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**SALES AND LOGISTICS MANAGEMENT**

Winter 2000 Prof. Dr. Füsun Ülengin

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**Supply Chain Management and Analysis**

What is Supply Chain Management (SCM)? What is the difference (if any) between SCM and Business Logistics Management? Supply Chain Definition (G.C. Stevens, 1989): “. . . a connected series of activities which is concerned with planning, coordinating and controlling materials, parts, and finished goods from supplier to customer. It is concerned with two distinct flows (material and information) through the organization.” The Basic Problem: Get the right amounts of the right products to the right markets at the right time in the most economical way.

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**The Supply-Chain Materiall Flow Credit Flow Supplier Manufacturing**

VISA Materiall Flow Credit Flow Supplier Manufacturing Retailer Consumer Supplier Wholesaler Retailer Order Cash Schedules Flow Flow 9

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**The Supply Chain Customer Supplier Manufacturer Distributor**

Inventory Distributor Manufacturer Customer Market research data scheduling information Engineering and design data Order flow and cash flow Ideas and design to satisfy end customer Material flow Credit flow 10

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**Key Supply Chain Activities**

Customer Service Standards Cooperate with marketing to: Determine customer needs and wants for logistics customer service Determine customer response to service Set customer service levels Transportation Mode and transport service selection Freight consolidation Carrier routing Vehicle scheduling Equipment selection Claims processing Rate auditing

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**Key Supply Chain Activities**

Inventory management Raw materials and finished goods stocking policies Short-term sales forecasting Product mix at stocking points Number, size, and location of stocking points Just-in-time, push, and pull strategies Information flows and order processing Sales order-inventory interface procedures Order information transmittal methods Ordering rules Cooperate with production/operations to Specify aggregate quantities Sequence and time production output

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**Supply Chain Support Activities**

Warehousing Space determination Stock layout and dock design Warehouse configuration Stock placement Materials handling Equipment selection Equipment replacement policies Order-picking procedures Stock storage and retrieval

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**Supply Chain Support Activities**

Purchasing Supply source selection Purchase timing Purchase quantities Protective package design for Handling Storage Protection from loss and damage Information maintenance Information collection, storage, and manipulation Data analysis Control procedures

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**Additional Factors to Consider**

Product design for manufacture and distribution, i.e., the constraints that product characteristics place on ease of manufacture and distribution. Product mix from a marketing standpoint, i.e., which products the chain will carry.

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**Evolution of Logistics**

Pre-1950 :Dormant years Development Years Shift in consumer attitude and demand pattern Cost pressure in industry Improvement in computer technology Experience of military logistics The Take-off Years Vital importance Costs Supply and Distribution Lines are Lengthening (Toyota example) Logistics is Important to Strategy(Benetton example) Customers Increasingly Want Quick Customized Response Logistics in Non-manufacturing Areas(Service industry,Military etc.)

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**Logistics Strategy and Planning**

Three objectives of logistics strategy: Cost reduction (variable costs) Capital reduction (investment, fixed costs) Service Improvement (may be at odds with the above two objectives). Primary Logistics Planning Areası: Short term(operational level) How to load trucks for delivery How much stock to allocate to each warehouse from a current production run Vehicle routing, vehichle scheduling example(dispatching the trucks: Sweep algorithm) Tactical level purchasing, production decisions, inventory policies, transportation strategies including the frequency with which the customers are visited Long term(Strategic level) Facility location Example(warehouse territory definition: landed cost method) Specification of the customer service standards

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**An Example to Operational Plan: TSP Formulation**

Minimize Subject to:

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**Coincident Origin and Destination: The TSP**

Often firms maintain one or more warehouses which stock goods and make periodic deliveries to customers. The firm maintains a fleet of vehicles at the warehouse and when customers require delivery the vehicle transports the goods to one or more customers and returns to the warehouse. If vehicle must travel to one customer and back, problem reduces to finding shortest path to the customer. If vehicle must deliver to two customers, then we only have two points to visit and the problem reduces to finding the shortest path to customer 1, finding the shortest path between customers 1 and 2, and then finding the shortest path between customer 2 and our depot (we assume that distances are symmetric).

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**Coincident Origin and Destination: The TSP**

If, however, the vehicle must deliver to more than two customers, we must decide the order in which we will visit those customers so as to minimize the total cost of making the delivery. We first suppose that any time that we make a delivery to customers we are able to make use of only a single vehicle, i.e., that vehicle capacity is not an issue. We need to dispatch a single vehicle from our depot to n - 1 customers, with the vehicle returning to the depot following delivery. This is the well-known Traveling Salesman Problem (TSP). The TSP has been well studied and solved for problem instances involving thousands of nodes. We can formulate the TSP as follows:

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TSP Formulation In the TSP formulation if we remove the third constraint we have the simple assignment problem, which can be easily solved. The addition of the third constraint set, commonly called subtour elimination constraints, makes this a very difficult problem to solve. The subtour elimination constraints state the following: take any strict subset U of the nodes in the network (where the depot and each customer represent a node) and let E(U) denote the set of all arcs with both ends touching nodes in the set U. If we sum over all of the arc flow variables corresponding to the arcs in E(U), their sum cannot exceed one less than the number of nodes in the set U (|U| denotes the number of nodes in the set U) or we have a subtour.

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**Questions about the TSP**

Given a problem with n nodes, how many distinct feasible tours exist? How many arcs will the network have? How many xij variables will we have? How could we quantify the number of subtour elimination constraints? The complexity of the TSP has led to heuristic or approximate methods for finding good feasible solutions. The simplest solution is that of the nearest neighbor. Begin at the depot and calculate the distance to each of the remaining n – 1 nodes. Select the closest node as the one you visit immediately after leaving the depot. Call this node 1. Next determine the distance from node 1 to each of the remaining n – 2 nodes, and visit the node that minimizes this distance immediately following your visit to node 1. Continue choosing the ‘nearest neighbor’ until the only remaining choice is to return to the depot.

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**Illustration of subtours**

6 City TSP Network Illustration of subtours

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TSP Heuristics The sweep heuristic will perform much better in the ‘worst case’ then the nearest neighbor. The sweep heuristic basically attempts to make an outer loop around the nodes. To implement the sweep heuristic we need to create a map of the nodes we will visit. Then draw a straight line emanating from the depot (the direction of the line is not important). Next visualize the line as sweeping either clockwise or counter-clockwise through a circle of radius r. Each time the radius line intersects a customer location make that customer the next customer on the route. If we have ties, implement a tie breaking rule, such as that of first visiting the customer that is closest to the previous customer on the route.

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**Illustration of VRP Depot 50 76 39 88 29 44 58 90 77 89 57 59 65 98**

(Outlier) Depot 50 76 39 112 88 29 123 44 58 90 77 89 57 115 124 59 176 65 98 125 Truck Capacity = 250 What is the minimum # of trucks we would need? Maximum?

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Sweep Heuristic (Outlier) Depot 50 76 39 112 88 29 123 44 58 90 77 89 57 115 124 59 176 65 98 125 Truck Capacity = 250 Min # Trucks = 7, Max = 9 (so far) Start Sweep

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**Single Depot, Multiple Destinations, Vehicle Capacities**

When the depot contains many vehicles and vehicle capacity constraints come into play, the problem becomes even more complex. If each customer has enough demand to receive a full truckload the problem is easy and we simply use the shortest path to get the single truck to each customer. Otherwise, we must decide which customers will receive deliveries from the same truck, and then decide how to route the trucks to the customers on the route. We will look at a mixed-integer programming formulation of the Vehicle Routing Problem (VRP).

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**The Vehicle Routing Problem (VRP)**

VRP generalizes the TSP since we have K capacity constrained (homogeneous) vehicles at a depot, each of which must visit a subset of the n - 1 customers once and return to the depot. No two vehicles may visit the same customer. This means that each vehicle must complete a Hamiltonian tour (a Hamiltonian tour is a feasible TSP solution). The objective is to determine the minimum travel cost required to serve all customers. Let A denote the set of pairs of cities, and let k index trucks, each with capacity u. Assume that customer i has demand equal to di. In this formulation we require two types of variables, one set that tells us if we use a link (xij, as before) and another set that assigns a truck to a link if we use the link . We formulate the VRP as follows (node 1 is the depot):

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**VRP Formulation Minimize Subject to: (i, j) A (V1)**

i = 2, .., n, (V2) j = 2, …, n, (V3) (V4) k = 1, …, K, (V5) subsets U of {2, 3, …, n}, (V6) xij {0, 1} (i, j) A, (i, j) A, k = 1, …, K.

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**VRP Formulation Comments**

TSP is a special case of the VRP where we have a single vehicle with infinite capacity (K = 1, u = ). Constraints (V1) force assigning a truck to link (i, j) if we use the link. (V2) and (V3) force entering and leaving each city (customer) exactly once. (V4) force entering and leaving the depot K times (once for each truck). (V5) ensure that the demand of customers assigned to truck k does not exceed the truck capacity. (V6) provide subtour elimination for any subtours not including the depot (note that the depot will be included in exactly K subtours in every feasible solution).

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**VRP Heuristic Principles**

1. Try to assign customers in close proximity to the same truck. 2. Assign customers in close proximity (not on the same truck) to the same delivery day (to better manage capacity usage). 3. Build routes beginning with the farthest delivery and cluster around this delivery first. 4. Routes should form a “teardrop” pattern (similar to sweep heuristic for TSP). 5. Allocate largest vehicles to routes before small vehicles. 6. Plan pickups during deliveries, not after all deliveries have been made. 7. Outliers are candidates for alternate means of transport. 8. Avoid time windows if possible.

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VRP Heuristics Given the difficulties in solving the TSP, we cannot expect to have great success solving large VRP problems without heuristic approaches. We use several guiding principles in developing these heuristics. Note that the above formulation does not consider additional practical restrictions such as limits on driver time, time window delivery restrictions, or return of goods from customers to the depot.

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**An Example To Strategic Plans: Warehouse Territory Definition**

Warehouse Warehouse cost Transportation Cost ($/ton) Fixed(($/ton) Variable($/ton.km) A B C D

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