The Logistic Network: Design and Planning ©Copyright 1999 D. Simchi-Levi, P. Kaminsky & E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Lecture Outline 1) The Logistics Network 2) Warehouse Location Models 3) Solution Techniques ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi The Logistics Network The Logistics Network consists of: Facilities: Vendors, Manufacturing Centers, Warehouse/ Distribution Centers, and Customers Raw materials and finished products that flow between the facilities. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Customers, demand centers sinks Field Warehouses: stocking points Sources: plants vendors ports Regional Warehouses: stocking points Supply Inventory & warehousing costs Production/ purchase costs Transportation costs Transportation costs Inventory & warehousing costs

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Network Design The Key Issues: 1. Number of warehouses 2. Location of each warehouse 3. Size of each warehouse 4. Allocation of products to the different warehouses 5. Allocation of customers to each warehouse ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Network Design The objective is to balance service level against Production/ purchasing costs Inventory carrying costs Facility costs (storage, handling and fixed costs) Transportation costs That is, we would like to find a minimal-annual-cost configuration of the distribution network that satisfies product demands at specified customer service levels. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Data for Network Design 1. A listing of all products 2. Location of customers, stocking points and sources 3. Demand for each product by customer location 4. Transportation rates 5. Warehousing costs 6. Shipment sizes by product 7. Order patterns by frequency, size, season, content 8. Order processing costs 9. Customer service goals ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Too Much Information Customers and Geocoding Sales data is typically collected on a by-customer basis Network planning is facilitated if sales data is in a geographic database rather than accounting database 1. Distances 2. Transportation costs New technology exists for Geocoding the data based on Geographic Information System (GIS) ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Aggregating Customers Customers located in close proximity are aggregated using a grid network or clustering techniques. All customers within a single cell or a single cluster are replaced by a single customer located at the centroid of the cell or cluster. We refer to a cell or a cluster as a customer zone. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Impact of Aggregating Customers The customer zone balances 1. Loss of accuracy due to over aggregation 2. Needless complexity What effects the efficiency of the aggregation? 1. The number of aggregated points, that is the number of different zones 2. The distribution of customers in each zone. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Why Aggregate? The cost of obtaining and processing data The form in which data is available The size of the resulting location model The accuracy of forecast demand ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Demand Forecast The three principles of all forecasting techniques: Forecasting is always wrong The longer the forecast horizon the worst is the forecast Aggregate forecasts are more accurate ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Recommended Approach Use at least 200-300 aggregated points Make sure each zone has an equal amount of total demand Place the aggregated point at the center of the zone In this case, the error is typically no more than 1% ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Product Grouping Companies may have hundreds to thousands of individual items in their production line 1. Variations in product models and style 2. Same products are packaged in many sizes Collecting all data and analyzing it is impractical for so many product groups ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Product Grouping In practice, items are aggregated into a reasonable number of product groups, based on 1. Distribution pattern 2. Product type 3. Shipment size 4. Transport class of merchandise It is common to use no more than 20 product groups. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Transport Rate Estimation Huge number of rates representing all combinations of product flow An important characteristic of a class of rates for truck, rail, UPS and other trucking companies is that the rates are quite linear with the distance. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi UPS 2 Day Rates for 150 lb. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi LTL Freight Rates Each shipment is given a class ranging from 500 to 50 The higher the class the greater the relative charge for transporting the commodity. A number of factors are involved in determining a product’s specific class. These include 1. Density 2. Ease or difficulty of handling 3. Liability for damage ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Basic Freight Rates With the commodity class and the source and destination Zip codes, the specific rate per hundred pound can be located. This can be done with the help of CZAR, Complete Zip Auditing and Rating, which is a rating engine produced by Southern Motor Carriers. Finally to determine the cost of moving commodity A from City B to City C, use the equation weight in cwt  rate ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Yellow Freight (LTL) Rates for Shipping 4000 lb. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Other Issues Mileage Estimation 1. Street Network 2. Straight line distances ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Mileage Estimations Straight line distances: Example: Suppose we want to estimate the distance between two points a and b where Lona and Lata are the longitude and latitude of the point a and similarly for b. Then where Dab is the straight line distance (miles) from a to b. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Mileage Estimations Straight line distances: The previous equation is accurate only for short distances; otherwise we use This is of course an underestimate of the road distance. To estimate the road distance we multiply Dab by a scale factor, . Typically =1.3. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Other Issues Future demand Facility costs 1. Fixed costs; not proportional to the amount of material the flows through the warehouse 2. Handling costs; labor costs, utility costs 3. Storage costs; proportional to the inventory level Facilities capacities ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Other Issues How to measure storage costs? Define Inventory turnover ratio = annual sales  = average inventory level In our case it is the ratio of the total flow through the warehouse to the average inventory level. If the ratio is  than the average inventory level is total flow over  ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Customers, demand centers sinks Field Warehouses: stocking points Sources: plants vendors ports Regional Warehouses: stocking points Supply Inventory & warehousing costs Production/ purchase costs Transportation costs Transportation costs Inventory & warehousing costs

The Impact of Increasing the Number of Warehouses Improve service level due to reduction of average service time to customers Increase inventory costs due to a larger safety stock Increase overhead and set-up costs Reduce transportation costs in a certain range Reduce outbound transportation costs Increase inbound transportation costs ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Warehouse Location Models When locating new facilities such as warehouses, a number of requirements have to be satisfied: 1. Geographical and infrastructure conditions 2. Natural resources and labor availability 3. Local industry and tax regulations 4. Public interest As a result, there is only a limited number of locations that would meet all the requirements. These are the potential location sites for the new facilities. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

A Typical Network Design Model Several products are produced at several plants. Each plant has a known production capacity. There is a known demand for each product at each customer zone. The demand is satisfied by shipping the products via regional distribution centers. There may be an upper bound on total throughput at each distribution center. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

A Typical Location Model There may be an upper bound on the distance between a distribution center and a market area served by it A set of potential location sites for the new facilities was identified Costs: Set-up costs Transportation cost is proportional to the distance Storage and handling costs Production/supply costs ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Complexity of Network Design Problems Location problems are, in general, very difficult problems. The complexity increases with the number of customers, the number of products, the number of potential locations for warehouses, and the number of warehouses located. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Solution Techniques Mathematical optimization techniques: 1. Exact algorithms: find optimal solutions 2. Heuristics: find “good” solutions, not necessarily optimal Simulation models: provide a mechanism to evaluate specified design alternatives created by the designer. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Heuristics and the Need for Exact Algorithms Single product Two plants p1 and p2 Plant p2 has an annual capacity of 60,000 units. The two plants have the same production costs. There are two warehouses w1 and w2 with identical warehouse handling costs. There are three markets areas c1,c2 and c3 with demands of 50,000, 100,000 and 50,000, respectively. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Heuristics and the Need for Exact Algorithms ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi The Heuristics Approach Heuristic 1: For each market we choose the cheapest warehouse to source demand. Thus, c1, c2 and c3 would be supplied by w2. Now for every warehouse choose the cheapest plant, i.e., get 60,000 units from p2 and the remaining 140,000 from p1. The total cost is: 250000 + 1100000 + 2*50000 + 260000 + 5140000 = 1,120,000. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi The Heuristics Approach Heuristic 2: For each market area, choose the warehouse such that the total costs to get delivery from the warehouse is the cheapest, that is, consider the source and the distribution. Thus, for market area c1, consider the paths p1w1c1, p1w2c1, p2 w1c1, p2w2c1. Of these the cheapest is p1w1c1 and so choose w1 for c1. Similarly, choose w2 for c2 and w2 for c3. The total cost for this strategy is 920,000. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

The Optimization Model The problem described earlier can be framed as the following linear programming problem. Let x(p1,w1), x(p1,w2), x(p2,w1) and x(p2,w2) be the flows from the plants to the warehouses. x(w1,c1), x(w1,c2), x(w1,c3) be the flows from the warehouse w1 to customer zones c1, c2 and c3. x(w2,c1), x(w2,c2), x(w2,c3) be the flows from warehouse w2 to customer zones c1, c2 and c3 ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi The problem we want to solve is: min 0x(p1,w1) + 5x(p1,w2) + 4x(p2,w1) + 2x(p2,w2) + 3x(w1,c1) + 4x(w1,c2) + 5x(w1,c3) + 2x(w2,c1) + 2x(w2,c3) subject to the following constraints: x(p2,w1) + x(p2,w2)  60000 x(p1,w1) + x(p2,w1) = x(w1,c1) + x(w1,c2) + x(w1,c3) x(p1,w2) + x(p2,w2) = x(w2,c1) + x(w2,c2) + x(w2,c3) x(w1,c1) + x(w2,c1) = 50000 x(w1,c2) + x(w2,c2) = 100000 x(w1,c3) + x(w2,c3) = 50000 all flows greater than or equal to zero. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi The Optimal Strategy ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Simulation Models and Optimization Techniques Optimization techniques deal with static models: 1. Deal with averages. 2. Does not take into account changes over time Simulation takes into account the dynamics of the system ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Optimization Techniques and Simulation Simulation models allow for a micro-level analysis: 1. Individual ordering pattern analysis 2. Transportation rates structure 3. Specific inventory policies 4. Inter-warehouse movement of inventory 5. Unlimited number of products, plants, warehouses and customers ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

Optimization Techniques vs. Simulation The main disadvantage of a simulation model is that it fails to support warehouse location decisions; only a limited number of alternatives are considered The nature of location decisions is that they are taken when only limited information is available on customers, demands, inventory policies, etc, thus preventing the use of micro level analysis. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi Recommended approach Use an optimization model first to solve the problem at the macro level, taking into account the most important cost components 1. Aggregate customers located in close proximity 2. Estimate total distance traveled by radial distance to the market area 3. Estimate inventory costs using the eoq model Use a simulation model to evaluate optimal solutions generated in the first phase. ©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi