1. arpan.math@gmail.com nitahshah@gmail.com
Tuesday, August 07, 2018
Optimal Cycle Time and Preservation Technology Investment for Deteriorating Items with Price-sensitive Stock-dependent Demand Under Inflation Nita H. Shah & Arpan D. Shah Department of Mathematics, Gujarat University, Ahmadabad – Gujarat, India
International conference, ScieTech 2014,Jakarta
International Conference,ScieTech 2014

2. OBJECTIVES Analysis of production lot size model
Tuesday, August 07, 2018
OBJECTIVES
Analysis of production lot size model
Imperfect quality production
Price-Sensitive stock-dependent demand
Effect of inflation is incorporated
Items are deteriorating in nature
Preservation technology investment is made
Random fraction of defective items
International conference, ScieTech 2014,Jakarta
International Conference,ScieTech 2014

3. OBJECTIVES Objective to maximize total profit Optimal order quantity
Optimal cycle time
Optimal preservation technology investment
Optimal order quantity
Optimal Selling price
Objective to maximize total profit
International conference, ScieTech 2014,Jakarta

4. Tuesday, August 07, 2018
ASSUMPTIONS
The inventory system involves a single deteriorating item over an infinite planning horizon.
Existence of deterioration items assumed with the initiation of production and the proportion reduced because of preservation technology are taken to be uniform.
There is no repair or replacement of deteriorating items during the period under consideration.
Shortages are not allowed.
International conference, ScieTech 2014,Jakarta
International Conference,ScieTech 2014

5. ASSUMPTIONS
Defective items are sold at a discounted rate after screening process.
Screening process ends at time which is pre-specified.
The demand rate,
is a non-negative power function of selling
price under inflation.
Replenishment occurs instantly and effect of inflation is incorporated.
International conference, ScieTech 2014,Jakarta

6. NOTATIONS A : Replenishment cost per order C : Purchase cost per unit
P : Selling price per unit (P>C) (a decision variable)
h : Unit inventory holding cost per unit time
T : Cycle length (a decision variable)
I(t): Inventory level at time t
Q : Order quantity per cycle ( a decision variable)
D(P,I(t)) : Demand rate
International conference, ScieTech 2014,Jakarta

7. NOTATIONS Cs : Screening cost per unit
Ps : Selling price of defective unit
θ : Deterioration rate (0 ≤ θ ≤ 1)
u: Preservation technology investment per unit to reduce deterioration rate ( a decision variable)
f(u) : Proportion reduced deterioration rate,
r : Discount rate representing the time value of money
k : Inflation rate per unit time
International conference, ScieTech 2014,Jakarta

8. NOTATIONS
η : Price elasticity Markup cost, η>1 R: Net inflation rate = (r-k) λ : Proportion decrease in selling price (defective items) ϵ : Proportion of defective items t1: ξ T where, 0< ξ < 1 Π (P,T,u): Profit function
International conference, ScieTech 2014,Jakarta

9. Total expected profit model
Mathematical model
Total expected profit model
International conference, ScieTech 2014,Jakarta

10. variations in P Sensitive positively : h,C,A,Cs
Sensitive negatively : α,m
International conference, ScieTech 2014,Jakarta

11. variations in Q Sensitive positively : α,m,A,ϵ,k
Sensitive negatively : h,c,Cs,r
International conference, ScieTech 2014,Jakarta

12. Variations in preservation technology investment
Sensitive positively : α,m,A,λ,θ,k
Sensitive negatively : h,ϵ,r
International conference, ScieTech 2014,Jakarta

13. Change in expected profit
Sensitive positively: α,ϵ,k
Sensitive negatively : θ,h,C,A,Cs,λ,r
International conference, ScieTech 2014,Jakarta

14. Deterioration rate vs preservation technology
. The trend suggests that higher investment is required for high deterioration of items in inventory system and investment is not required when the rate is marginal.
International conference, ScieTech 2014,Jakarta

15. Optimum value of profit with respect to T,P,u
Each of the figure shows optimum value of the respective parameters when it attains maximum profit.
International conference, ScieTech 2014,Jakarta

16. ANY QUESTIONS..?
International conference, ScieTech 2014,Jakarta

17. Thank you…
International conference, ScieTech 2014,Jakarta