University:
Massachusetts Institute of Technology
Course:
15.992 | S-Lab: Laboratory for Sustainable Business
Academic year:

2023
Views:

342

Pages:

35
Author:

dontbehatin077e

Forecasting and Inventory Management of Short Life-Cycle Products A. Kurawarwala and H. Matuso Presented by Guillaume Roels Operations Research Center Short Life-Cycles Causes { { Procurement Issues { { { Fast Changing Consumer Preferences Rapid Rate of Innovation Forecasting with no historical data Long lead-times Perishable Inventory Introduction Time Outline Forecasting new product introduction Procurement issues { { { Model Formulation Optimal Control Solution Discussion Case Study New Product Introduction No past sales data { Time-series useless But multiple-product environment { { Some level of predictability Independence (serve different needs) Diffusion Theory “[Innovation] is communicated through certain channels over time among members of a social system” Marketing application: { { Mass Media Word of Mouth The Bass Model Noncumulative adoption Internal Influence External Influence time The Bass Model: Assumptions Market potential remains consistent over time Independence of other innovations Product and Market characteristics do not influence diffusion patterns Competition? The Bass Model: Sales Evolution Current Sales Remaining market potential dN t Nt ⎞ ⎛ (m − N t ) α t = ⎜p+q ⎟ dt m ⎠ ⎝ Mass Media Word-of-Mouth Seasonality Coeff. Case-Study: PC Manufacturer Monopolist (strongly differentiated) Life-cycle: 1-2 years * Peak sales timing is predictable T { Typical seasonal variation in demand α t { Christmas peak End-of-quarter effect Information on total life-cycle sales m Numerical Example (M2) Time O ct Au g Ju n Ap r Fe b De c O ct Au g Ju n 800 700 600 500 400 300 200 100 0 Ap r. Sales (units) Sales Evolution of High-End Computers (M2) Parameters Estimation Estimation of p, q, m, α t Nonlinear Least Squares R-squared above .9 Numerical Example (M2) Bass Model (M2) 800 700 600 500 400 300 200 M2 sales Bass Model Oct Aug Jun Apr Feb Dec Oct Aug Jun Apr. 100 0 Outline Forecasting new product introduction Procurement issues { { { Model Formulation Optimal Control Solution Discussion Case Study Procurement Issues Need to place orders in advance { { Long lead-times Cost advantage, timely delivery Inventory/Backorder costs Schedule the procurement to meet the (random) demand, evolving according to Bass’ Model Model Description State: Cumulative Procurement Vt Control: Instantaneous Procurement Transition function Vt = ut V0 = 0 Finite-Horizon T Optimization Discounted cost at rate r Cost Parameters Instantaneous trade-off between { { Inventory holding costs h(Vt − N t ) + + p N − V ( ) Backorder costs t t Pt (Vt − N t ) Terminal trade-off between { { Salvage inventory loss l (VT − NT ) + + Shortage costs s ( NT − VT ) QT ( NT − VT ) Optimal Control Model T min J = ∫ e − rt ∫ Pt (Vt − N t )ψ ( N t )dN t dt + e − rT u 0 Nt ∫ Q (V T T − NT )ψ ( NT )dNT NT such that: Vt = ut and ut ≥ 0 Timely delivery of customer orders? What if we do not want to serve all the demand? Why no chance constraints instead? Hamiltonian function Define λt = ∇V J (t , Vt ) * * Hamiltonian H (V , u , λ ) = Pt (V , u ) + λu Pontryagin Minimum Principle 1. Adjoint Equation 2. Boundary Condition ∂H (Vt * , ut* , λt ) λt = − ∂Vt d λT = dVT 3. ⎡ ⎤ ⎢ ∫ QT ( NT − VT )ψ T ( NT )dNT ⎥ ⎢⎣ NT ⎥⎦ Optimality of Control ut* = arg min H (Vt * , u , λt ) u ≥0 Case I: b s ≤ b+h s+l Maintain the same service level b Ψ t (Vt ) = b+h Impulse at the end of horizon s Ψ T (VT ) = s+l Procurement Policy Cumulative units Cumulative Inventory Expected Cumulative Demand Time Case II: b s > b+h s+l ^ For 0 ≤ t ≤ t , keep the same service level ^ b Ψ t (Vt ) = b+h For t ≤ t ≤ T , { { Do not purchase anymore Decrease gradually the service level down to s s+l Desired/Effective Service Level In practice, backorder costs are hard to evaluate… b Instead, evaluate the desired SL b+h Terminal service level: switch the customers to an upgraded model { { Loss of goodwill Higher cost Case II is typical in practice { Terminal SL < Lifetime SL Procurement Policy Cumulative Inventory Cumulative units ^ V Phase-Out Period Expected Cumulative Demand ^ t Time Revised Multiple-Period Implementation Units Update the estimation of p, q, m Model Update Cumulative Procurement Expected Cumulative Demand Lead-time Time Time-varying costs Time-varying costs { { Decreasing purchase costs 30% in less than 6 months Underage Costs { { { Backorder penalty b Save the cost decrease ct Save from the cost of capital − rct Decreasing over time Hence, increasing service level Outline Forecasting new product introduction Procurement issues { { { Model Formulation Optimal Control Solution Discussion Case Study PC Manufacturer: New Product Introduction 1. 2. When should it be launched? May or August? How much and when should we order? Sensitivity Analysis on the Lifetime Service Level Parameters Estimation Randomness summarized in m, p, q Estimation of the size of the market m * Estimation of the peak time T { Relation between p and q Past Product Introductions (M1-M4) { { Estimation of the distribution of q Sensitivity Analysis on variance Demand Estimation (May) 700 600 500 400 Demand 300 200 100 M ar ch Se pt em be r N ov em be r Ja nu ar y Ju ly M ay 0 Service Levels Lifetime service level { 95% vs. 99%? Terminal service level: 33% Hence, Case II, i.e. { { Purchase period Phase-out period Procurement Decisions (May) 1000 900 800 700 600 500 400 300 200 100 0 Demand 95%Procurement 99%Procurement Ju Se ly pt em be r N ov em be r Ja nu ar y M ar ch Longer Phase-Out with low SL Reduce Procurement after peak season M ay Safety Stock Evolution 1200 1000 Demand 800 95%-Safety Stock 600 400 99%-Safety Stock 200 M ar ch 0 Ju Se ly pt em be N r ov em be r Ja nu ar y Deplete SS in the last quarter Avg SS=5 or 8 weeks of demand M ay Additional Insights Launching the product early requires less inventories With decreasing costs, { { Reduced service levels (but increasing over time); hence, less inventory Delayed procurement cutoff time Conclusions Application-driven research { { Adapt Bass’ Model Optimal Control Additional issues: { { { Effectiveness of Bass’ Model? Backorder costs vs. Service Level? Terminal shortage penalty vs. Stopping time?