A Logistic Management System Integrating Inventory Management and Routing

Transcription

1 A Logistic Management System Integrating Inventory Management and Routing Ana Luísa Custódio* Dept. Mathematics FCT UNL Rui Carvalho Oliveira** CESUR/Dept. Civil Engineering IST UTL July 22

2 Outline 1. Framing 2. The Case Study (Vagelpam) 3. Daily Demand 4. The Basic Model (Phase I) 5. Results (Phase I) 6. Sporadic Demand (Phase II) 7. Safety Stocks 8. Feasibility Analysis of the Solution 9. Conclusions

3 1. Framing Classical Approaches Routing Optimization of frequency and replenishment quantities Integrated approach of inventory management and routing Inventory Routing Problem (IRP) Strategical problem not daily management problem

4 2.1. The Case Study (Vagelpam) Nestlé s frozen products 151 products 321 delivery points 3937 items Distribution made from a central depot located near Lisbon delivery points located south of Coimbra Capacity (pallets) Fleet Number of vehicles

5 2.2. The Case Study (Vagelpam) Delivery Point Order Note Nestlé Delivery Stock Vagelpam Replenishment Order Note Emergency Order Order Note Order s Database

6 2.3. The Case Study (Vagelpam) Cost Structure variable transportation cost delivery fixed cost inventory holding cost order fixed cost Distance Matrix use of VisualRoute Journey Duration- maximum of 13 hours Times involved: transportation time average traveling speed of 7km/h waiting time for delivery delivery time related to quantity

7 2.4. The Case Study (Vagelpam) Orders % 9% 8% 7% 6% 5% 4% 3% 2% 1% % % 9% 8% 7% 6% 5% 4% 3% 2% 1% % % 8% 6% 4% 2% % Number of delivery points by product More More Number of products ordered by delivery point Number of orders by item Quantity Fre que ncy Order quantity (boxes) by product 142 More 1% 9% 8% 7% 6% 5% 4% 3% 2% 1% % More Order quantity (boxes) by delivery point 1% 9% 8% 7% 6% 5% 4% 3% 2% 1% % Order quantity (boxes) by item 1% 9% 8% 7% 6% 5% 4% 3% 2% 1% %

8 2.5. The Case Study (Vagelpam) Pareto Analysis on Quantity 7% 2% 1% Result Excluding 7% of items (2761 items) Representing 5% of total quantity ordered Daily Demand 25% of items with 5 or less records Power Law for % 9% 8% 7% 6% 5% 4% 3% 2% 1% % 5 Variance Estimation Number of records/item

9 3.1. Daily Demand Power Law for 2 σ = Cµ Variance Estimation P Scatterplot (NEW.STA 4v*662c) y=-,133+2,165*x+eps ( σ ) = D + P ( ) log 2 with D = log ( C) log µ, LOGVAR LOGMED 4 Normal Probability Plot of Residuals 3 Expected Normal Value Residuals Residuals Analysis R² adjusted =,947 F(1,66)=11813, p<. Estimate t(66) p-level D -,133-4,535, P 2,165 18,687,

10 3.2. Daily Demand Variable VAR1 ; distribution: Lognormal Kolmogorov-Smirnov d =,84971, p = n.s. Chi-Square:, , df = 2, p =, (df adjusted) No of obs Expected Lognormal Distribution Category (upper limits) Variable VAR1 ; distribution: Normal K-S d =,24333, p = n.s. Lilliefors p <,15 Chi-Square: 22,43448, df = 2, p =, (df adjusted) Sum of 4 lognormals No of obs Expected Category (upper limits)

11 4.1. The Basic Model (Phase I) Multiples Power of Two Policies T = T B 2 j, j {,1, 2, 3,... } T 2 f f 2 ( T ) * ( T ) * T, 2 2T * 1.6 T 2 optimal replenishment period of a multiple power of two

12 4.2. The Basic Model (Phase I) Viswanathan and Mathur s heuristic (1997) items allocated to clusters different clusters replenished by distinct vehicles allocation based on minimal replenishment period EOQ formulae power of two policies Vehicles capacities cyclic; decreasing order TSP s resolution: nearest neighbor minimal cost insertion 2-optimal procedure

13 4.3. The Basic Model (Phase I) begin create a new empty cluster for all the items not yet allocated to clusters do compute fixed replenishment cost of the item in an empty cluster for all the clusters with sufficient vehicle capacity and available journey duration compute fixed joint replenishment cost of the item in that cluster choose the minimum fixed cost choose the minimum T 2 compute T 2 create new route in the cluster and allocate the item to the route and to the cluster Yes Is T2 of the new route > T2 of the last route in the cluster? No merge routes compute replenishment time for the new route No verify vehicle capacity and journey duration Yes Are all the items allocated? Yes end Is vehicle capacity or journey duration exceeded? Yes No reduce replenishment time of the route Is there an empty cluster? No create a new empty cluster

14 5.1. Results (Phase I) 89 clusters (75 seconds) % 8% 6% 4% 2% % % 9% 8% 7% 6% 5% 4% 3% 2% 1% %,1,2,9 More More,3,4,5,6,7,8 Vehicle Occupation Rates Journey Duration (hours) Average vehicle occupation rate = 89% Journey duration (including traveling, unloading and waiting times) Average = 8.21 h Maximum = 13.1 h

15 5.2. Results (Phase I) Vehicles maximum of 2 routes (87% only one) average daily demand is a key factor for route construction geographical proximity between localities belonging to the same cluster More Number of Localities 1% 8% 6% 4% 2% % More Number of Delivery Points 1% 8% 6% 4% 2% % low number of visited localities 9% visit up to two localities low number of delivery points 8% supply one or two delivery points

16 5.3. Results (Phase I) Vehicles % 8% 6% 4% 2% % number of products replenished variable 58% up to 1 products 92% up to 3 products More Number of Products

17 6.1. Sporadic Demand (Phase II) represents only 5% of total quantity ordered sufficient available capacity to allocate the overall quantities to be delivered Use of several heuristics starting with items with: the highest daily demand the lowest daily demand choosing from within the routes, that serve the corresponding locality, the one with: the highest available capacity the lowest requirement the highest ratio available capacity/lowest requirement

18 6.2. Sporadic Demand (Phase II) Best results Highest daily demand/ Lowest requirement Only 38% of the remainder quantity allocated Not allowed: route expansion order splitting among routes Daily operations management problem

19 7. Safety Stocks ( Final Stock < ) = P( Q + R < ).1 P T < - safety stock R T - demand during replenishment cycle R T = R i i= 1 Normal or Lognormal T 7 1% Safety Stocks (boxes) More 8% 6% 4% 2% % 62% less then 1 boxes Future Work: Dimensioning of the safety stocks intern to model

20 8. Feasibility Analysis of the Solution Capacity (pallets) Heuristic Number of vehicles needed Total= 89 Capacity (pallets) Fleet Number of vehicles needed Total= 7 1 vehicle with routes every 2 k days 2 j-k pseudo-vehicles with routes every 2 j days (j k)

21 9. Conclusions Feasible solution in an acceptable computational time Key-factors for route construction: geographical proximity daily demand Vehicles with: high occupation rates small number of distinct routes visiting small number of different localities and delivery points replenishing a high number of distinct products