Service levels, system cost and stability of production inventory control systems

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1 Service levels, system cost and stability of production inventory control systems Author:D.Bijulal,Jayendran Venkateswar and N.Hemachandra Reporter:Zhang Yiqing

2 Outline 2

3 1 Introduction uthe classical automatic pipeline variable inventory and order-based production control system has been modified to help achieve higher serviceslevels in the face of random demand(i.i.d.normal demand scenario). uthis article analyses the production-inventory system performance in terms of service level(i.e.order fill rate) and average system costs, under stable settings of the control parameters. uthe service level and average cost are affected by the control parameters as well as the smoothing factor in demand forecasting. uthis article puts forward five propositions which give light to general system performance based on the parameters selection. 3

4 1 Introduction Points of innovation : The classical APVIOBPCS model uses only the demand forecast (without any safety stock) to determine the target or desired inventory and desired WIP. The model has been modified by including a safety stock component in the determination of the desired inventory and WIP levels. 4

5 2 Basic Methodology & Control Policies Methodology:System dynamics(sd) Production-inventory control policies: APVIOBPCS Stability analysis methodology: z-transforms Production inventory control system model: The model has been assumed that the capacities of storage and processing stages are sufficiently large,so that non on-linear effects arise due to capacity saturation. In each period,the production system faces independent and identically 2 distributed(i.i.d.) random demand of the form N( µ D, σ D ). The customer demand which is not completely satisfied from the system stock in the current period are back ordered to be fulfilled in a future period. 5

6 2 Basic Methodology & Control Policies System model: 6

7 2 Basic Methodology & Control Policies Demand forecast: WIP adjustment: INV adjustment: Target stock modification: 7

8 2 Basic Methodology & Control Policies Setting of safety stock: The safety stock ssis treated as avariable, dependent on FD n The target stock or desired inventory becomes : Safety factor z has been fixed based on the service level requirements as Factor v is coefficient of variation of demand, i.e.ifdemand in each period ~N(100,1), v=

9 3 Stability Analysis System transfer function with L=3: 9

10 3 Stability Analysis The selection of parameters within the stable region makes the system stable against any change in the input. The output eventually convergesto a steady value with or without initial oscillations. Parameter selection on the boundary makes the system to continue sustained oscillations; while parameter selection outside the boundary causes the system variables to continue oscillations with exponentially increasing amplitude. 10

11 4 Expected System Performances Expected system performances: Proposition4.1: The average inventory in the system in the parameter setting α>β will be greater than the average inventory with parameter setting α<β. Proposition4.2: The average inventory is independent of the smoothing factor ρ in forecast. Proposition4.3: A smaller smoothing constant ρ can increase the overshoot, settling time and the amplitude of oscillations in the system response. Proposition4.4: Set the parameter such that α>β will increase the severity in system fluctuations while α<β will reduce the severity in system fluctuations. Proposition4.5: Smaller values of ρ reduce the magnitudes of error correction in the system and hence reduce variations in INV about its average value. 11

12 5 Simulation Experiments 12

13 5 Simulation Experiments 13

14 5 Simulation Experiments 14

15 6 Managerial insights and Conclusions ucontrol parameters election based on system stability alone will not ensure the desired service level. uthe general replenishment policy with α<1,and β<1,is better than the pure order-up-to replenishment policy, i.e α=β=1, to achieve the desired order fill rate. uα=β line forms an upper bound for the parameter setting to keep the average system cost at lower levels with ρ=1. 15

16 6 Managerial insights and Conclusions uthe average system inventory is a function of (α, β ) pairs while the average cost is a function α, β and ρ. uproper selection of (α, β ) pairs and ρ can offer lower cost as well as higher service levels. usafety stock for DOFR can offer a higher OFR. 16

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