Integrated Consolidation Facility Location and Inventory Routing for Supply Networks

1. Integrated Consolidation Facility Location and Inventory Routing for Supply Networks Ronald G. Askin ron.askin@asu.edu with thanks to Mingjun Xia School of Computing, Informatics, and Decision Systems Engineering Arizona State University

2. Overview • Introduction • Problem Definition and Background • Multi-Product Integrated Supply Chain Network Model • Multi-product FLP with Approximated IRC Function • Inventory Routing Problem • Integrated Problem’s Results and Analysis • Consolidation Facility Location & Demand Allocation • Global Sourcing Options for Multistage Production • Conclusion and Future Work

3. Who’s That Speaker? Ronald G. Askin, Director School of Computing, Informatics, and Decision Systems Engineering Arizona State University Tempe, AZ 85287-8809 USA Ron.askin@asu.edu

4. Arizona State University

5. The State of Arizona

6. Background and Activities • BS in IE, Lehigh University (in the time of punch cards) • MS OR and PhD in Industrial and Systems Engineering, Georgia Tech • Professor of Industrial Engineering • Fellow of Institute of Industrial Engineers (IIE) • Former IIE Board of Trustees Member • Former Chair of Council of Industrial Engineering Academic Dept Heads • Former President of INFORMS M&SOM Society • Editor-in-Chief IIE Transactions

7. IIE Transactions The flagship journal of the Institute of Industrial Engineers and hopefully your preferred choice for publication. http://www.tandfonline.com/toc/uiie20/current • Methodological focus in most papers • Real world applications/impact • Original, innovative contribution required • Novel problems and models encouraged

8. Logistics: Facility Layout to Supply Networks • Queuing Networks • Material Flow & Capacity Models • Facility Layout • Production Control Systems • Supply Chain Design • Batch Sizing/Lot Streaming

9. Introduction • Supply Chain Management (SCM) The goal: To deliver the right product to the right place at the right time for the right price, while minimizing system-wide costs and satisfying service requirements.

10. Supply Chain Management Decisions • Corporate objectives • Capacity / Facilities • Markets to operate • Location • Resources Strategic Level Long Term Facility Location Problem (FLP) • Aggregate planning • Resource allocation • Capacity allocation • Distribution • Inventory management Tactical Level Medium Term Inventory Control Problem (ICP) • Shop floor scheduling • Delivery scheduling • Truck routing Operational Level Near Term Vehicle Routing Problem (VRP)

11. Motivation • Lots of research has been done in each area in SCM, but few models comprehensively address the integrated network. • To achieve a global optimal (or near optimal) solution, it is necessary to consider the entire system in an integrated fashion and include all trade-offs in a realistic fashion. • We will look at the Distribution side (post production). • Inventory Strategy • Forecasting • Inventory decisions • Purchasing and supply scheduling decisions • Storage fundamentals • Storage decisions Customer service goals • Transportation Strategy • Transport fundamentals • Transport decisions • Location Strategy • Location decisions • The network planning process

12. Our Distribution Problem Made Here in Volume

13. Distribution Problem Scenario Product Mixes Sold here by the Item at many Outlets

14. Global Reality – But let’s start regionally

15. Our Distribution Problem • Assume (global) manufacturing system is defined. • Goal: Distribute completed products to retail outlets. • Assume goal is a (distribution) system optimal solution. • Assume a relatively stable environment. • Assume system to be designed from scratch – (any existing facilities could be sold for value or are on short-term leases).

16. Planning Decisions Where to place Distribution Centers? How large to make DCs? How to ship from Factory to DC – Quantity, frequency, form, mode? How to take advantage of load consolidation opportunities? How to serve each retail outlet – from where and how often? How much safety inventory to keep and where to keep it?

17. What’s Relevant? • Locations of Producers • What Else? • Locations of Retailers • Cost of Transportation • Cost of Facilities by site/capacity(Fixed, Variable Operating) • Vehicle Capacities • Demands and Patterns • Product Substitutability • Inventory and Shortage Costs/Policies • Product Lifetime • Supply Dependability and Lead Times

18. Important (Real-World) Factors Ignored Insert your list here: • Stochasticity of demand • Dynamic nature of demand (multiple periods) • Substitutability of products • Strategic corporate initiatives (profit, service, competitiveness) • Financial risk and return on investment • Taxes, duties, exchange rates if multinational • Reverse logistics (collection, refurbishment) • Direct shipments

19. Facility Location Problem (FLP) • Fermat-Weber (1909): A simple facility location problem in which a single facility is to be placed, with the only optimization criterion being the minimization of the sum of distances from a given set of point sites. • More complex problems: the placement of multiple facilities, constraints on the locations of facilities, and more complex optimization criteria. • The goal: to pick a subset of potential facilities to open, to minimize the sum of distances from each demand point to its nearest facility, plus the sum of fixedopening costs of the facilities. • The facility location problem on general graphs is NP-hard to solve optimally, by reduction from (for example) the Set Cover problem. • Daskin (2002), Ozsen (2008): include inventorycontrol decisions in FLP.

20. Inventory Control Problem (ICP) • Harris (1913): Economic order quantity (EOQ) • Clark and Scarf (1960): Multi-echelon Inventory • Inventory control: the supervision of supply, storage and accessibility of items in order to ensure an adequate supply without excessive oversupply. • Where to hold inventory? • Whento order? • How much to order each time? • The goal: the order quantity and the reorder point are determined such that the total cost is minimized. • Total cost = Purchasing cost + Setup Cost + Holding Cost + Shortage Costs • The single-item stochastic inventory control problem is NP-hard even in the case of linear procurement and holding costs. (Halman et al. , 2009)

21. Vehicle Routing Problem (VRP) • Dantzig and Ramser (1959):To deliver goods located at a central depot to customers who have placed orders for such goods. • The goal: to minimize the cost of distributing the goods. • The vehicle routing problem in general is NP-hard as it lies at the intersection of these two NP-hard problems: • Traveling Salesman Problem • Bin Packing Problem • Inventory Routing Problem (IRP): An extension to include inventoryconcerns. Kleywegt, Nori, Salvesbergh, Transportation Science, 2002

22. How Good are the Models? “A conclusion that can be drawn from the literature devoted to the uncapacitated facility location problem and its extensions is that the research field has somehow evolved without really taking the SCM context into account. Features … have been included in the models in a rather general way and specific aspects, that are crucial to SCM, were disregarded. In fact, extensions seem to have been mostly guided by solution methods.” - Melo et al. EJOR, 2009

23. Principles to Keep in Mind 1. Pooling Synergy Safety Stock Di Di Di Di Di Di Assumes independence

24. Principles to Keep in Mind 2. Inventory vs. Service Level What’s the Traditional Perspective? 100% Fill Rate Inventory

25. Comment on Second Principle: Little’s Law In Steady State, AverageInventory = Consumption Rate x Ave. Time in System N = XT or L = λW Diminishing Returns: Beyond the “elbow” more inventory is just more cost and more opportunity for degradation, loss, congestion and cost!

26. But it’s even worse Beyond a threshold increasing inventory reduces sales! • Congestion slows service response • Inventory is outdated • Forecast horizons too long for accuracy Carburetors vs. Fuel Injection

27. Empirical Profile: Know When Enough is Enough Remember L =λW N = XT In theory, there’s no difference between theory and practice, in practice there is. – Yogi Berra

28. Multi-Product Integrated Supply Chain Network Model

29. Existing Research is Helpful but Not the Same • Shen, Z.J.M, Qi, L., 2007. Incorporating inventory and routing costs in strategic location models. European Journal of Operational Research 179, 372-389. • Single Producing Plant (One Supplier, One Product) • Uniformly located customers across an area • (Q,r) inventory ordering/replenishment model for DC • Fixed and identical routing frequency from DC to customers • Single routing tour from each DC (1 vehicle) for cost estimation • Uncapacitated DCs • Javid, A.A., Azard, N., 2010. Incorporating location, routing and inventory decisions in supply chain network design. Transportation Research Part E 46, 582-597. • Single product, no transhipment • (Q,r) inventory model for DC • Known delivery route frequency • Fixed vehicle capacity per year

30. Our Problem (Model) Integrated supply chain network design: location, transportation, routing and inventory decisions • Multi-product and plant supply chain network. • Transshipments between DCs. • Non-uniformed (clustered) customer locations. • Multiple routes with model-determined frequencies from DCs. • Nonlinear inventory costs (safety stock). • Full truck load deliveries to DCs with choice of truck size.

31. Consolidation and Transportation Centers Fixed Location Cost V.S. Transportation savings Easy management

32. Multi-Product Integrated Supply Chain Network Model

33. Problem Description • Locationdecision: How many DCs to locate, where to locate, how much capacity at each opened site. • Transportationdecision: Allocate facilities and retailers to opened DCs. • Routingdecision: Routing tours and frequencies to retailers. • Inventorydecision: How often to reorder, what level of inventory stock to maintain.

34. Problem Description Facility – DC – Retailer: • Each production facility supplies a single product. • Retailers are clustered in the service region. • Demand follows a known stationary distribution. • Single source: all products at one retailer should be delivered by one DC. • Full truck load (FTL) shipping is used from plants to DCs and between DCs, multiple truck size choices exist. • Routing delivery is used for shipment from DCs to retailers.

35. Research Scope and Activities Two-phase: Phase I: Multi-product FLP with Approximated IRC Function • DC Locations and plant/retailer assignments • Approximate cost function for routing delivery cost(Shen, Z.J.M, Qi, L., 2007). Phase II: Inventory Routing Problem • Routing tours and frequencies • Solve the routing problem for each open DC and retailers assigned to it.

36. Cost Components FC: Annualized fixed cost of locating DCs SC:FTL Shipping cost from plants to DCs and between DCs Qpj Q = total shipped/time q = quantity per trip (shipping mode capacity) A = cost per trip T = if use that truck size Qpj’j p j, j’ i

37. Cost Components SSC: Safety stock inventory holding cost at DCs RIC: Regular inventory holding cost at DCs Qpj Qpj’j Ypjj’I binary route indicator variables

38. Phase I: Multi-product FLP with Approximated IRC Function

39. Approximated IRC Function IRC: Annual inventory routing cost from DCs to retailers rji a computationally estimated parameter to represent the annual IRC at retailer i if assigned to DCj Routing cost Inventory cost Nearest insertion method

40. Approximated IRC Function IRC: Annual inventory routing cost from DCs to retailers rji a computationally estimated parameter to represent the annual IRC at retailer i if assigned to DCj direct shipping method

41. Problem Formulation Minimize (FC + IRC + SC + SSC + RIC) Subject to: Single source Single path Link variables Maximum number of PWs Single capacity level Truck size selection Throughput Capacity limit

42. Single Plant Warehouse Case (n = 1) Optimal truck size from plants to PWs and transshipment between DCs DSRIC: direct shipping and regular working inventory holding cost TSRIC: Transshipment and regular working inventory holding cost Shared transhipment loads

43. Nonlinear Terms Safety stock Working inventory Recursive procedure to update safety stock parameters, Gebennini et al. (2009) Same holding rate

44. TabuSearch-Simulated Annealing (TS-SA) • Tabu search can avoid search cycling by systematically preventing moves that generate the solutions previously visited in the solution space. • Simulated annealing allows the search to proceed to a neighboring state even if the move causes the value of the objective function to become worse, and this allows it to prevent falling in local optimum traps. • Construction stage • Greedy method • Minimizing initial Fixed Cost (FC) • Minimizing initial Inventory Routing Cost (IRC) • Improvement stage • Location improvement • Close an opened DC; Open a closed DC • Assignment improvement • Assign one retailer to another reachable DC • Assign one PW to another opened DC

45. Ad-Hoc Heuristics Fixed Cost (FC) and Inventory Routing Cost (IRC) are two major cost components FC 24% Vs. IRC 50% (Shen and Qi, 2007) FC Heuristic: Minimizing initial FC • Set covering problem: minimizing total number of DCs • To include cost consideration • Open all necessary DCs • Open additional DCs to save total cost Improvement stage: TS-SA

46. Ad-Hoc Heuristics Inventory Routing Cost (IRC) is a major cost component IRC accounts for 50% of total (Shen and Qi, 2007) IRC Heuristic: Minimizing initial IRC • Open all DCs and assign retailers to its nearest DC • Close unnecessary DCs to save total cost Improvement stage: TS-SA Nothing new, sounds like variable selection in regression.

47. Lower Bound: Without considering transshipment between DCs. n =1

48. Parameter Settings • All points (plants, DCs, and customers) are geographically dispersed in a 500 * 500 miles region. • Plants are randomly distributed, retailersare clustered into m groups with the centers of gravity also randomly distributed in this space. • 8 different data sets with each set including 15 scenarios with sizes ranging from 20 to 200 retailers and 5 to 20 products. • Data sets differ in fixed location cost rate (low, high), demand rate (case 1, case 2) and holding cost rate (low, high). • All the computational times are obtained on a Intel(R) Core(TM)2 T5550 at 1.83 GHz using Windows 7. Three introduced heuristics are applied in Microsoft Visio Studio C++. IBM ILOG CPLEX Optimization Studio is used to solve the modified model and lower bound model.

49. Partial Results

50. Partial Results