1 Introduction to Industrial Engineering (II) Z. Max Shen Dept. of Industrial Engineering and Operations Research University of California

2 IE and Systems Industrial engineering really takes a system-level perspective The tools and techniques of the IE allow the IE to examine the system, the interactions among the components of the system, all while keeping in mind the objective or purpose of the system An IE seeks to optimize systems

3 Supply Chain Structure

4 Example: Military Supply Chain Army Lt. Gen. Ricardo Sanchez, the senior U.S. military commander in Iraq from June 2003 until the summer of 2004, complained last winter to the Pentagon that a poor supply situation was threatening the Army's ability to fight. “The lack of key spare parts for tanks, helicopters and other systems was such a severe problem that I cannot continue to support sustained combat operations with rates this low”. It is reported that U.S. Army combat units fighting in Iraq last year had to resort to capturing key supplies such as lubricants and explosives from enemy stockpiles. In addition, food supplies barely met demand, and stocks of ammunition and spare parts were nearly depleted during combat.

5 Example: TSP Given a set of n nodes and distances for each pair of nodes, find a roundtrip of minimal total length visiting each node exactly once.

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8 Facilities Concerns How many? Where to locate? How to assign customers to facilities?

9 Example Ambulance location  A number of facilities for ambulances should be located in various places of a city.  Driving time/distance is a critical factor in rescues, and should be minimized.

10 Absolute 1-Center problem on a tree A BC G E F D H

Step 1: Pick any point on the tree and find the vertex that is farthest away from the point that was picked. Call this vertex e 1. A BC G E F D H e1e1

12 A BC G E F D H Step 2: Find the vertex that is farthest from e 1 and call this vertex e 2. e2e2 e1e1

13 A BC G E F D H Step 3: The absolute 1-center is at the midpoint of the path from e 1 to e 2. The vertex 1-center is at the vertex of the tree that is closest to the absolute 1-center. e1e1 e2e2

14 Step 1: Using the algorithm for the absolute 1-center, find the absolute 1- center. Absolute 2-Centers A BC G E F D H e1e1 e2e2

15 Step 2: Delete from the tree the arc containing the absolute 1-center.(If the absolute 1-center is on a node, delete one of the arcs incident on the center which is on the path from e1 to e2.) This divides the tree into two disconnected subtrees. A BC G E F D H e1e1 e2e2

16 Step 3: Use the absolute 1-center algorithm to find the absolute 1-center of each of the subtrees. These locations constitute a solution to the absolute 2-center problem. A BC G E F D H e1e X1*X1* X2*X2*

17 Median Problem Find the location of P facilities on a network so that the total cost of serving demands is minimized. Inputs:  h i : demand at node i  d ij : distance between demand node i and candidate site j

18 1-median problem on a tree If half or more of the total demand is at any node then one optimal solution consists of locating the facility at that node.

19 A B CE D h A =10 h B =5 h C =7 h E =14 h D = Example (P=1): 1-median problem on a tree

20 Example (cont’d) We start with node A Fold the demand onto the node that is incident to node A (B) Delete node A B CE D h C =7 h D= 12 h E =14 h B=15 Figure 2 Effect of folding tip node A onto B

21 Example (cont’d) In Figure 2 none of the nodes has more than half of the total demand. Select a tip node Fold it onto the node which is incident. B CE 7 10 h C =19 h E =14 h B=15 Figure 3

22 Example (cont’d) In Figure 3 none of the nodes has more than half of the total demand. Select a tip node Fold it onto the node which is incident. BC 7 h B =15 h C =33 Now the demand at node C is over half of the total demand. Optimal location for the 1-median on the tree is node C d AC *h A +d BC *h B +d EC *h E +d DC *h D = 15*10+7*5+10*14+5*12 = 385 Figure 4

23 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.

24 A Typical Network Design 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

25 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.

26 Solution Techniques Mathematical optimization techniques:  Exact algorithms: find optimal solutions  Heuristics: find “good” solutions, not necessarily optimal Simulation models: provide a mechanism to evaluate specified design alternatives created by the designer.

27 Heuristics and the Need for Exact Algorithms Single product Two plants p1 and p2  Plant p1 has an annual capacity of 200,000 units.  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.

28 Heuristics and the Need for Exact Algorithms

29 Why Optimization Matters? D = 50,000 D = 100,000 D = 50,000 Cap = 60,000 Cap = 200,000 $4 $5 $2 $3 $4 $5 $2 $1 $2 Production costs are the same, warehousing costs are the same $0