT SIZE q SENSITIVITY STUDIES ON CLASSICAL LOT-SIZE MODEL Avg. Inventory = q/2 Total cost TC Carrying cost TCmin Inv. Level ANNUAL COSTS q Order cost q* q1 q2 Sensitivity Q = bq*, b > 0

module 9:Tactical Decisions and Review Back to main indexexitback to module contents EOQ WITH QUANTITY DISCOUNTS Total annual cost = Annual usage Example Annual demand = 5000 parts Order cost = Rs 49 Inventory carrying cost = Re 1 per part/year Discount schedule

module 9:Tactical Decisions and Review Back to main indexexitback to module contents TAC(Rs 5) TAC(Rs 4.85) TAC(Rs 4.75) 25,700 25,098 24,995 ANNUAL COSTS 700 1000 2500 q TOTAL ANNUAL COSTS for THREE ORDERING POLICIES OPERATING AT A LOT-SIZE of 1000 rather than EOQ of 700 is WARRANTED HERE

module 9:Tactical Decisions and Review Back to main indexexitback to module contents 100 and over Re 1 ANNUAL COSTS q EOQ=79 100 112 AN EXAMPLE ILLUSTRATING SHIFT OF EOQs D = 250/yr C3 = Rs 5/order i = 20% IN THIS CASE A LOT SIZE OF 112 RESULTS IN MINIMUM COST

module 9:Tactical Decisions and Review Back to main indexexitback to module contents Imax Rate of rise p-d Rate of fall, d 0 t1 t2 t4 t3 -b tp t DETERMINISTIC SINGLE ITEM MODEL NOTATION d = demand rate (units per unit time) P = production rate (unit per unit time) Q = order/production quantity T = cycle length B = maximum backorder level permitted Imax = maximum on-hand inventory level C = unit item cost C1 = inventory carrying cost in Rs/unit/unit time = iC C2 = shortage cost in Rs/unit/unit time (back logged demand) C2 = shortage cost/unit short independent of time (lost sales) C3 = set up cost per order/batch

module 9:Tactical Decisions and Review Back to main indexexitback to module contents Cycle time t = q/d Time to produce a lot, tp = q/p max. inventory, Imax = t1 = time for backorder b to be cleared once production starts t2 = time for inventory level to build up from zero to Imax t3 = time for inventory level to drop to zero from Imax at constant demand, d t4 = time for backlog b to buildup at a demand rate, d

module 9:Tactical Decisions and Review Back to main indexexitback to module contents t1 t2 t4 t3 COSTS/CYCLE During (t2 + t3) there is inventory and carrying costs = ½ Imax (t2 + t3) c1 During ( t1 + t4) there is shortage cost = ½ b (t1 + t4) C2 + C’2 b Ordering / replenishment cost per cycle = C3 Notice that

module 9:Tactical Decisions and Review Back to main indexexitback to module contents K (b, q) = K (b, q) = AVERAGE ANNUAL COSTS K (q, b) Substituting for t, (t1 + t4), (t2 + t3) & Imax in terms of q, b we obtain

module 9:Tactical Decisions and Review Back to main indexexitback to module contents and OPTIMAL RESULTS Annual cost is K (b, q) The solution of these simultaneous equations yields the optimum values q* and b* as follows:

module 9:Tactical Decisions and Review Back to main indexexitback to module contents FAST vs SLOW MOVING ITEMS • Slow moving items • Low level of demand • Frequent periods of no usage Thresholds difficult to define [ depend on item nature] • Likely to be between 50-100 units/yr Peterson & Silver (1979) recommend classifying items according to demand over the replenishment lead time: An expected lead time demand of 10 units or larger puts the item in the fast mover’s class, while an expected lead time demand of less than 10 units defines a slow mover

module 9:Tactical Decisions and Review Back to main indexexitback to module contents Amt. of inventory on hand Amt. used during Lead time Q Reorder level, R U1 U3 U2 Order qty, Q Q Avg. lead time usage (U) LT1 LT3 Safety stock (s s) LT2 Time Amt. of inventory on hand Amt. of inventory on hand Amt. of inventory on hand Amt. of inventory on hand Amt. of inventory on hand Amt. of inventory on hand CONTINUOUS (PERPETUAL) REVIEW SYSTEM WITH REPLENISHMENT ORDER QTY. Q AND REORDER LEVEL R

module 9:Tactical Decisions and Review Back to main indexexitback to module contents Z COMPUTATIONS FOR R U = Lead time demand LT = Lead time (working days) D = daily demand Probability of stockout • Z is obtained from the NORMAL TABLES based on • A pre specified stockout probability, P • Optimal stockout frequency based on costs of shortage and carrying inventory either or

module 9:Tactical Decisions and Review Back to main indexexitback to module contents EXAMPLE (p305, ch. 10) Per unit holding cost = Re 1/yr Ordering policy : 4 times a yr Pre specified service level : 1 stockout/3 yrs SQ/yr = 0.33 LEAD Times from SUPPLIER Month/ day

module 9:Tactical Decisions and Review Back to main indexexitback to module contents LT = 7 + 12 +25 + 16 + 14 + 15 = 14.83 days 6 Var (LT) = (7 – 14.83)2 + (12 – 14.83)2 + … = 34.97 (day)2 6 -1 d = 40 units/day Var (d) = 30 (units/day)2 EXAMPLE (p305, ch. 10) (contd.) Similar data on demands for last six months yield

module 9:Tactical Decisions and Review Back to main indexexitback to module contents Units demanded per lead time Z EXAMPLE (contd.) Units per lead time Desired SO/yr = 0.33 (as stated earlier) Order cycles/yr = 4 (given) = n P = desired probability of stockout per order cycle 0.083 From tables Z = 1.39 SS = 1.39 (237.5) = 330.1 R = 593.3 + 330.1 = 923.4

If var (LT) = 0 Then var (U) = 30 X 14.83 = 444.9 u = 444.9 = 21.09 units per lead time (compared to the original 237.5) module 9:Tactical Decisions and Review Back to main indexexitback to module contents IMPROVING RELIABILITY OF LEAD TIME Safety stock = 1.39 (21.09) = 29 ( compared to 330 earlier) R = 622 (compared to 923 earlier) • Inventory lowered by 301 units • Annul savings = Rs 1 X 301 = Rs 301 Thus it is worthwhile to improve reliability of lead time

module 9:Tactical Decisions and Review Back to main indexexitback to module contents  optimal SO/yr = 1/10 = 0.10 P* = SO/yr = 0.01 = 0.025 n 4 OPTIMAL STOCKOUT FREQUENCY AND IMPLIED BACKORDER COSTS Cost of shortage X Optimal SO/yr = Inventory carrying cost Shortage cost = Rs 10 Z = 1.96 (from normal tables)  R* = 593.3 + 1.96(237.5) = 593.3 + 465.5 = 1058.8 For R = 926 SO/yr = C1/shortage cost 0.33 = 1/shortage cost CB = 1/0.33 = Rs 3 (implied shortage cost)

Project and Production Management