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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.20 No.3 pp.412-428
DOI : https://doi.org/10.7232/iems.2021.20.3.412

A Profit-Based Model of Integrated Inventory-Production (IPP) Considering Imperfect Quality: A Case Study of Indonesian Food Manufacturing Industry

Ilyas Masudin*, Yudha Firmansyah, Dana Marsetiya Utama, Dian Palupi Restuputri*, Evan Lau
Industrial Engineering, University of Muhammadiyah Malang, Indonesia
*Corresponding Author, E-mail: masudin@umm.ac.id, restuputri@umm.ac.id
November 23, 2020 ; April 4, 2021 ; April 14, 2021

Abstract


This study aims to control several decision variables, namely the frequency of ordering raw materials (m), the frequency of delivery of finished products (n), and the production cycle time (T) to maximize the total profit per unit time of the inventory-production integration system. The method used for this study is the optimization of mathematical models with non-linear equations. To optimize the model used MATLAB software by utilizing a genetic algorithm (GA) tool. The output of this research is the proposed policy in managing inventory-production. The results of numerical calculations show that the research model policy provides a better total profit than the company’s policies. This research develops the integrated inventory-production (IIP) model considering imperfect quality (products return). Model performance is measured based on the total profit of the inventory-production integration system



초록


    1. INTRODUCTION

    Food security is one of the main problems throughout the world. In 2012-2014, the UN Food and Agriculture Organization reported that more than 800 million (15%) people in the world were still malnourished (FAO, 2014). Despite this fact, roughly 1.3 billion tons of food for human consumption or one-third of the food produced is wasted per year throughout the world at various stages in the supply chain. Data from the National Development Planning Agency (Bappenas) states that Indonesia ranks second as the world’s largest food waste producer by 2018. The food industry recalls expired products for disposal as a form of environmental preservation and branding company (Grenchus et al., 2001). In the supply chain, 40% of losses occur in overproduction in the post-processing stage due to a lack of coordination among the supply chain (Gustavsson et al., 2011). This supply-demand mismatch can be prevented by synchronizing production and supply policies along the supply chain with demand. Food products flow through various stages throughout the supply chain, where their quality decreases with different damage behavior depending on their shape (Heldman, 2013). Therefore, adjustments to the production process are needed to maintain the quality of the finished goods. Tsiros and Heilman (2005) reported that customer willingness to pay for a product decreases as it approaches the expiration date. During this period of degradation, without any action such as a decrease in price (discount), the demand level would decrease and create high expired products that would expire. Thus, in other words, it leads to a reduction in profits due to a decrease in sales and a considerable expense to manage an outdated product.

    Integrated Inventory-Production (IIP) was first discussed by Goyal and Deshmukh (1992), namely, a mathematical model that integrates raw materials from suppliers to retailers’ finished products. The model continues to grow, including involving many aspects in the mathematical model, such as pricing (Huang et al., 2018;Taleizadeh et al., 2016), backorders (Masudin et al., 2019a;Rad et al., 2014) and carbon emission (Hammami et al., 2015). A study by Dev et al. (2020) reveals that the diffusion of returned materials issues during inventory and production planning affects significantly on the financial and operational performance of the company. The decline in the quality of raw materials that occur linearly is illustrated in the study of Fauza et al. (2016). In their research, model of IIP is formed by integrating the raw material inventory system at the factory to deliver the finished product at retail. However, the integration model has not considered the finished product returned. Thus, to solve the supply chain integration problem, this research develops the IIP model by adding the variable number of return products to determine supply chain decision variables. In this study, the optimal variable’s determination is done by computing Matlab using a Genetic Algorithm to find a solution close to optimal. The IIP model developed will be evaluated for its potential application in the food industry. It is expected to be an alternative policy in managing supply chain activities and maximizing total company profit.

    The rest of the paper is organized as follows: section 1 (introduction) discusses the background of this study and fills the gap of previous studies. Section 2 discusses the related studies that contributed to developing the framework. Then, the model development is discussed in the next section, followed by the section 4, which discussed the results analysis. The later section of this article will be the sensitivity analysis for discussion. Then, the final section of this article is the conclusion

    2. LITERATURE REVIEW

    2.1 Inventory-Production Integration

    Coordinating the production and supply policy of food products is very complicated, both of which will naturally decline in quality over time. The study was initiated by Ghare (1963), who proposed a mathematical model to represent the inventory of perishable goods. In subsequent studies, a mathematical model that considers the level of product damage has more to do with stock I (t), which is depleted instantly due to the level of demand D (t) and the rate of quality loss (k). Since its introduction, this model has been adopted as the primary production inventory policy model for perishable goods. Park (1983) integrates the production-inventory policy to assume that raw materials rot in storage before being used by the production process. Raafat (1985) expanded it to include a decline in the quality of finished goods. Goyal and Deshmukh (1992) proposed the IPP (Integrated Procurement- Production) model is an integrated inventory model from the inventory system of raw materials to finished products at the factory. Fujiwara and Parera (1993) introduced the development of the EOQ model that had not previously considered the quality reduction that each product waiting for would be charged a penalty, so it was appropriate for products that experienced deterioration, such as food products. Kim and Ha (2003), with a joint economic lot size JELS model is an integrated inventory model from the inventory system of raw materials and finished products in factories to retailers. Then, Yang and Wee (2003) and Rau et al. (2004) further develop the JELS model by advancing a model that considers several downstream shipping policies through the production cycle in a multi-stage supply chain. Furthermore, in the study of Yu et al. (2012) and Taleizadeh et al. (2015) studied multi-stage models with different damage characteristics of raw materials and finished goods. Wu et al. (2006) and Ouyang et al. (2006) introduced a noninstantaneous model of quality loss, that is, only after a certain period in storage the inventory level began to deteriorate, with demand dependent on stock. Then, Chang et al. (2010), and Geetha and Uthayakumar (2010) extend the model from Wu (2006). Chang et al. (2010) changed the object to maximize total profits, while Geetha and Uthayakumar (2010) allowed shortages with partial backlogs. Food products run in various stages throughout the supply chain where the quality of the product decreases with different damage behavior depending on its shape (Heldman, 2011). For example, the quality of peanuts as raw material, in terms of physical condition will decrease with storage time (Mioe, 2003). Therefore, adjustments to the production process are needed to maintain the quality of the finished goods. Then, on the retailer shelf, customers usually feel the value of the product from the remaining life. Tsiros and Heilman (2005) report that the customer’s willingness to pay (WTP) for a product begins to decrease as it approaches the expiration date. During this period of degradation, without any action, for example, providing a discounted price, the level of demand will decrease, thereby reducing profits due to an increase in the number of items in expiration.

    The development of inventory-production model continues by considering other aspects of inventory and production processes such as setup costs, shortage, demand, and lot sizing techniques. A study by Dey et al. (2019) considers setup up costs and shortage in inventoryproduction model and found that setup cost and shortage play a significant rule on the total revenue. Other studies discuss the impact of demand on the model of inventoryproduction problems. The stochastic or deterministic demands would influence the model of production rate that change the total cost of supply chain (AlDurgam et al., 2017). Moreover, Kim and Ha (2003) concluded that lot size techniques should be considered when modeling inventory and production problems. This is because lot sizing approach such as EOQ, EPQ and lot for lot method is the main point of inventory system which affect total inventory costs (Nobil et al., 2020).

    2.2 Inventory Production Integration with Quality Deterioration

    The study of the integration of procurement and production is a combined system to get maximum benefit by considering several cost constraints and resource availability capacity. Many previous studies have been conducted by including other echelons in the supply chain network, especially inventory. Ashayeri and Selen (2003) consider inventory costs into the aggregate inventory planning model. Kim and Ha (2003) carry out the integration model by considering the inventory system by incorporating the model’s just-in-time approach. In contrast, Yang and Wee (2003) and Chowdhury et al. (2015) model inventory and production integration by considering multi- lot-size production. Inventory and production integration related to meeting customer demand has also been carried out in several studies related to stock-dependent demand and backlogging (Mashud et al., 2018) and backorder (Masudin et al., 2019a).

    The problem of integrating production and inventory models is mathematically modeling the forward supply chain network and considering the backward supply chain network’s direction. The integration model by considering product quality is an issue that has received enough attention. Research with a close loop supply chain approach that considers a decrease in product quality due to the product life cycle factor has received attention from researchers and practitioners. Rau et al. (2004) modeled an integrated inventory model by considering product deterioration, while Blackburn and Scudder (2009) and Taleizadeh et al. (2015) modeled the integration of production inventories taking into account quality degradation for food products. The product expiration and shelf-life factors have been considered factors that influence prices and profits in the inventory and production integration models (Fauza et al., 2018a).

    2.3 Inventory and Production Integration Approaches

    The approach used in completing the inventory and production integration model that considers the quality loss in the supply chain network will depend on the objective function to be achieved. Some inventory and production integration studies before the 2000s were carried out using more classical heuristic approaches such as dynamic programming (Budijati and Iskandar, 2018;Crowston et al., 1973), Tabu search (Masudin et al., 2019b) and branch and bound (Masudin, 2015;Schwarz and Schrage, 1975). While lately, the metaheuristic approach is more widely used to solve inventory and production integration. Several approaches from inventory and production model research that considers quality degradation can be found in Yu et al. (2012), which uses mixed integer programming to determine total inventory costs and quality degradation. Simultaneously, Rong et al. (2011) use a simple algorithm to solve an inventory and production integration model to minimize total costs, including the cost of quality degradation. Other studies conducted by Fauza et al. (2018b) and Tarhini et al. (2019) uses a genetic algorithm approach to solve inventory integration models to determine the minimum total inventory cost.

    3. MODEL DEVELOPMENT

    In this study, the Integrated Inventory-Production model from Fauza et al. (2016) will be developed by adding a notation of the number of products returned by retail. Supply Chain Activity Model by considering product return in the company can be shown in Figure 1.

    Figure 1 explains that the forward logistic flow is produced and distributed as much as a specified number of batches returns demand (Dret) from retail and expired products.

    3.1 Model Development Considering Product Returns

    This study developed an inventory-production model of Fauza et al. (2016) with retail products’ return. The number of products returned is food products from companies that have reached the expiration period of retail to be disposed of or destroyed to pollute the environment. The assumptions used in this study is related to the number of products that can be returned by retail to the manufacturing process, which fulfills a total of 1 batch sent from the company. Suppose it does not reach the quantity of 1 batch, products will not be accepted for a return to the manufacturer if less than that. Returns of expired products increase the production demand because the manufacturer will offer new products with a more extended expiration period at the retail number of products returned. Thus the production limits change to be as follows:

    P > D + R

    • Information:

    • P : The rate of production at the company

    • D : Demand for each retail

    • R : Total number of retail return products

    3.2 Returns Costs

    Product returns incur costs borne by the company as the final performer of the product flow. Costs incurred by the company to follow up on the return of expired items are product management (destruction). For the product return equation as follows:

    R e t u n s   c o s t s = j = 1 N R r e t j . c R

    • Notation:

    • Rretj : Number of product returns from retail j

    • cR : Return costs

    Thus the objective function equation used to minimize total TCmfc costs is added to the product return management notation as follows:

    T C m f c ( n , T ) =   c m f c D + A m f c T + H m f c [ j = 1 N d r e t j l = 1 j d r e t 1 T n P   T 2 j = 1 N d r e t j ( 1 D P   1 n ) ] + j = 1 N R r e t j . c R

    3.3 Mathematical Model Development

    Figure 2 shows two levels of inventory in a supply chain with a single supplier - multiple buyers. The first inventory system is raw material inventory. Manufacturers (producers) place an order of raw materials from suppliers as many times m times with order quantities q r a w   = D . T / m . Raw materials are consumed at the P level during the production time (τrun), where τ r u n = D . T / P . Thus, raw materials arrive at the factory warehouse at time intervals τrun/m during one production cycle T. The second inventory system is the inventory of finished products in manufacturing and retail. Manufacturers process requests from all retailers during T and then send them n times at the same interval for each retail. In the delivery of finished products, the age of each batch ( E i j ) , is known. It is the length between when the first product in a batch is produced and when it is sent. Accordingly, the age of the batch i received by retail j may differ from other batches, depending on the storage time before shipping. The first shipment is immediately carried out after production meets the batch size ( q r e t j ) , while the next shipment is carried out at the τΔ interval. The size of shipment of finished products to retailers q r e t j =   d r e t j . T / n , as long as the product at retailer j is consumed at a constant level of d r e t j .

    The mathematical model developed to solve the problem of inventory-production integration in this article consists of three stages. The first is linearly modeling the quality of raw materials. Then the second model represents the price function based on shelf life. The third model is the total profit of the integrated system. Linear degradation of raw material quality can be calculated using Equation (1).

    Q ( t ) = Q m a x k t
    (1)

    where Q(t) is the product quality at the time (t) . Therefore, the value of quality loss during the 0-t (i.e., from Qmax to Q(t)), denoted by ΔQ(t) , d can be calculated using Equation (2).

    Δ Q ( t ) = k t
    (2)

    The total cost caused by a decrease in the quality of raw materials or L(m,T) can be calculated using Equation (3).

    L ( m , T ) = c l o s s m P T 0 D T m P Δ Q ( t ) d t
    (3)

    The next step is to model the value of losses that arise due to quality degradation in the finished product. The final product is food that has an expiration date on the packaging. According to Fauza et al. (2015), customers feel the product’s value decreases as it approaches the expiration date. So the retailer applies the price reduction policy (see Figure 3) using Equation (4).

    p ( t ) = { p m a x P m i n p m i n +   P m a x   p m i n τ s l   τ S t a r t ( τ s l t ) t     < τ S t a r t       τ S t a r t t < τ s l t    τ s l           a r e a   I   a r e a   I I       a r e a   I I I
    (4)

    Because each product’s price in a batch may not be the same (depending on the remaining shelf life), the batch transfer age from manufacturer to retailer needs to be considered because it can affect total revenue. The formula for calculating the period of batch 1 for all retailers ( E 1 j ) can be done using Equation (5), while for the remaining batches (i = 2, 3,…, n), and the age of the product can be calculated using Equation (6).

    E 1 j =   d r e t j T n P
    (5)

        E i j =   d r e t j T n P + ( i 1 ) [ T n j = 1 N n d r e t j T n P ]
    (6)

    It is expected that retailers only accept batches that have E i j less than start τstart to generate more revenue. Thus, each batch i received from the retailer will follow in the following 3 cases depending on the time the product was last consumed or E i j + τ Δ .

    • Case 1: E i j + τ Δ < τ s t a r t , then the monthly revenue obtained from this batch is determined by Equation (6.1)

      R i j ( n , T ) = d r e t j T P m a x τ Δ
      (6.1)

    • Case 2: τ S t a r t E i j + τ Δ s l , then the monthly revenue from a batch is shown in Equation (6.2).

      R i j ( n , T ) = d r e t j T [ P m a x ( τ S t a r t E i j ) + τ S t a r t E i j +   τ Δ p ( t ) d t ]
      (6.2)

    • Case 3: E i j + τ Δ s l , then Equation (7) represents the monthly revenue function of this batch.

      R i j ( n , T ) = d r e t j T [ P m a x ( τ S t a r t E i j ) + τ s t a r t τ s l p ( t ) d t + p m i n ( E i j + τ Δ τ s l ) ]
      (7)

    The next step is to model the total cost to accommodate the integration system to get the maximum total profit. The manufacturing department will incur expenses for the procurement and handling of raw materials, T C r a w ( m , T ) , consisting of purchase costs, shipping costs, inventory storage costs, and cost of quality degradation. The total cost is shown in Equation (9).

    T C r a w ( m , T ) = c r a w D +   A r a w m T + H r a w D 2 T 2 m P +   c l o s s m P T 0 D T m P Δ Q ( t ) d t
    (8)

    Manufacturing bears some costs associated with handling finished products before going to retailers. The average inventory of finished products in manufacturing (Imfc) can be calculated by subtracting the average retail inventory from the total system inventory shown in Equation (9).

        I m f c = j = 1 N d r e t j l = 1 j d r e t 1 T n P   T 2 j = 1 N d r e t j ( 1 D P   1 n )
    (9)

    Costs for storing inventories of finished products are obtained by multiplying the average by the cost of keeping inventory per unit item per month. Therefore, the total costs for processing and handling finished products are charged to manufacturers, T C m f c ( n , T ) , consisting of production costs, setup costs, storage costs, and return costs for expired products represented by equation (10).

    T C m f c ( n , T ) =   c m f c D + A m f c T + H m f c [ j = 1 N d r e t j l = 1 j d r e t l T n P T 2 j = 1 N d r e t j ( 1 D P   1 n ) ] + j = 1 N R r e t j . c R
    (10)

    With the selling price per unit of manufacturing product, the total profit per month from manufacturing, T P m f c ( m , n , T ) , can be obtained by subtracting the total cost from total revenue, shown in Equation (11).

    T P m f c ( m , n , T ) = c r e t D T C r a w ( m , n , T ) T C m f c ( m , n , T )
    (11)

    The retailer’s portion bears several relevant costs: purchase costs, ordering costs, and holding costs formulated by the Equation (12).

    T C r e t ( n , T ) =   c r e t D + n T j = 1 N A r e t j + j = 1 N H r e t j d r e t j T 2 n
    (12)

    The total monthly profit of all retails, T P r e t ( n , T ) , is obtained by subtracting Equation (12) of total monthly income as in Equation (13).

    T P r e t ( n , T ) = j = 1 N i = 1 n R i j ( n , T ) T C r e t ( n , T )
    (13)

    Total profit from the entire supply chain, TP(m, n, T) , is obtained by adding total manufacturing and retail profits. Therefore, an integrated supply-production strategy can be expressed by equation (14).

    T P ( m , n , T ) = T P m f c ( m , n , T ) + T P r e t ( n , T )
    (14)

    Subject to:

    P   D + R
    (15)

    m   τ r u n τ m a x
    (16)

    E i j < τ s t a r t ; for i = 1 , 2 , , n and j = 1 , 2 , , N
    (17)

    T > 0
    (18)

    m , n > 0 ( Integer ) ;
    (19)

    • Maximizing:

    The next step of this research is to conduct a numerical test on a case study to determine the decision variables m, m, T that maximize the total profit of the integrated inventory-production system (JTP).

    • Notations:

    • For manufacturer

    P

    : production rate (product unit/time unit)

    D

    : total demand level from all retails (product units/time units)

    R

    : Total number of retail return products

    α

    : the ratio of total demand to production levels

    K

    : deterioration rate (unit quality/time unit)

    η

    : the reaction factor of the kinetic model reaction

    Qmax

    : maximum quality level of raw materials (unit quality)

    Qmin

    : minimum quality level of raw materials (unit quality)

    Q (t)

    : the level of quality of raw materials remaining at time t (unit quality)

    τmax

    : the maximum duration of raw materials stored in a warehouse (unit of time)

    craw

    : cost of purchasing raw materials ($/unit of product)

    Araw

    : shipping cost of raw materials ($/shipping)

    qraw

    : the size of raw material order (product unit)

    Hraw

    : storage costs for raw materials ($/unit of product/unit of time)

    Closs

    : loss of quality costs ($/unit quality/unit time)

    CR

    : return costs

    L (m, T)

    : total cost of losing quality ($/unit time)

    TCraw (m, T):

    : total cost of procuring and handling raw materials ($/unit time)

    Cmfc

    : production costs ($/unit of product)

    Amfc

    : production set-up fee ($/arrangement)

    Hmfc

    : cost of storing finished goods at the factory ($/Unit of product/unit of time)

    Imfc

    : the average inventory of finished goods at the factory (product unit)

    τrun

    : operating time of production, where τrun = D. T / P (unit of time)

    TCmfc (m, T)

    :total costs for processing and handling finished goods ($/unit time)

    TRmfc

    : total manufacturing revenue ($/unit time)

    TPmfc (m, n, T)

    : total profit from manufacturing ($/unit of time)

    • For retailer

    Cret

    : the selling price of products from manufacturing to retail ($/unit of product)

    dretj

    : retailer demand level j (product unit/ time unit)

    Hretj

    : cost of storing finished goods at retail j ($/unit of product /unit of time)

    Aretj

    : transportation costs for sending products to retailers j ($/shipping)

    Rretj

    : Number of product returns from retail j

    τsl

    : product shelf life (unit of time)

    τstart

    : the time when the quality of the finished product begins to decrease (unit of time)

    Pmax

    : maximum product price ($/product unit)

    pmin

    : minimum product price ($/unit of product)

    p (t)

    : product price at age t ($/unit of product)

    Eij

    : age of batch i when it arrives at retail j (unit of time)

    qretj

    : shipping size for retailer j (product unit)

    τΔ

    : delivery interval for finished goods (unit of time)

    TCret (n, T)

    : total cost in the retail system ($/unit of time)

    Rij (n, T)

    : batch i income at retailer j ($/unit of time)

    TRret

    : total retailer income ($/unit of time)

    TPret (n, T)

    : total profit from retailers ($/unit of time)

    TP (m,n,T) :

    : total profit from integrated supply chain systems ($/unit of time)

    • Indeks

    i

    i : i-th batch is sent to retail (i = 1, 2, ..., n)

    j

    : jth retail (j = 1, 2, ..., N)

    • Decision variables

    m

    : the frequency of ordering raw materials for one production cycle

    n

    : frequency of delivery of finished products for one production cycle

    T

    : Production cycle time in manufacturing (unit of time)

    4. RESULTS AND DISCUSSION

    This research uses the Inventory-Production Integration Model, where the functions discussed in the previous chapter aim to find the company’s total profit. The inventory- production integration model in this article also considers product returns to accommodate expired products. The parameter setting of the Genetic Algorithm (GA) tool refers to Fauza et al. (2016) such as population size of 100 individuals, crossover rate of 0.7, migration for every 20 generations with a rate of 0.2, stopping rule is a maximum of 100 generations, lower bound [1 1 0], the upper bound: [100 100 1]. Other parameters are set the same as the default values. Furthermore, these parameters are used in Equation (14) and run in the Genetic Algorithm (GA) tool using the Matlab R2014a software.

    4.1 Genetic Algorithm Numerical Results

    Because the decision variable sought is the values of m, n, T, the variable is used as chromosome-forming genes. The limit values of variables m, n, and T are real numbers 0 to 1 as input parameters in the GA Tool. Then the variable real numbers m, n, T generated by GA Tools are converted to integer numbers with the following conditions:

    • Max value = [100 100 1]

    • Min value = [1 1 0]

    • m = round (min value (1) + x (1) * (max value (1) –min value (1)))

    • n = round (min value (2) + x (2) * (max value (2) –min value (2)))

    • T = min value (3) + x (3) * (max value (3) –min value (3))

    Integer numbers for variable m are represented with ranges from 1 to 100, variables n with ranges from 1 to 100, and variables T with ranges from 0 to 1. This is to represent supply chain activity decisions during the production cycle.

    4.2 Initialization Process

    According to predetermined limits, the initialization process is carried out by generating the chromosome’s initial values on the chromosome with random values. In generating gene values, the formula = BB + r x (BA – BB) is used, where r is a random number between (0, 1), BA is the upper limit, and BB is the lower limit. In this case, using 0 ≤ xi ≤ 1Thus mathematically for gene 1 on chromosome [1] can be written as follows:

    x 1 = BB + r x  ( BA – BB ) = 0 + 0.0842 x  ( 1-0 ) = 0.0842 x 2 = 0.0942 x 3 = 0.3650 m =round (min value (1)+x(1) * (max value (1) - min value (1))) = round (1+0.0842 * (100 - 1)) = 9 n = round (min value (2)+ x(2) *(max value (2) - min value (2))) = round (1 + 0.0942 * (100 - 1)) = 10 T = min value (3) + x(3) * (max value (3) - min value (3)) = 0 + 0.3650 * (1 - 0) = 0.3650 p o p u l a t i o n = [ 9 10 0.3650 10 8 0.3650 8 9 0.3250 9 10 0.3550 8 11 0.4650 ]
    (1b)

    In this case, the population is determined to be 5, then:

    • Chromosome[1] = [m; n; T] = [ 9; 10; 0.3650]

    • Chromosome[2] = [m; n; T] = [10; 8; 0.3650]

    • Chromosome[3] = [m; n; T] = [8; 9; 0.3250]

    • Chromosome[4] = [m; n; T] = [9; 10; 0.3550]

    • Chromosome[5] = [m; n; T] = [8; 11; 0.4650]

    4.3 Chromosome Selection

    The selection process makes a chromosome with a large total profit (objective function) with a high probability of being chosen or has a high probability value because the fitness function is directly related to the objective function. For the case of maximization, the fitness function F (x) = f (x) is used, where f (x) is the objective function of the problem being solved. The results of the calculation of fitness in the five samples can be seen in Table 1.

    Then the probability value is determined to find out what chromosome will be chosen in the next generation. The formula for finding probabilities is:

    P[i] = fitness [ i ] total fitness
    (1c)

    From the probabilities above, the 3rd chromosome has the greatest fitness; then, the chromosome has a greater probability of being selected in the next generation than the other chromosomes. Next, for the selection process using the roulette wheel mechanism, a cumulative value of probability is needed.

    • C[1] = 0.2004

    • C[2] = 0.2004 + 0.2002 = 0.4006

    • C[3] = 0.2004 + 0.2002 + 0.2008 = 0.6014

    • C[4] = 0.2004 + 0.2002 + 0.2008 + 0.2003 = 0.8017

    • C[5] = 0.2004 + 0.2002 + 0.2008 + 0.2003 + 0.1983 = 1

    In roulette wheel selection, the value of each chromosome has a chance to be selected. The area in this circle shows the opportunity for each solution to be chosen. The highest opportunity to be selected for parents is chromosome 4 and 5 because it has the greatest fitness value. The chromosome selection opportunity area can be seen in Figure 4.

    After obtaining the cumulative probability value, the selection process using the roulette wheel can be carried out. The first process is carried out by generating random numbers (R) from 0 to 1. If R[k] < C [1] then select chromosome 1 as the parent, in addition select the kchromosome as the parent with the condition C[k- 1] < R < C[k]. Furthermore, the roulette wheel mechanism is carried out five times (generating random numbers). The random number (R) is paired with one chromosome for the new population at each value. The cumulative probability value results and generating random numbers (R) can be seen in Table 2.

    Then based on Table 2, the cumulative probability value is compared with random numbers on each chromosome. The following calculations:

    • R [1] = 0.4006 <0.5839 <0.6014, (selected Cum [3])

    • R [2] = 0.6014 <0.6262 <0.8017, (selected Cum [4])

    • R [3] = 0.8017 <0.9153 <1, (selected Cum [5])

    • R [4] = 0.2004 <0.3987 <0.4006, (selected Cum [2])

    • R [5] = 0.932 <0.2004, (selected Cum [1])

    Based on the above calculation, the first random number R [1] is more significant than C [2] and smaller than C [3], so choose chromosome [3] as the chromosome in the new population, and so on. From the random numbers generated above, the latest chromosome population from the selection process is as follows.

    • Chromosome[1] = chromosome[3]

    • Chromosome[2] = chromosome[4]

    • Chromosome[3] = chromosome[5]

    • Chromosome[4] = chromosome[2]

    • Chromosome[5] = chromosome[1]

    The new chromosome results from the selection process:

    • Chromosome[1] = [8; 9; 0.3250]

    • Chromosome[2] = [9; 10; 0.3550]

    • Chromosome[3] = [8; 11; 0.4650]

    • Chromosome[4] = [10; 8; 0.3650]

    • Chromosome[5] = [9; 10; 0.3650]

    4.4 Crossover

    The method used is the one-cut point, randomly selecting one position in the parent chromosome, then ex- changing genes. The parent chromosome is chosen randomly, and the number of chromosomes undergoing crossover is affected by the crossover_rate (Pc) parameter. In this case, a crossover probability value of 0.7 is determined; it is expected that in one generation, there will be 70% of chromosomes undergoing a crossover process. The first process carried out is to generate random numbers (R) as much as the population. The next chromosome to k will be selected if R[k] <Pc. The following can be seen in the population experiencing crossovers in Table 3.

    Based on Table 3, from the random number (R) above, chromosome [1], chromosome [3], and chromosome [4] are used as the parent. After making the parent selection, the next process is to determine the position of the crossover. This process is done by generating random numbers with a limit of 1 to the chromosome’s length. There are 3 genes in the chromosome, so random numbers are generated using limits 1 to 3 to determine the cutpoint crossover’s position. Suppose that the crossover position is 1, the parent chromosome will be cut from the 1st gene then the gene pieces are exchanged between the parents.

    Chromosome[1] >< chromosome[3]

    Chromosome[3] >< chromosome[4]

    Chromosome[4] >< chromosome[1]

    The next step for the crossover treatment is on chromosome [1] with chromosome [3]

    The cut-point crossover position was selected using random numbers 1-3, obtained the value of R = 2

    IEMS-20-3-412_Meq3c.gif

    In the same way a crossover process between chromosome [3] with chromosome [4] and chromosome [4] with chromosome [1]. The following can be seen the parent chromosome that u undergoes a crossover in Table 4.

    Thus the chromosome population after undergoing a crossover process becomes:

    • Chromosome[1] = [8; 11; 0.4650]

    • Chromosome[2] = [9; 10; 0.3550]

    • Chromosome[3] = [10; 8; 0.3650]

    • Chromosome[4] = [10; 8; 0.3250]

    • Chromosome[5] = [9; 10; 0.3650]

    4.5 Mutation Processes

    The mutation rate parameter determines the number of chromosomes mutated in a population. The mutation process is carried out by replacing one randomly selected gene with a new value that is randomly obtained. The first process is to calculate the total length of genes in a population. In this case, the total length of the gene is as follows:

    total_gene =  ( number of genes in chromosome ) x number of population = 3 x 5 = 15

    In choosing the mutated gene’s position, it is generated by generating random integers between 1 to total gene, which is 1 to 15. If the random number generated is smaller than the mutation rate variable (Pm), then select that position as a sub-chromosome that has a mutation. In this case, a Pm value of 0.1 is determined; it is expected that there are 10% of the total genes that have mutations.

    Number of mutations  = 0.1 x 15 = 1.5 = 2

    Then there are two populations of chromosomes that will mutate. After that, generate random integer numbers between 1 and 15 to determine the exchange position (exchange point). Then generate random numbers between 0 and 1 to determine the population of chromosomes that will undergo mutations. The following results from generating random numbers, and the selected chromosome will undergo a mutation process, as shown in Table 5.

    Table 5 shows a chromosome with mutations, namely the 2nd chromosome and the 4th chromosome. It shows that the exchange position (exchange point) for chromosome [2] in gene number 5 and chromosome [4] in gene number 10. Furthermore, the value of genes in that position is replaced with random numbers (R) between 1 and 22.

    Table 6 shows the generation of random numbers (R) to substitute gene values with a range of 1 to 22, the replacement value for chromosome 2 is 11, and chromosome 4 is 9. Table 7 shows the maximum total profit from the decision variables (m, n, T) in Matlab processing. The policies given are shipping raw materials eight times, shipping finished products eight times/month, and production cycle time of 0.3250.

    As seen in Table 7, from the inventory-production integration model developed in this study, it was obtained the optimal results of the frequency of sending raw materials (m) 7 times (m = 7) and the frequency of product shipments (n) being as many as 8 times (n = 8) for 0.3041 months (T = 0.3041). The integration model’s total profit gives the combined total profit of the system (profits at the manufacturing and retail levels) of $ 218,869.29. This profit is higher than 17% of the policies that companies without system integration. In addition, Table 1 also shows that the policy of the integration model of invento- ry and production, taking into account the returns in this article, has been proven to affect the total cost of the factory/ manufacturing, which has decreased from $111,333 to $66,711.43 or 44% lower than the model without integration.

    5. SENSITIVITY ANALYSIS

    Sensitivity analysis is carried out on several parameters involved in the model to determine its effect on the decision variable and the total profit. In this article, sensitivity analyzes are carried out on the parameters of production level (p), the rate of decline in the quality of raw materials (k), changes in costs as a result of quality degradation (Closs), and changes in the initial deterioration time (Tstart). This analysis is carried out to aim that decision- makers can take various policy alternatives to optimize the objective function of the model.

    5.1 Impact of Changes in Production Rate (P)

    The effect of changes in the level of production (P) on the total profit is tested. Changing the value of production levels by giving α, starting from 0.1 to 0.9, provides a significant profit change. The results are shown in Figure 5.

    Figure 5 shows that the smaller the value of α will cause the production cycle (T) to increase and the delivery of finished products to increase. This indicates that if the amount of demand that can be produced will reduce setup costs. Moreover, the number of finished products shipped will impact the amount of company revenue, thereby potentially increasing total profit. Furthermore, the closer to 1, the potential to increase manufacturing inventory costs. Due to the lack of products that can be produced, the number of finished products decreases, and the total profit decreases. Based on the analysis carried out in this article, regulating production levels close to the demand level tends to improve supply chain performance. So with these results, the company can increase the production level by adding production machines to maximize revenue. This is in line with research conducted by Blackburn and Scudder (2009), which explains that strategies for perishable types of products can be anticipated by controlling their production levels to reduce quality degradation throughout the supply chain and maximize profits.

    5.2 Impact of Declining Quality of Raw Materials (k)

    The effect of change in the rate of decline in raw materials (k) is performed to the total profit. Figure 6 shows that the higher the value of k, the frequency of delivery of raw materials also increases. This is to avoid the risk of greater loss of quality in raw materials that experience a linear decline in quality. With the higher k value, the total profit decreases. The raw material for food products in warehouses has reduced quality to increase the cost of quality loss (Closs). Based on the analysis carried out in this article, the manufacturer can provide other alternatives in the warehouse management so that the conditions, temperature, and environment of the storage room follow the characteristics of the raw materials to reduce the level of quality loss. This is in line with Rong et al. (2011), who found that temperature is one of the main aspects to maintain food quality.

    5.3 Cost Changes due to Quality Loss (closs)

    Figure 7 shows that the higher the quality loss (Closs), the frequency of delivery of raw materials also increases. The high costs incurred to bear the number of raw materials that are of low quality will add to the manufacturer’s expenditure. The company can carry out a policy to increase the ordering of raw materials (m) to ensure the quality of raw materials produced at a higher quality level to avoid spending greater costs. This has also been studied previously, with an increasing quantity of raw materials and production levels that will reduce the cost of quality loss (Fauza et al., 2015).

    5.4 Impact of changes in Initial Deterioration Time (T_start)

    A further sensitivity analysis is carried out to see the effect of changes in the initial deterioration time (Tstart) on the total retail revenue. The results are shown in Figure 7.

    Figure 8 indicates that the smaller the Tstart, the frequency of delivery of finished products increases. This happens to avoid the risk of decreasing the finished product’s value because of the faster initial deterioration time (Tstart) will increase the frequency of finished products and decreased total retail revenue. According to Tsiros and Heilman (2005), the decline in retail income occurs because if the product is nearing the expiration period will be less attractive to consumers, so it is reluctant to buy. This situation makes the income received by retailers decline. But on the contrary, if the product has a long deterioration period (Tstart) then the decrease in income is not too significant or even does not decrease at all if the product runs out before the expiry time. It can be concluded that food products with shorter shelf life need to be handled more accurately to ensure that the supply chain system is running the best performance. Therefore, companies need to arrange delivery of finished products so that retailers get products with a relatively long expiration period and implement a policy of price reduction (discounts) to be sold immediately.

    5.5 Managerial Implications

    The results of this study indicate that regulating production level have a significant influence on the operational and financial performance of the developed models. This information is important for the middle management of the company to forecast the demand accurately. Collaborative Planning, Forecasting and Replenishment (CPFR) could be applied to maintain the variations between demand and manufacturing. The benefits of CPFR implementation on supply chain management performance have been studied in different level of supply chain such as manufacturing (Cristea and Khalif Hassan, 2018), vendor managed inventory (Choudhury et al., 2018), supplier (Alptekin et al., 2017). Moreover, the CPFR ensures the vocal companies and their partners along the supply chain have the same accurate information about the demand. The coordination between all parties from different chain channels would have ability to perform their best effort to meet the demand (Alptekin et al., 2017).

    Other significant results of this study are related to the relationship between the length of the product’s deterioration date and the company financial performance. As shown by Figure 7, it shows that the shorter products’ expiration date delivered to retailers, the increase income loss. Thus, the management of warehousing should be paid more attention by management. Some warehousing approach to arrange the deliveries from manufacturing to retailers based on the length of product’s expiration date. Warehousing management classification based on First Expired First Out (FEFO) could be applied ensures the products are delivered based on their expiration date. This approach is superior for the integration model of production – distribution problems with multi products and multi replenishment (Masudin et al., 2019b;Sazvar et al., 2016).

    The results of this study also found that there is an implication of the decline of raw material quality on company profit. It shows that the external environment such as temperature, air circulation and storage conditions impact seriously on the food raw material quality. It is clear that temperature and humidity significantly affect the quality of perishable material/products (Mahmood et al., 2019). Thus, traceability system should be applied along the supply chain to make sure that raw material delivered among each party had an appropriate treatment. The delivered raw material from previous processes should be labeled with information of temperature, humidity and storage condition. Tracking and tracing system information would be the alternative way for safety and quality of raw material and finished products (Aung and Chang, 2014;Masudin et al., 2021a;Masudin et al., 2021b).

    6. CONCLUSION

    These research models integrate inventory-production (IIP) systems in manufacturer-retailers by considering imperfect quality. In this study, a model of production and distribution problems was developed using mixed-integer programming and solved by using a genetic algorithm approach. The model built shows that the decline in product quality significantly affects the company’s financial performance. As a consequence, several variables related to quality deterioration are very important for management to pay attention to because they will also affect company revenue such as the frequency of ordering raw materials (m), frequency of delivery of finished products (n) and production cycle time (T). The integration of inventory- production problems and the implications of changing model’s variables on the company’s financial performance are important inputs for management to consider several managerial and operational policies by strengthening supply chain collaboration and some technical improvements on the production floor. For further research, it is recommended to extend the inventoryproduction model involving routing problems which considers carbon emission as the objective of the model. Moreover, future works could also consider adding the model with re-manufacturing processes for the returned product for the secondary market demand.

    Ilyas Masudin is a Professor of logistics and supply chain in the Department of Industrial Engineering, University of Muhammadiyah Malang, Indonesia. His research interests include logistics optimization and supply chain management.

    Yudha Firmansyah is a researcher in the Department of Industrial Engineering, University of Muhammadiyah Malang, Indonesia. His research interests are in statistics and operations management.

    Dana Marsetiya Utama is a lecturer and researcher in the Department of Industrial Engineering at the University of Muhammadiyah Malang, Indonesia. His research interests are in the area of optimization engineering, scheduling, and modeling.

    Dian Palupi Restuputri is a lecturer in the Department of Industrial Engineering at the University of Muhammadiyah Malang, Indonesia. Her research interests are in ergonomics and human factor engineering.

    Evan Lau is an Associate Professor in the Faculty of Economics and Business, Universiti Malaysia Sarawak, Malaysia. His research interests are in business economics, modeling and management.

    Figures

    IEMS-20-3-412_F1.gif

    Inventory-production model considering return product.

    IEMS-20-3-412_F2.gif

    Inventory of manufacturing systems - integrated retail.

    IEMS-20-3-412_F3.gif

    Price function based on the product shelf life of the batch (qretj).

    IEMS-20-3-412_F4.gif

    Chromosome selection probabilities.

    IEMS-20-3-412_F5.gif

    The effect of α changes on total profit.

    IEMS-20-3-412_F6.gif

    The effect of imperfect quality rate (k) on profit.

    IEMS-20-3-412_F7.gif

    The effect of quality loss (k) on profit.

    IEMS-20-3-412_F8.gif

    Initial deterioration time vs. retail revenue.

    Tables

    Fitness value recapitulation

    Cumulative recapitulation of probabilities and random values

    Selection of crossover populations

    Crossover results

    Determination of mutations in chromosome

    Gene value substitution

    Optimal result of the decision variables

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