an integrated production-inventory model for food products based on ...

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6 International Conference on Operations and Supply Chain Management, Bali, 2014

AN INTEGRATED PRODUCTION-INVENTORY MODEL FOR FOOD PRODUCTS BASED ON SHELF-LIFE PRICING Gusti Fauza School of Engineering, University of South Australia, Dept. of Food Science and Technology, Sebelas Maret University, Surakarta, Indonesia E-mail: [email protected] Yousef Amer School of Engineering, University of South Australia, Sang-Heon Lee School of Engineering, University of South Australia, Hari Prasetyo Study Centre of Logistics and Optimization Industry, Industrial Engineering, Muhammadiyah University Surakarta, Indonesia

ABSTRACT Existing studies on integrated production-inventory models for perishable items demonstrate that an inventory for such products will diminish due to demand and deterioration. They mostly assume that the quantity of stored item starts to deplete immediately. It does happen for certain perishable items such as gasoline, alcohol or radioactive materials. Over the self-life of numerous food products, such as vegetables, meat and bread, however, the quantity remains constant but the quality or value does deteriorate as the self-life approaches the expiration date. Unfortunately, less research is found addressing this circumstance particularly when a multi-echelon supply chain system is considered. For this reason, this research proposes a mathematical model of an integrated production-inventory system incorporating value degradation which is better suited to food products. This system comprises a manufacturer and a retailer. A shelf-life based pricing represents the value degradation at the retailer since the customers typically examine the quality of the purchased items based on its best-before-date (BBD). The objective function of the resultant model is to maximise the joint profit per unit time which is achieved by optimising the length of production cycle (T) and the ordering number of finished goods (n) over the production cycle. The conducted numerical test demonstrates that the established model could yield a significant potential saving compared to the existing models. Keywords: perishable items, inventory model, value degradation, shelf-life based pricing

1. INTRODUCTION Recently, the growth of research in the supply chain management area has created a new way in managing inventories of a multi-echelon system (Ben-Daya et al., 2008). A conventional inventory management approach where a company only focuses on its own inventory, disregarding their partner’s situation, may lead to sub-optimal improvement. Due to fiercer competition in the market nowadays, each company is advised to work collaboratively with their partners in managing the inventory across the supply chain to achieve the optimal performance of the whole system. 156

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A collaborative approach in managing the production and inventory between two parties i.e. manufacturer and retailer, can be achieved by determining the economic production and ordering lot sizes jointly between these two parties. This concept was initially introduced by Goyal (1977). In this scenario, the production and order quantities are decided by considering the joint variable cost between the manufacturer and the retailer. The model assumed an infinite production rate and a lot for lot shipment policy. Later, Hill (1997) relaxed this assumption to a general shipment policy and a finite production rate. Many other studies in this field (Banerjee and Kim, 1995, Ha and Kim, 1997, Kim and Ha, 2003) eradicated the limitation of the requirement to have the production lot being completed before delivering the ordering batches to the retailer. More recently, other factors such as investment to reduce some related costs, stochastic demand and three layer systems are investigated by many scholars in this area (Ben-Daya et al., 2008). All of the studies mentioned above, however, assume that the stored items can be stored infinitely. In real life, it is often found that numerous items such as fruit, vegetables and milk start deteriorating during the storage period. Ghare and Schrader (1963) firstly introduced a mathematical model of inventory for deteriorating items (Eq. 1). ( )

+  ( ) = − ( )

(1)

where I(t) refers to the inventory level over t, D(t) represents the demand rate at time t, and  is the deterioration rate of the item. The equation explicitly demonstrates that an inventory for perishable items is depleted by demand rate and a fixed fraction of the inventory or I (t ) which diminishes over time. Since the model was firstly introduced, it has been continuously developed to be more representative of capturing real life cases. Substantial literature reviews by Raafat (1991), Goyal and Giri (2001), Bakker et al. (2012) reveal that the majority research in perishable inventory areas can be referred to this model, where extensive extensions have been conducted to accommodate various conditions such as, different characteristics of demand (e.g. time varying, stock dependent and price dependent demand) and different types of systems (e.g. single echelon and multi-echelon system). The main drawback of these models is that the quantity of the stored items starts to deplete immediately once they arrive in the storage due to deterioration. The previous models might be accurate for representing inventory characteristics of some perishable items such as alcohol, gasoline and radio-active materials (Nahmias, 2011). They are however hardly applied to address an inventory for food products since for food products for over the shelf-life the quantity diminished only due to demand, while the quality is deteriorated over time. Customers typically perceive a fresher or younger product as a better quality product. They generally examine the product freshness in two ways, namely observing the sensory quality of the products (e.g. fruits or vegetables) or checking the product shelf-life e.g. bakery, noodles, milk and fully packed products (Entrup, 2005). Regarding the former, a study by Blackburn and Scudder (2009) introduced a product’s marginal value of time (MVT) of a fresh product such as water melon. They observed that as the value of water melon loses over time in the supply chain, controlling the picking rate and the transfer batch size can be an appropriate strategy to minimize the value loss and maintain the product freshness across the supply chain. Unfortunately, this approach is not suited for managing food products with explicit expiration date, such as bakery, noodles, etc. With food retailers, it is common that a customer justifies the freshness of a fully packed product from its BBD. As a result, they will tend to purchase products with a longer remaining 157

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lifetime. Research by Tsiros and Heilman (2005) reported that the customers’ willingness to pay (WTP) for a product decreases once the product’s life is approaching its expired date. Consequently, the demand rate of the product during the WTP decreasing period will be slower. To manage this situation, retailers will initiate a reduced or discounted price to maintain the demand and prevent the product being outdated. The issue discussed above makes the strategy to manage perishable items more complicated. An integrated production-inventory model for food products between a manufacturer and a retailer needs to consider this situation when deciding the production and ordering lot sizes. Yan et al. (2011) extended an integrated production-inventory model of Kim and Ha (2003) by considering deteriorating items. This model, however, still viewed the deterioration as a function of inventory i.e. a fraction number of inventory is instantaneously and continually lost over time. Therefore, this research proposes a new approach in managing food inventory by accommodating the degradation value of the product perceived by customers based on its remaining shelf-life. The aim is to determine the manufacturer’s production cycle and the delivering number to the retailer over the production cycle such that the total profit of the manufacturer-retailer system is maximised. The remaining sections of this paper are organised as follows: Section 2 presents model assumptions and notation while Section 3 discusses the modelling formulation stages. Numerical tests explaining the behaviour of the proposed model are provided in Section 4, and the last section summarises this paper. 2. ASSUMPTIONS AND NOTATION 2.1. Assumptions The model is developed based on these following assumptions: a. Deterministic operation environment b. The manufacturers’ production rate and the retailer’s demand rate are constant. c. The production rate is greater than the demand rate d. The retailer pays transportation and order handling costs e. Lead time is neglect able. f. No shortage is allowed g. Customers’ willingness to buy products decrease linearly once the product reaches Tstart or time to deteriorate 2.2. Notation The following notations are adopted in the model. 1. For the entire supply chain : price maximum before customers’ WTP start decreasing pmax : product shelf-life TSL : time when customers’ WTP start decreasing Tstart : the age of batch i when entering retailer system and ready for sale Ei : duration time of batch i at retailer before customers’ WTP start Ai decreasing or ranged from Et i to Tstart : Ad i duration time of batch i at retailer before expired date or ranged from Et i to TSL R(n,T) : revenue 158

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TC(n,T) n T TP ( n, T )

: : : :

joint total cost between a manufacturer and a retailer the number of deliveries per production cycle (a decision variable) production cycle (a decision variable) total profit of the integrated system

2. For the manufacturer : production rate P : manufacturing cost per unit Cm S : setup cost for a production cycle : inventory holding cost hm 3. For the retailer : demand rate D : ordering cost Oc : inventory holding cost hr : fixed transportation cost per delivery F V : unit variable cost for order handling and receiving 3. MODEL DEVELOPMENT This section presents procedure for formulating a new inventory model considering food shelf-life and customers’ WTP. 3.1 Shelf-life Based Pricing It is a common phenomenon in a retailer that customers prefer to buy a product with a longer remaining lifetime i.e. the customers’ WTP decrease once the product approaches its expiring date (Tsiros and Heilman, 2005). Consequently, to maintain the demand and avoid outdated items, the retailer offers a discount to those outdating products. It is also mentioned that the WTP decrease can be linear such as in carrots, milk and yoghurt or exponential such as in beef and chicken. In this research, a linear WTP decrease is assumed before establishing the model (Figure 1).

Figure 1.Customers’ WTP starts decreasing at time = Tstart

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From Figure 1, three possible conditions of price are defined as represented by Equation 2.  p max 0  t  Tstart  p max TSL  Tstart  t  Tstart  t  TSL p (t )  (2) TSL  Tstart TSL  t  C t  0 where p(t ) represents the shelf-life based price function and Ct refers to the cycle time of each batch over one production cycle T or or C t  T / n . After defining the price function, then the revenue of any batch can be generated. Figure 2 present factors which influence revenue e.g. cycle time Ct , age of batch when received by retailers Ei , WTP decreasing time Tstart and product shelf-life TSL . Using the shelflife based price function in Equation 2, therefore, the structure of retailers’ revenue of each batch can be defined as the followings: 1. Case 1: if 0  C t  Ai then the maximum revenue can be obtained by selling all product in batch i as defined by Equation 3 R  DC t p max (3) 2. Case 2: if Ai  C i  Ad i then the revenue of selling batch i is defined by Equation 4 R  DAi p max  D

p max TSL  Tstart

Ct

T

SL

(4)

 t  Ei

t  Ai

3. Case 3: if C t  Ad i then Equation 5 represent the revenue function of this condition R  DAi p max  D

p max TSL  T start

Ad i

 TSL  t  E i  D

t  Ai


Ct

T

SL

t  Ad i

Figure 2. Shelf-life based price function of batch i 160

 t  Ei

(5)

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Since there will be no demand after the products’ expired date or TSL , then last equation, D

p max T SL  Tstart

Ct

T

SL

 t  E i , is equal to zero and the revenue function is changed into Equation 6.

t  Ad i

R  DAi p max  D


Ad i

T

SL

 t  Ei

(6)

t  Ai

3.2 An Integrated Production-Inventory Model Considering Shelf-Life Based Price Function This research is an extension of the integrated production-inventory model of Kim and Ha (2003) by applying shelf-life based price function to accommodate the quality or value loss of a food product because of WTP. From Equation 4-6, it can be seen that the age of batches entering the retailer or Ei is essential for maximizing the revenue of each batch. The earlier the batches enter the retailer the more revenue will be. Assuming that the lead time is insignificant or can be considered as zero, then Ei is equal to the storage time of any batch in manufacturer St i or time to deliver batch i . From Figure 3, the value of St i can be obtained using Equation 7. T DT St i  i  1  i  2 (7) n nP

Figure 3. Inventory in manufacturer-retailer system Total profit of the system is obtained by subtracting the total cost (Eq. 8) from total revenue as represented by Equation 9. 161

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 S DT  D n DT  Oc DT   TC (n, T )     hr   2  n   n  1 hm   F  V  T n  T 2n    T 2n  P TPn, T   R(n, T )  TC (n, T )

(8) (9)

4. NUMERICAL EXAMPLES A numerical test is conducted to examine the behaviour of the model and a benchmark to the previous model is presented as well. Similar to Yan et al. (2011), parameters in Kim and Ha (2003) are adopted in this test as can be seen in Table 1. Using optimisation tools in Matlab R2014a, the value of n and T are obtained as 8 times deliveries during 74 days of production cycle. The total profit using this approach is $ 31,442 per year. Further, a benchmark of the proposed model with the previous models is presented in Table 2. Table 1. Parameters in the proposed model

Parameters D P S hm

Value 4800 19200 600 6 7 25 50 1 50 0.167 0.125

hr Oc F V pmax TSL Tstart

unit/year unit/year $/cycle $/unit.year $/unit.year $/order $/deliver $/unit $/unit year year

Table 2 shows that the total profit of the proposed model is the highest compared to the previous models. As Kim and Ha (2003) ignored the fact that the value is deteriorated over time, the ordering cycle or T , therefore, is the longest among others (86 days or equal to 1130 unit per production cycle). This leads to $25,385 profit per year or 23.8% lower than the proposed model. Contrarily, Yan et al. (2011) assumed that the quantity is depleted by demand and decay and as a result the value of T is shorter (73 days) or equal to 959 units per production cycle. The total profit of this model is $26,828 per year or 17.19% lower than the proposed model. Table 2. The proposed model compared to the previous models

Model

Kim and Ha (2003)

Yan et al. (2011)

The proposed model

Production Cycle (T in days)

86

73

74

Number of deliveries (n)

3

3

8

Prod. lot size (Q)

1130

959

962

162

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Delivery lot size (q)

376

319

121

Outdating products

235

78

0

Total cost

11388

12014

11473

Total revenue

36773

38842

42915

Potential profit

25385

26828

31442

%increase in profit

23.8%*

17.19%*

*

percentage of the increase in profit from the proposed model compare to the corresponded model

The result in Table 2 also reveals that considering WTP of the products may increase the number of deliveries and consequently, reduce the number of outdating items. It appears that aside from potentially increasing the total profit, the proposed model is also beneficial to reduce the outdated items. 5. CONCLUSION A production-inventory model applying shelf-life based price function which accommodates value loss because of customers’ perception on product quality has been completed. The numerical test reveals that considering the value loss may lead to reduction in the number of outdating items and increase in total profit of the manufacturer and retailer system. It is also essential, however, to integrate the production schedule with a procurement raw materials plan. This integration may lead to a global optimal solution rather than a sub-optimal. Noting that deterioration in food as raw materials may be different from food as finished goods, the effort needed to prolong product shelf-life can be challenging as well. Therefore, extending this model to an integrated production-inventory system which covers a raw material procurement strategy and accommodating a preservation effort to lengthen the product shelf-life could be potential for further research. 6. ACKNOWLEDGEMENT The first author would like to thank the Australian Government Overseas Aid Program (AusAid) for supporting this research and Wendy Hartley for her assistance in the proof-reading of the manuscript. 7. REFERENCES Bakker, M., Riezebos, J. & Teunter, R. H. 2012. Review of inventory systems with deterioration since 2001. European Journal of Operational Research, 221, 275-284. Banerjee, A. & Kim, S. L. 1995. An integrated JIT inventory model. International Journal of Operations & Production Management, 15, 237-244. Ben-Daya, M., Darwish, M. & Ertogral, K. 2008. The joint economic lot sizing problem: Review and extensions. European Journal of Operational Research, 185, 726-742. Blackburn, J. & Scudder, G. 2009. Supply chain strategies for perishable products: The case of fresh produce. Production and Operations Management, 18, 129-137. Entrup, M. L. 2005. Advanced Planning in Fresh Food Industries : Integrating Shelf Life into Production Planning. 1 ed. Dordrecht: Springer. Ghare, P. & Schrader, G. 1963. A model for exponentially decaying inventory. Journal of Industrial Engineering, 14, 238-243. 163

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Goyal, S. 1977. An integrated inventory model for a single supplier-single customer problem. The International Journal of Production Research, 15, 107-111. Goyal, S. K. & Giri, B. C. 2001. Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134, 1-16. Ha, D. & Kim, S.-L. 1997. Implementation of JIT purchasing: An integrated approach. Production Planning & Control, 8, 152-157. Hill, R. M. 1997. The single-vendor single-buyer integrated production-inventory model with a generalised policy. European Journal of Operational Research, 97, 493-499. Kim, S.-L. & Ha, D. 2003. A JIT lot-splitting model for supply chain management: Enhancing buyer–supplier linkage. International Journal of Production Economics, 86, 1-10. Nahmias, S. 2011. Perishable inventory systems, Springer. Raafat, F. 1991. Survey of Literature on Continuously Deteriorating Inventory Models. The Journal of the Operational Research Society, 42, 27-37. Tsiros, M. & Heilman, C. M. 2005. The effect of expiration dates and perceived risk on purchasing behavior in grocery store perishable categories. Journal of Marketing, 114-129. Yan, C., Banerjee, A. & Yang, L. 2011. An integrated production–distribution model for a deteriorating inventory item. International Journal of Production Economics, 133, 228232.

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