The Logistic Network: Design and Planning Chap 02 王仁宏 助理教授 國立中正大學企業管理學系 ©Copyright 2001 製商整合科技中心

Case: The Big Corporation (1/3) A soft drinks company 2 plants in Atlanta and Denver 3 warehouses in Chicago, Dallas, and Sacramento 120,000 accounts (retailers or stores) Value of each SKU is $1,000 for all products

Case: The Big Corporation (2/3) Redesign the logistics network: –about 10,000 accounts should received deliveries directly from the plants –group the accounts into 250 zones –group the different products into 5 families –delivery time should be no more than 48 hours, i.e., the distance within 900 miles –expand old plants instead of building a new one

Case: The Big Corporation (3/3) Questions: –How many distribution centers should be established? –Where should they be located? –How should the plants’ output of each product be allocated between warehouse? –Should production capacity be expand? When and where?

Lecture Outline 1) The Logistics Network 2) Warehouse Location Models 3) Solution Techniques

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.

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

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 space for products in each warehouses 6. Allocation of customers to each warehouse

Network Design The objective is to balance service level subject to: Production/ purchasing costs Inventory holding costs Facility costs (storage, handling and fixed costs) Transportation costs (different transportation mode) 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.

The More Warehouse, the more... Improvement in service level inventory costs due to increased safety stock overhead and setup costs reduction in outbound transportation costs (from warehouses to customers) inbound transportation costs (from plants to warehouses)

Data Collection 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

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)

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.

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.

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

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.

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

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 The variability faced by the aggregated customer is smaller than the combined variabilities faced by the two existing customers

Recommended Approach Aggregate demand points for 150 to 200 zones. Make sure each zone has an equal amount of total demand Place the aggregated point at the center of the zone Aggregate the product into 20 to 50 product groups In this case, the error is typically no more than 1%

Transport Rate Estimation 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. Huge number of rates representing all combinations of product flow

UPS 2 Day Rates for 150 lb.

Mileage Estimation Street Network Straight line distances Geographic Information Systems (GIS)

Mileage Estimations Straight line distances: Example: Suppose we want to estimate the distance between two points a and b where Lon a and Lat a are the longitude and latitude of the point a and similarly for b. Then where D ab is the straight line distance (miles) from a to b.

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 D ab by a scale factor, . Typically  =1.3 for metropolitan areas,  =1.14 for continental Unite States

Warehouse Costs Fixed costs: proportional to the warehouse capacity in a nonlinear way Handling costs: labor costs, utility costs, proportional to annual flow through the warehouse Storage costs: proportional to the average inventory level Inventory turnover ratio annual sales (flow) = average inventory level

Warehouse Capacity The requires storage space is approximately twice of the average inventory level. Also require empty space for access and handling: aisles, picking, sorting, AGV,… Multiply requires storage space by a factor (>1), a practical one is “3”.

Potential Warehouse Location 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.

Service Level Requirement Two types: –delivery time –specifying a maximum distance between customers and warehouse

A Typical Network Design Model (1/2) 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.

A Typical Network Design Model (2/2) 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

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 warehouses located –the number of potential locations for warehouses,

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.

Example 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.

Example 2.4.1

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   *   = 1,120,000. 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. The Heuristics Approach

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

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)  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) = x(w1,c2) + x(w2,c2) = x(w1,c3) + x(w2,c3) = all flows greater than or equal to zero.

The Optimal Strategy

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

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

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.

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.

Key Features of a Network Configuration DSS Customer-specific service level requirements existing warehouses expansion of existing warehouses specific flow patterns warehouse-to-warehouse flow Bill-of-Material effectiveness (robustness) reasonable running time

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

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

Yellow Freight (LTL) Rates for Shipping 4000 lb.