Not All SKUs are Created Equal: The Return on Investment of Order Fulfillment System Design

Transcription

1 Not All SKUs are Created Equal: The Return on Investment of Order Fulfillment System Design Russell D. Meller Department of Industrial Engineering University of Arkansas NSF PASI on Modeling, Simulation and Optimization of Globalized Physical Distribution Systems Introducing Russell D. Meller Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 1 / 1000 B.S.E., University of Michigan 88, IOE Consultant, SysteCon, 89 M.S.E. & Ph.D., University of Michigan 90 & 92, IOE Faculty Member: Auburn University ( ) & Virginia Tech ( ) Faculty Member: Univ. of Arkansas (2005 present) & Graz University of Technology (Austria; 2011 present) Research and Teaching Interests: Facility logistics and OR applications to logistics systems and forestry Personal: Married, 2 children (Grace (10), Henry (7)) Outside Stuff: Running, hiking, skiing, camping, traveling. eating, and drinking red wine! Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 2 / 1000

2 Academic Area: Facility Logistics Definition Facility Logistics involves facility design and material handling for manufacturing, distribution, and service facilities. Research topics include both design and operational aspects of material and information flow within facilities to improve productivity and performance. Specific topics include facility layout, material handling, storage/retrieval systems, order fulfillment, sensor deployment, and inventory tracking and control, among others. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 3 / 1000 PASI Workshop: Fulfillment System Design 4 / 1000 Distribution Center 101 Russell D. Meller, Ph.D.

3 Outline Carton-Level Fullfillment Item-Level Fulfillment Design Exercise Automated Item-Level Fulfillment Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 5 / 1000 Carton-Level Fulfillment Manual system, carton, case, break-bulk facilities Material adapted from Chapter 7 of Warehouse & Distribution Science, Bartholdi and Hackman, Version 0.95, Aug. 22, 2011 (available for free at: Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 6 / 1000

4 Motivating Facility: Break Bulk Facility for Toys R Us Picking Cartons Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 7 / 1000 Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 8 / 1000

5 Functional Flow Network Decision Full-Pallet Quantity Picks Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 9 / 1000 Theorem In a pallet rack reserve area, full-pallet quantity picks should always be made from the reserve area (directly) if the objective is to minimize cost. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 10 / 1000

6 Non-Full-Pallet Quantity Picks Now what about the non-full-pallet quantity picks? As mentioned before, will put most of these in a forward area: increase the pick-density reduce the travel time cost restocking cost Carton Picking in a Forward Area Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 11 / 1000 Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 12 / 1000

7 Carton-Picking Area Design Result Theorem (7.1 (Law of None, One, or All)) Any sku that is picked from pallets should either not be in the fast-pick area at all; or it should have one pallet; or it should have all its on-hand inventory in the fast-pick area. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 13 / 1000 Benefit of Storing in the Forward Area Net Benefit for sku i = 0 if x i = 0; sp i c r d i if l i x i < u i s(p i + D i ) if x i = u i. Example carton LT-pallet Pallet picks demand demand min max sku (p i ) (d i ) (D i ) (l i ) (u i ) A B C Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 15 / 1000

8 Benefit of Storing Max in the Forward Area Set of skus where the benefit per opening is greater at the max than at the minimum level; i.e., s(p i + D i )/u i > (sp i c r d i )/l i. These are items that are: low u i high D i low p i /d i The set of skus with this property = CI (immediate candidates for complete inclusion). Theorem (7.2) If, by storing all of its pallets, a sku offers greater net-benefit per pallet-position than if stored in the minimum amount, then it should either be stored completely in the forward area or else not at all. Auction Analogy Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 17 / 1000 Competition for space in the fast-pick area may be viewed as an auction. CI Items Will bid s(p i + D i )/u i for u i spaces. CI Items Will initially bid (sp i c r d i )/l i for l i spaces; if successful, will bid sd i +c r d i u i l i for u i l i spaces. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 19 / 1000

9 Greedy Heuristic for Forward Allocation Problem Greedy Heuristic Avail = N, i = 1, B = 0 Determine which set each sku i falls into If sku i CI, then b i = s(p i + D i )/u i and c i = u i Else, b i = (sp i c r d i )/l i and c i = l i ; and b n+i = sd i +c r d i u i l i and c i = (u i l i ) Rank the skus on b i values (highest to lowest) and use i as the new index (break ties in descending order of c i ) While Avail c i 0 B = B + b i c i Avail = Avail c i i = i + 1 End while Theorem (7.3) The Greedy Heuristic for the knapsack problem generates a feasible and near-optimal solution to the problem of allocated pallet positions. Revisit Previous Example Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 20 / 1000 Example carton LT-pallet Pallet picks demand demand min max sku (p i ) (d i ) (D i ) (l i ) (u i ) b i c i b i+n c i+n A B C Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 21 / 1000

10 Summary Design of these systems is straightforward with None, one or all Rule assuming you have all the data. Unfortunately it can be difficult in all cases to estimate s and some of the other data needed. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 23 / 1000 Item-Level Fulfillment Manual system, item, each, distribution centers, order fulfillment centers Material adapted from Chapter 8 of Warehouse & Distribution Science, Bartholdi and Hackman, Version 0.95, Aug. 22, 2011 (available for free at: Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 25 / 1000

11 Concept: A Fast-Pick Area Generally speaking, the fast-pick area is either picking cartons directly from pallets, or picking eaches (or inner packs) from rack/shelving. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 26 / 1000 Fast-Pick Area Operations for Item Fulfillment We are concerned with two questions: 1. Which sku s should occupy the fast-pick area? 2. In what quantities? Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 27 / 1000

12 Estimating Restocks We assume a fluid model of product flow, where flow for a product is measured by ( ) ( ) # items/yr ft flow, ft 3 3 /yr = # items/case case If item i flows at f i ft 3 /yr, we can estimate that it incurs and cost of restocking is c r f i /v i. f i v i restocks/yr, Assumption: We restock when sku i has been depleted (fully) and the cost of a restock event is independent of v i. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 28 / 1000 Allocating Space in the Fast-Pick Area We wish to minimize total restock cost, or n Minimize c r f i /v i subject to Theorem (8.1) n v i V i v i > 0 To minimize total restocks over all sku s, each sku i should be stored in the amount ( fi v i = n j=1 i fj ) V. (8.2) Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 29 / 1000

13 Simple Example Example Consider a problem with V = 100 ft 3 and the following data: sku flow optimal (i) (f i ) alloc. (ft 3 ) A 900 B 400 C 100 Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 30 / 1000 Two Common (but Flawed) Schemes Equal Space Allocation Allocate the same amount of space to each sku; that is, allocate v i = V /n for all i. Equal Time Allocation Allocate an equal ( time supply to each sku; that is, allocate v i = f i /( ) j f j) V for all i. Theorem (8.2) For a given set of sku s, Equal Time and Equal Space Allocations produce the same number of restocks. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 31 / 1000

14 Simple Example, Revisited Example Consider a problem with V = 100 ft 3 and the following data: sku flow optimal number equal space number equal time number (i) (f i ) (ft 3 ) restocks (ft 3 ) restocks (ft 3 ) restocks A B C Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 32 / 1000 Additional Properties of Optimal Allocations Observation (8.1) The more diverse the rates of flow of sku s the better the performance of Optimal Allocations versus Equal Time/Space. Theorem (8.5 Law of Uniform Restocking) Under Optimal Allocations, each unit of storage space is restocked at the same frequency. Implication: This gives an easy way to assess the quality of an allocation. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 33 / 1000

15 Summary Design of these systems is straightforward with the allocation equation assuming you have all the data. The text talks about many real-world constraints that can be handled with the model. The interesting case is how to apply the model when the pick time is a function of V. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 34 / 1000 Design Exercise Segue: Applying the Models Manual system, forward-reserve problem, fast-pick area design Material adapted from Thomas and Meller, Analytical Models for Warehouse Configuration, IIE Transactions, to appear. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 35 / 1000

16 Motivating Company National manufacturer and distributor of health care supplies and services. Manufactures and distributes more than 100,000 medical products. 36 distribution centers ranging between 150,000 to 750,000 square feet. A View of the Facility Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 36 / 1000 Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 37 / 1000

17 Flow Within the Facility for Case Picks Design Problem Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 38 / 1000 Decisions: 1. Should we have a forward area? 2. If so, how big? 3. Which products and what quantities? The Forward-Reserve Problem answers these questions. Can we apply the previous auction-based algorithm to this problem? Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 39 / 1000

18 Impact of Design Solution Savings per pick (s) is a function of this decision. Results Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 40 / 1000 Sorry, PASI students. I m not supposed to distribute the results from this company electronically. But the graph was convex and showed that their current rule-of-thumb should be adjusted and adjusted to a different percentage for each of their facilities. Note that the company has implemented this and saved $25,000 at small facilities/year and up to $100,000/year at larger facilities. Russell D. Meller, Ph.D. PASI Workshop: Fulfillment System Design 41 / 1000