Optimization of Multi-Commodities Consumer

Optimization of Multi-Commodities Consumer Supply Chains Part II: Simulation Modeling 1

Zeinab Haji Abolhasani1, Romeo M. Marian1, Lee Loung1, School of Engineering, University of South Australia, Adelaide, Australia Email: [email protected] (Corresponding author)

Abstract - This paper aims to demonstrate a simulationoptimization modeling approach to examine the efficiency of a mathematical model in Optimization of MultiCommodities Consumer Supply Chain (MCCSC)- Modeling. Simulation is one of the most widely used tools in model validation. It enables identifying system's behaviors under different circumstances. To this end, in the present work, a supply chain system simulation model is developed within the context of production-distribution (P-D) decision making. Also, taking into account real-life constraints, an integrated MCCSC case study is created to predict the consequences of variable changes. The performance of the model is then evaluated using SimEvents toolbox in conjunction with Simulink toolbox of MALAB®. Finally, Genetic Algorithms are utilized to minimize the total cost of the entire system. Keywords – Supply Chain; Optimization; Simulation; SimEvents;

I.

INTRODUCTION

The majority of today’s systems are large, complex, stochastic and dynamic in their nature. These attributes result in difficulties in various areas like: representing their actual behavior, planning, optimizing, and anticipating their performance [1]. Examples include manufacturing, production planning, product development, sequencing, scheduling, transportation, distribution, supply chain, etc. Supply Network (SN) is comprised of many systems and sub-systems with complex mutual relationships that incorporate end-to-end supply chain costs [2]. Due to ever changing global market, such as tax regulations, availability of materials and expertise, structure of costs, new market entry and many others, to remain competitive in the market, companies have changed their planning strategies to an integrated planning [3]. However, determining the right approach is still a challenge. SNs can be found in Manufacturing Facilities (MF), Distribution Centers (DC), Warehouses (W) and Retailers (R). Managing the information flows between these entities and in general in the whole supply network has always received a great attention from practitioners and researchers. Since, the more reduction in costs leads to better improvement in service level; thus, with the assist of simulation techniques, simultaneous management of information both in upstream and downstream in a multidecisional and complex problem like supply chain, can be achieved. The key characteristic which has highlighted simulation as one of the best modeling approach is its capability to create, analyze, and evaluate what-if scenarios.

This paper, as a continuations of the first partOptimization of Multi-Commodities Consumer Supply chain : Modeling [4], aims to demonstrate a simulation modeling approach to examine the efficiency of the presented mathematical model. Therefore, MCCSC problem is investigated to observe system’s behaviors under different circumstances. It should be noted that, based on the proposed algorithm, the results of this phase will be used as an input of the next phase - optimization. More details about the particularities of the heuristic method (Genetic Algorithms) employed to optimize the total cost of this problem will be discussed in part III of this study. The costs are production cost (Cp), operation cost (Co), holding cost (Ch), transportation cost (Ct) and penalty cost (Cp). Interaction between SN systems is subject to a welldefined set of constraints. Thus, connections among components should be taken into account. Also, the granularity of the model, the level of details up to what the system needs to be designed, has to be investigated. In this study, a typical three echelon planning model is presented for a supply chain over a short term planning horizon. As shown in Fig.1, commodities can be delivered either directly to R or indirectly, through DC. The information that flows to downstream is in the form of stock-quantities in the network layers whereas the information flows in the opposite direction is about ordersquantities.

Fig. 1 Three echelon Supply Chain

Simulation Model for the event-driven supply chain system will be created through SimEvents toolbox of MALAB® software. It is capable of developing a model to simulate the passing entities (orderi) through a network of different modules; queues, servers, gates, switches etc. based on events [5]. Within an integrated environment SimEvents, (a set of time-driven and event-driven components) and Simulink (a traditional time-driven simulator [6]) it is possible to model the MCCSC system in continuous- time, discrete- time and discrete-event modes

or a combination of them. However, the focus of this study is on discrete-time modeling. This paper is structured as follows. In the next section SC is presented as a discrete event system. Section three will review SimEvents toolbox which is utilized in modeling and simulating of discrete event systems. The simulation results are provided in section four. Finally, conclusion and future works are outlined in section five. II. SUPPLY CHAIN: A DISCRETE EVENT SYSTEM A system is defined as a collection of entities, attributes, activities, states and events where the inputs are absorbed in order to produce the outputs based on some specific goals and objectives [7].1 A discrete-event system is a system in which system’s states (xi) vary at a particular instant of time (ti). For example, in an Inventory Control System, state variables are the number of orders in the queue and the available inventory level (stock). The values of these parameters are changed only when an order (entity – ei) arrives or when it is received and departs. Consequently, any changes in system’s states can simply be implemented through computer based modeling programs. In the context of supply chain, the most commonly used modeling approaches are Discrete Event Simulation (DES) and System Dynamic (SD). While strategic decision making is simulated via SD, problems at operational and tactical levels are modeled with DES [8]. As it is depicted in Fig.2 system modeling concepts can be applied and adapted to a range of different scenarios. III. CREATING DISCRETE EVENT SYSTEM IN MATLAB USING SIMEVENTS AND SIMULINK TOOLBOXES

According to the literature, there are several discreteevent driven simulation tools that can be used for modeling purpose. Examples of such simulation tools include DEVSJAVA [9], SimEvents [10], Ptolemy, Arena [11], Simprocess [12]. However, MATLAB® software package provides the user with both modeling and simulation toolboxes. This capability of MATLAB® along with other properties will facilitate technical computing and modeling environments. SimEvents and Simulink are two available toolboxes of MATLAB® .Unlike Simulink, SimEvents is developed by Mathworks to model and simulate discrete-event systems. It deals with a so called item entity. Entity is a discrete item of interest (any physical moving thing through simulation) which can carry information known as attributes in SimEvents and pass through a network of blocks. These predefined blocks make modeling easy and so accurate. Basically, through employing SimEvents discrete sequence of events which represents the operation of a system will be modelled at an instance of time [7]. In practice, occurrence of each event can be monitored at a particular instant in time which leads to changes in the

state variable, output, or occurrence of the other events of the system. Assuming no change taking place between any two consecutive events, simulation can directly jump from one event to the next scheduled event in time [13]. Even though, graphical representation of events is impractical; their consequences can be observed through employing available events graphical block in SimEvents software. More key features of SimEvents as an event-driven simulator is outlined below: i. Multi-domain modeling framework for complex systems in conjugation with Simulink via predefined components (i.e. Gateway blocks); ii. In-model animation supplied facility for model visualization (i.e. Instantaneous Event Counting Scope); iii. Equipped with event-based and time-based signal converting ports (i.e. gates, function calls); iv. Embedded with a well set of probability functions for randomly event generating; v. Possible transition of discrete events asynchronously. Due to the large size of manufacturing system model, the second echelon of SC model is illustrated in Fig. 3. IV. MCCSC SYSTEM DESCRIPTION AND SIMULATION MODEL USING SIMEVENTS TOOLBOX

A. Multi-Commodities Consumer Supply Chain System (MCCSC) A MCCSC problem is a hybrid, discrete-event and time-based model that simulates a P-D process in supply chain. Due to the larger number of system’s component, the entire system is very complicated.

Fig. 2 Discrete Event Simulation block diagram [14]

Generally, P-D problem deals with two networks namely production and distribution networks. Materials assembly and/or transformation into final commodity is focused on in the first network while transferring commodities from MU to DC and then delivering to retails (end-users) is considered in the second network [15]. Based on the received order i=1,2,3,..,n from any specific retailer (Rj=1,2,3,…,n) by DC, different commodities (Pi=1,2,3,..n) will be transported from MU to DC and then

to Rj. Fig. 4 represents the block diagram of MCCSC system. The main objective of simulation modeling is to predict consequences of variable changes. This means, a model should be a close approximation of a real system including most of its specifications and characteristics [16]. B. Simulation Modeling Problem Technically, in every model at least one validation technique must be utilized to verify and validate the model outputs. Simulation is one the most used tools in this regard. For a set of configurations, simulation is capable of comparing the input conditions and model outputs. Also, it permits engineers to ascertain new layouts with correct size and test various decision making alternatives subject to different conditions [3]. The focus of the present work is on simulation modeling of MCCSC and the last 50 meters of the supply chain, from distribution center to retailers. Since, this type of problems is extremely large as a multidecisional context, for simplicity and easy tracking, a set of assumptions are considered. Based on these assumptions, a scenario is developed and then simulated with the aid of MATLAB®.

Fig. 3. Distribution Centre Module of MCCSC system Model

Fig. 4. Block diagram of MCCSC system

C. Scenario Development for Simulation A simulation model of MCCSC can be developed into two different modes. Either all echelons reproduces as a whole single model, or each echelon designs separately and in an integrated manner run a single cooperation simulation [3]. In this study, the second approach is chosen with the following assumptions:

1- Operational planning horizon of four weeks is selected. Therefore, simulation end time will be 4×7×24×3600 time frame (unit is the second); 2- Manufacturing facilities produce five types of commodities, T1 ,T2 T3,T4 , and T5 respectively; 3- There is one distribution centre through which retailers are served; 4- There are three retailers located randomly in the network, R1, R2, R3; 5- The distances between MU to DC, DC to Ri and MU to Ri are calculated based on Euclidean distance. 6- Each order is generated randomly within the range of minimum 100 and maximum 5000 number of commodities; 7- Once an order served in DC, it will be placed in a container and then delivered to the specific retailer; 8- Maximum container capacity is 150 kg; D. MCCSC System Model Description Since, this system model is too large and complex, in this section; only one part of the model will be described. Using SimEvents Time-Based Entity Generator block, Order is generated as an entity with “Exponential” distribution function as the intergeneration times with mean value that can be altered by user via interface. Intergeneration time is the amount of time between generating of two entities. Through a similar procedure, Stock is generated too. This leads to keep inventory level updated and be able to calculate back ordering, receiving and remaining number of commodities. It should be noted that, both entities carry the following information which is set in attribute block. They only differentiate in one attribute (destination) which is excluded in stock configuration. For convenience, all notations used in the simulation model formulation are summarized in Table1. TABLE 1 Notation Cpi Production cost , indexed by i ord Q Order Quatity Chi Holding cost , indexed by i bck_ord_T1 Coi Operation cost , indexed by i Wc Total weight of the container Cti Transportation cost , indexed by i rmd_T1 Inventory level, indexed by i CP Penalty Cost, indexed by i Mui Monitoring unit ord1i Quantity of order1 opr No. of operational tasks Wi Net weight of commodityi km2i Distance between DC to REi Ti Commodity type km12 Fixed distance between MU to Qi Commodity quantity stk2i Commodityi is being held in DC/day REj Retailer, indexed by i st_T1_Q Total number of container rcv_Ti Total quantity of commodityi Nc

Next, the orders sent by retailers must be placed in a queue with an infinite capacity (inf) waiting to be served by servers. Using FIFO queue, entities are stored in sequence of arrival. By the arrival of each order, a timer clock starts calculating the total time of processing of one order. This variable will be used later in computing the penalty.

(1) a. Production Cost (2) b. Operation Cost .

(3)

Generally, operation tasks are assumed to be loading, unloading, shifting to shop flooor both from MU to DC and from DC to RE. Therefore, in the context of the developed scenario the number of operatioon is considered ′5′. c. Transpiration Cost (4) Fig. 5. User interface for identifying mean andd retailer values

d. Holding Cost . Fig. 6. A typical queue system usedd in DC

During order processing in DC, Input and Output switches based on the allocated attribute (Ti); select an entity with required information for depparture. This allows the user to have multiple outputs deriveed from one input. Outputs of this stage are event-based siggnals. Hence, timebased signals should convert to time domain. Another alternative in signal conversion is ussing Get Attribute block. Thus, utilizing this block the folllowing inputs data stk_T1_Q, and ord_Q are defined as input arguments of MATLAB function block (inventory) to return outputs data values rcv_T1, bck_ord_T1, and rmd__T1 subject to the following conditions accordingly. vc=0 rcv_T1= stock bck_ord_T1= order - stock rmd_T1=0; vc=1 rcv_T1= order bck_ord_T1= 0 rmd_T1=stock-order

where vc is a corresponding value to t the signal vc in Release Gate block to open the gate if i and only if the specified condition is satisfied. In this case, c an order will be sent if the quantity of commodity1 inn the placed order is equal or greater than the quantity of commodity c 1 in the stock. Therefore, the specified retailerr will receive the exact value of the claimed item (rcv_T T1). Consequently, inventory level (rmd_T1) is resulted from m order and stock differentiation. Obviously, under such ciircumstances back ordering (bck_T1) is zero. The num mber of departed commodity1 is shown in Fig. 7 . Afterward, by means of cost structurre, the total cost of the entire network will be calculated. The T corresponding cost equations are given in (1) to (5). Priior to calculating of these costs, total number of containeers which will be received at retailer site (Nc) is calculatedd via Eq.1.

(5)

Parameter stk2 is calcuulated once the following conditions (Table 2) are satisffied. It should be noted that, calculation policy of stk2 in week w 1 is slightly different to the other weeks. Bellow four different sets of conditions are represented. Subscripts i, j and k are presenting commodity type, retailer and number n of week respectively. Finally, through sum of the mentioned m costs the total cost (6) will be calculated.

TAB BLE 2 CONDITION SE ETS FOR stk2 Set 1 if wk=1 & stk1ijk< ord1 rcvijk = stkijk bck_ordijk = ord1ijk - stkijk stk2ijk = 0 Set 3 if wk ~ =1 & stkijk< ord2ijk ord2ijk =ord1ijk +bck_ordijk-1 stkijk = stkijk+ stk2ijk-1 rcvijk = stkijk bck_ordijk = ord2ijk - stkijk

Set 2 if wk=1 & stk1ijk ≥ ord1 r ijk = ord1ijk rcv b bck_ord ijk= 0 s 2ijk = stk ijk - ord ijk stk Set 4 if wk ~ =1 & stkijk ≥ ord2ijk b bck_ord ijk = 0 r ijk = ord2ijk rcv s 2ijk = stkijk – ord2ijk stk

Fig. 7. Number of departed d commodity1

V. RESULTS AN ND FUTURE WORKS In the current problem, simulation and optimization of the total cost (CT) is achieeved. The end result of the simulation phase then is fed into i the optimization phase

Family Product

TABLE 2 CHROMOSOME STRUCTURE FOR 10 PRODUCTS FOR RETAILER1 AT WEEK 1 2159 1221 52 278 1715 2567 3177 4992 4671 4459

Time Horizon (Week) 1395 4612 2975 2668 3988 1760 4816 3584 2735 224 4599 2874 230 4006 3494 1040 1911 3033 1847 153 304 719 223 912 1551 3421 4261 2647 287 4507

4836 4962 1369 2037 2480 816 3084 3694 1789 754

Fig. 8. Chromosome structure: (Solution 1) All family products for 5 retailers for 4 weeks

Fig. 9. Total cost (CT)

Cost (MU)

where each chromosome will be produced accordingly. The structure for each chromosome is as below: Ch (pro,re,w) is the 3-D matrix that represents the number of products, retailers and weeks respectively as its first, second, and the third dimensions. Table 2 indicates one set of chromosomes, Chk_m(:,1,1) for 10 products for re1 and at w1 . Fig 10 and Fig 11 demonstrate the total cost of all retailers for one horizon (4 weeks) and total cost of all products for 4 weeks respectively. Optimization procedure is consisting of 10 chromosomes in each generation. With around 200 as the number of generations, the algorithm converges to 850000 monetary units (MU), which results in approximately 30% reduction in total cost of the production- distribution system. More details about chromosome evaluation and applying GA operators on them will discuss in part III (Optimization of multi-commodities consumer supply chain– Genetic Algorithm operators and results). Also, more sophisticated scenarios with different constraints such as multi MF and multi DC and over different planning horizon, tactical and strategic planning, will be developed accordingly.

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