SELECTED ASPECTS OF ORGANIZING ORDER-PICKING PROCESS WITH DYNAMIC MATERIAL TO LOCATION ASSIGNMENT. Konrad LEWCZUK

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1 Abstract SELECTED ASPECTS OF ORGANIZING ORDER-PICKING PROCESS WITH DYNAMIC MATERIAL TO LOCATION ASSIGNMENT Konrad LEWCZUK Warsaw University of Technology, Faculty of Transport Koszykowa 75, Warsaw, Poland, Article presents one of the warehouse designing issues. Dimensioning and organizing order-picking areas with dynamic material to location assignment influences the quality of warehouse services. It is crucial for order fulfilment time and ability to react for unpredictable demand. Article gathers theoretical aspects of organizing and implementing order-picking process with dynamic assignment of skus to locations. It provides formal description of the problem, selected criteria of process evaluation, algorithm of simulation tool revealing correlations between particular parameters of the process, results of simulations and conclusions. Keywords: Warehousing, dynamic order-picking, simulation, assignment. 1. INTRODUCTION Picking and shipping materials according to customer orders is a fundamental warehousing process affecting the quality of services. One of the quality criteria is the order execution time, especially the ability to plan exact time of order realization [3]. All other activities in the warehouse are subordinated to order picking phase. For this reason the design of picking areas in warehouses has considerable importance. Mistakes made on this step are reflected in customer satisfaction [4] Order picking areas dispose most valuable locations in warehouse. They ensure a clear access to small amounts of all types of offered skus (storage keeping units). For this reason they are expensive to maintain from one hand, and key for warehousing process from another hand [2], [3], [4], [5], [8], [9], [10]. In most warehouses it is impossible to represent all skus in order picking area (i.e of skus in automotive distribution centre). Warehouse activity profiling provides the knowledge about items popularity and their flow density. In most cases assortment from groups A and X (in ABC and XYZ classifications), on which labour consumption is concentrated, is assigned permanently to locations in order picking areas (static order-picking). It makes possible to plan effective handling of those items. Literature presents a plenty of examples for that ([1], [2], [5], [6], [7], [9]). But there is a wide group of skus with lower or/and not predictable demand, or characterized by outlying dimensions restricting representing them in standard locations. These items can be offered in order picking areas with dynamic assignment of skus to locations. Items are assigned to locations in pursuance of current demand. Area is replenished by units of materials which stay there only for specified time. After they are used in orders completion they are retrieved and transported back to reserve areas. When location becomes empty, it is available for reassignment. Thanks to that it is possible to perform order-picking process with limited storage capacity of order-picking area. The trade-off is the necessity of additional handling [2]. Organization of order-picking area with dynamic assignment must take into account additional conditions: Materials handled in the area should be placed on carriers (i.e. pallet units) to be easily moved. Area should be located close to reserve areas in order to shorten replenishment cycles. Warehouse should have a broken case/pallet handling capability. There must be formulated policy of gathering and working out the clients orders (to plan replenishment).

2 Area emptying level should be found. It is the level of area fulfilment that when exceeded will start the procedure of retrieving materials. When level is not exceeded materials stay in the area until they are required to complete order or will be taken to free a space for other items. 2. ORGANIZING ORDER-PICKING WITH DYNAMIC SKU ASSIGNMENT FORMAL DESCRIPTION Let there be an order-picking area with dynamic material assignment with a storage capacity of D equallyprivileged locations. Let 12,,...,a,...,A A denote the set of numbers of skus to be picked from the area. Each sku is characterized by an equal probability of being ordered. The area is serviced by auxiliary devices replenishing locations and retrieving units of materials if necessary. The set of numbers of auxiliary devices is denoted as U 12,,...,u,...,U. Let there be a set 12,,...,k,...,K K of numbers of picking devices. The duration times of operations performed in the area are described by random variables: T p for time of picking, T rp for time of replenishing, and T rt for time of retrieving operation. The appropriate probability distributions theoretical or empirical are known. Let Lz a lz: a,lz 1; a A ; lz 1,Lz be the vector of clients orders, where a,lz 1 if lz-th order is for a-th sku. Lz is a total number of orders to be picked. The emptying level C 01, is given. Order-picking process starts in the moment t = 0 when first order is assigned to realization and finishes in moment t = T cm cm when last order is completed. Then the set 0, 1, 2,...,t,...,T,...,T T of equal time periods allows stating all time measures in the problem. Labour consumption R of order-picking process is equal to summary time T sm of completion of batch of orders. Average order completion time is T av = T sm / Lz. At any t-th moment area fulfilment process starts area fulfilment Z t Z 0 0. Additional assumptions have been made: D expressed in number of occupied locations is known. When Orders are picked in the sequence as they appear in the system. The next order is unknown until the current one is realized. One order is always for one type of material and is interpreted as order line. Order is assigned to k-th device as soon as this device is free. There is no situation when picking device waits for order. At this stage of study the quantity of picked material is not considered. It is assumed that the quantity of material gathered in location (i.e. on the pallet unit) is significantly greater than average pick quantity and is enough to realize relatively large number of order lines. According to that the issue of estimating inventory of skus in order picking area is omitted. The duration times of picking, replenishing and retrieving operations are given as the probability distributions and are not dependent on location. The material is assigned to the first empty location with a lowest number. Single sku is represented only in one location in the picking area. Particular order can be completed in one of three variants as it is presented on Fig. 1. With reference to these assumptions it is stated that realization variants are independent random events: X 1 when order is completed according to variant I, X 2 when it is completed according to variant II, and X 3 when variant III occurs. Then probabilities P X P X P X The order can be assigned to k-th picking device when this device is free. There are three states in which device can be: 1/ free (no order assigned), 2/ waiting (for replenishing picking area with appropriate material), 3/ picking (according to client s order). Also auxiliary devices can fall into three states: 1/ device is free (when there is no necessity to replenish or retrieve), 2/ replenishing, 3/ retrieving. Picking device became free when it finishes order completion in t-th moment. When k-th picking device is free and there are

3 a) START E(T rt ) Set the order parameters Sku available in picking area NO Empty location available NO Retrieve unit from location (free location) NO All orders completed STOP Do picking Variant I Replenish order picking area (insert unit into empty location) E(T rp ) Variant II Variant III b) I. II. E(T rp ) Emptying level exceeded Any unit ready to be retrieved III. E(T rt ) E(T rp ) Fig. 1. Schematic representation of order picking process, a) block diagram, b) time components. still orders to complete it gets another one to carry on in moment t+1. In the same time it must be checked which of three ways of picking will be performed (Fig. 1). When probability of ordering each of skus is equal, and is: 1 P alz a / A ; a A; alz Lz (1) the probability of completing order assigned in t-th moment to k-th device according to first variant is: Zt P X1 (2) A the probability of completing order according to second variant is: A Z t P X2 P Z t D (3) A where: P Z t D is the probability of that in t-th moment at least one location in area is empty, the probability of completing order according to third variant is: A Z t P X3 P Z t D (4) A where: P Z t D is the probability of that in t-th moment there is no empty location. For a given number of orders Lz, the probability of the situation in which m orders is completed in first way, n in second way and o in third way can be expressed by multinomial distribution: Lz Lz! P m, n, o P X1 P X2 P X2 m! n! o! m n o Then the labour consumption R for all orders will be: p rp rt s R T Lz E T E T n o E T o, where m + n + o = Lz. (5). (6) If K = 1, then T sm = T cm.

4 Through the complete review of P values relative to m, n, o, for known P X, P X, P X Lz m, n, o find the expected value of labour consumption R. However probabilities P X 1, P X, P X , one can dependant to the parameters K, U, C, duration times T p, T rp, and T rt. and relations between these factors. Additionally the interrelation between area storage capacity D and the number of different skus A influences the probability P X 1. Therefore the ratio of these probabilities depends on set of parameters K, U, C, D, T, T, T. p rp rt Due to the impracticality of complete review, a simulation program was developed. Program allows identifying dependences between parameters of order picking area with dynamic skus assignment and its efficiency. Obviously this is only one of the possible patterns of organizing order-picking process with dynamic assignment. A lot of things depend on items characteristics, structure of client s orders, number and flow density of groups of skus, physical structure and layout of order-picking area and applied picking technology. Proposed approach can be modified to include these additional elements. 3, are 3. SIMULATION OF ORDER-PICKING PROCESS WITH DYNAMIC ASSIGNMENT OF SKUS TO LOCATIONS Simulation program takes into account all above features of order picking area. In general, primary practical application of this program was setting the values of parameters of order-picking process and order-picking area to support configuring Warehouse Management System. According to that, program allows using theoretical distributions of duration times of tasks like Gaussian, Poisson, exponential or uniform and empirical distributions like the interval distribution. Simulation program allows presenting the influence of disorders like reduction of number of devices or storage locations in area. It gives a precise estimation of average order completion time, total time of realizing the batch of orders and utilization of particular devices. For the needs of simulation a range of different data sets was analysed. Table 1. presents results of simulation for example empirical data. Green colour represents best results. All markings used in table are explained in text. Tab. 1. Results of simulation for example empirical data. No. of devices Lz = 500, A = 800, T rp : {N(190,70), cut off 40 X 500}, T rt : {N(150,60), cut off 50 X 400}, T p : {U 1 (90,110), P(U 1 )=0,6; U 2 (111,160), P(U 2 )=0,3; U 3 (90,110), P(U 3 )=0,1} D = 38, C = 0,5 D = 38, C = 0,9 D = 44, C = 0,5 D = 44, C = 0,9 D = 50, C = 0,5 D = 50, C = 0,9 U K T cm T av T cm T av T cm T av T cm T av T cm T av T cm T av h49'26'' 5'42'' 23h52'25'' 5'43'' 24h00'20'' 5'45'' 23h10'43'' 5'33'' 23h30'02'' 5'37'' 23h19'35'' 5'35'' h49'53'' 5'14'' 22h24'51'' 5'22'' 22h08'27'' 5'18'' 21h50'24'' 5'14'' 22h02'42'' 5'17'' 21h29'21'' 5'08'' h14'54'' 5'05'' 21h24'24'' 5'07'' 21h26'51'' 5'08'' 20h051'0'' 4'59'' 21h10'28'' 5'04'' 20h51'26'' 5'00'' h05'44'' 7'56'' 22h34'01'' 8'06'' 21h59'55'' 7'54'' 21h55'52'' 7'52'' 22h04'51'' 7'55'' 21h36'11'' 7'45'' h44'25'' 5'39'' 15h41'17'' 5'37'' 15h28'44'' 5'33'' 16h06'15'' 5'46'' 15h55'01'' 5'43'' 15h35'40'' 5'36'' h56'38'' 5'22'' 15h10'07'' 5'26'' 15h03'41'' 5'25'' 15h01'23'' 5'24'' 15h09'40'' 5'26'' 15h00'24'' 5'23'' h19'15'' 10'41'' 21h52'02'' 10'27'' 21h58'07'' 10'30'' 21h48'38'' 10'26'' 21h40'02'' 10'22'' 21h50'32'' 10'26'' h02'29'' 7'11'' 15h12'42'' 7'17'' 15h02'29'' 7'12'' 15h07'37'' 7'13'' 15h08'30'' 7'13'' 15h03'06'' 7'12'' h39'26'' 5'34'' 11h44'13'' 5'37'' 11h49'07'' 5'39'' 11h50'21'' 5'40'' 11h45'06'' 5'37'' 11h51'24'' 5'40'' Simulated values of average order completion time T av and total time of completing batch of 800 orders T cm, depending on the order-picking process parameters, are presented on figures 2. and 3. Additionally figure 4. presents area fulfilment level Z for selected simulation runs.

5 , Jeseník, Czech Republic, EU T av [sec.] U = C = D = K = Fig. 2. Average order completion time depending on the order-picking process parameters T cm [x sec.] U = C = D = K = Fig. 3. Total time of orders completion depending on the order-picking process parameters [%] U = 3, K = 4, D = 38, other parameters like in Tab. 1 [%] C = 0,5 C = 0,9 Z Z Fig. 4. Order picking area fulfilment level Z for selected simulation runs.

6 4. CONCLUSIONS The simulations have revealed relations between parameterization of order-picking process with dynamic assignment of skus to locations and efficiency of this process. Efficiency was expressed as the average time of single order completion, what is important while planning number of people and devices to perform process. From the other site simulation pointed that the value of this time is correlated with number of pickers and auxiliary devices, what creates cyclic reference. This favours simulation as a tool resolving complex problems and being useful in operational planning. Other efficiency measure evaluated in simulation was total time of completing batch of orders. This is important when orders must be realized within exact time window. Proposed way of simulating order-picking process allows warehouse manager to organize the process correctly, ensuring proper number of pickers, auxiliary equipment and number of locations in the area. Of course efficiency of the process should be combined with the costs of its realization. Proposed approach and simulation tool can be useful while configuring Warehouse Management Systems. WMS must get exact information about parameters of functional areas in order to direct warehouse operations. These parameters must be set up before system becomes operational according to rule that WMS is not optimizing process, but only realizes assumptions of the designer. If we are able to copy efficient process into management tool, we can expect its efficient realization. Simulation seems to be the cheapest way of finding best solutions for warehousing process organization. The problem of organizing order-picking with dynamic assignment contains more elements that must be included into considerations. Especially, the stochastic characteristics of the client s orders appearance and probability of ordering particular materials must be recognized. Moreover, factors disturbing picking process, the issue of estimating the amount of material in locations and routing issues should be included into the simulation. LITERATURE [1] FIJAŁKOWSKI J., Technologia magazynowania, Wybrane Zagadnienia, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa [2] FRAZELLE E., World-Class Warehousing and Material Handling, McGraw-Hill 2002 r. [3] HOMPEL t. M., SCHMIDT T., Warehouse Management. Automation and Organisation of Warehouse and Order Picking Systems, Springer-Verlag, Berlin Heidelberg [4] Institute of Material Management, Toward more efficient order picking, Cranfield Institute of Technology, [5] JACYNA M., KŁODAWSKI M., Czas procesu kompletacji jako kryterium kształtowania strefy komisjonowania, Logistyka 02/2011. [6] JACYNA M., KŁODAWSKI M., Matematyczny model kształtowania strefy komisjonowania, AUTOMATYKA 2011, z. 2., vol. 5., Wyd. AGH. [7] JACYNA M., KŁODAWSKI M., Selected aspects of research on order picking productivity in aspect of congestion problems, Conference Proceedings, The International Conference on Industrial Logistics (ICIL) 2012, Zadar. [8] LEWCZUK K. Organizacja procesu magazynowego a efektywność wykorzystania zasobów pracy, Logistyka 4/2011, pp [9] LEWCZUK K.: Efektywność dwustopniowych systemów komisjonowania ze względu na przepływ ładunków i informacji. Transport w systemach logistycznych, Prace Naukowe PW Transport vol. 60 pp , OWPW Warszawa 2007 r. [10] PETERSEN C. G., SIU C., HEISER D. R., "Improving order picking performance utilizing slotting and golden zone storage", International Journal of Operations & Production Management, Vol. 25 Iss: 10 pp. (2005)