A System for Supporting Supplier and Cold Storage Selection in the Fresh Fruit Supply Chain

Abstract

Nowadays, many fresh fruit companies choose produce suppliers and the subsequent fresh produce purchase arbitrarily. They do not consider the interaction between fresh fruit quality and the required cold storage technology. These decisions are critical because they have a great impact on final product quality and process efficiency. Since fruit harvesting is seasonal, the selection of suppliers and required refrigeration technology choice are made before or during the harvest season. However, many uncertainties arise such as market conditions, climate, exchange rates, and raw material shortage, among others. These dilemmas make it necessary to react quickly and flexibly when facing them. Therefore, a decision support system based on a mathematical programming model was developed in this study for supporting these tactical decisions. This system was named the FruitPS-DSS and was applied in a Chilean dehydrated fruit company to validate the system functionality. In this company, an analysis of different possible scenarios concerning changes in demand and fruit price during a supply-planning season was performed. Moreover, it was deployed and validated according to the experience of three operational managers who were in charge of the fruit purchase and storage processes of their respective companies. They positively valued the obtained reports and information, mentioning that it will allow them to make timely decisions under a user-friendly interface. Additionally, they pointed out that the FruitPS-DSS could facilitate ordering and handling information. Finally, it is important to notice that the FruitPS-DSS is flexible enough to be adapted to different kinds of fruit processing plants.

Appendices

Appendix 1

MILP model proposed by Soto-Silva et al. (2017).

Parameters

CC_pqt: Purchase cost for producer p of the fruit type q with storage time t (US$/tonnes)

O_pqt: Fruit supply from producer p of type q with storage time t (tonnes), where 1 = long term, 2 = medium term, 3 = short term

CT_p: Transport cost from producer p to the plant by tonnes of fruit (US$/tonnes)

CFT_l: Fixed cost of transport using truck type l

CA_p: Administration cost for producer p

M: Big M

D_qt: Demand for fruit type q with storage time t (tonnes)

QM_l: Maximum load for truck type l (tonnes)

CT_qtc: Cost of transport from the plant for fruit type q with storage time t destined for warehouse c (US$/tonnes)

CE_cn: Cost of keeping the fruit in warehouse c, in cold chamber n (US$/tonnes)

CA_c: Fixed cost for warehouse c

CF_cn: Fixed cost of chamber n in warehouse c

CFT_l: Fixed cost of transport using truck type l

qtyc: Number of available warehouses

W_cn: Storage capacity of cold chamber n in warehouse c (tonnes)

QM_l: Maximum load of truck type l (tonnes)

TE_cn: Type of refrigeration technology in cold chamber n in warehouse c (1 = long term, 2 = medium term, 3 = short term)

D_qt: Quantity of fruit to store of type q with storage time t (tonnes)

Decision Variables

W_pqtl: Tonnes of fruit to buy from producer p, of type q, with storage time t transported by truck type l

S_lpq: Quantity of trips for truck type l, from producer p, with fruit type q

X_pqt: Binary variable with the value 1 if fruit is purchased from producer p, of type q and storage time t, and otherwise the value is 0

C_p: Binary variable with the value 1 if the fruit is purchased from producer p and 0 if not

Z_qtcnl: Tonnes of fruit type q with storage time t in warehouse c in cold chamber n transported in truck type l

Y_lcn: Number of trips by truck type l to warehouse c to cold chamber n

A_c: Binary variable with value 1 if warehouse c is used and 0 if not

ME_cnqt:Binary variable with value 1 if fruit type q with storage time t is kept in warehouse c in chamber n

Mathematical Model

$$\begin{aligned} &\mathit{\operatorname{Minimize}}\sum_{p\ \epsilon\ P}\sum_{q\ \epsilon\ Q}\sum_{t\ \epsilon\ T}{CC}_{pqt}{X}_{pqt}{O}_{pqt}+\kern0.5em \sum_{p\ \epsilon\ P}\sum_{q\ \epsilon\ Q}\sum_{t\ \epsilon\ T}{CT}_p{X}_{pqt}{O}_{pqt}\\&+\sum_{p\ \epsilon\ P}{CA}_p{C}_p+\sum_{\textrm{l}\ \upvarepsilon\ \textrm{L}}\sum_{\textrm{p}\ \upvarepsilon\ \textrm{P}}\sum_{\textrm{q}\ \upvarepsilon\ \textrm{Q}}{CF T}_l\ {S}_{lpq}\\&+\sum_{q\ \epsilon\ Q}\sum_{t\ \epsilon\ T}\sum_{c\ \epsilon\ C}\sum_{n\ \epsilon\ N}\sum_{l\ \epsilon\ L}\left({CT}_{qtc}+{CE}_{cn}\right)\ {Z}_{qtc nl}\\&+\sum_{c\ \epsilon\ C}{CA}_c\ {A}_c+\sum_{c\ \epsilon\ C}\sum_{n\ \epsilon\ N}\sum_{q\ \epsilon\ Q}\sum_{t\ \epsilon\ T}{CF}_{cn}\ {ME}_{cn qt}+\sum_{l\ \epsilon\ L}\sum_{c\ \epsilon\ C}\sum_{n\ \epsilon\ N}{CF T}_l\ {Y}_{lcn}\kern0.75em \end{aligned}$$

(1)

Subject to:

$$ \sum_{q\epsilon Q}\sum_{t\epsilon T}{X}_{pqt}\le M{C}_p\forall p\epsilon P $$

(2)

$$ \sum_{p\ \epsilon\ P}\sum_{t\ \epsilon\ T}\sum_{l\ \epsilon\ L\ }\ {W}_{pqtl}\ge \sum_{t\ \epsilon\ T}{D}_{qt}\forall q\ \epsilon\ Q $$

(3)

$$ \sum_{l\ \epsilon\ L}\ {W}_{pqt l}\le \kern0.5em {X}_{pqt}\ {O}_{pqt}\kern7.75em \forall q\ \epsilon\ Q,p\ \epsilon\ P,t\ \epsilon\ T\kern1em $$

(4)

$$ \sum_{t\ \epsilon\ T}\ {W}_{pqtl}\le {QM}_l\ {S}_{lpq}\kern8.75em \forall q\ \epsilon\ Q,l\ \epsilon\ L,p\ \epsilon\ P $$

(5)

$$ \sum_{t\ \epsilon\ T}\ \sum_{q\in Q}{ME}_{cnqt}\le 1\kern9.5em \forall c\ \epsilon\ C,n\ \epsilon\ N $$

(6)

$$ \sum_{l\ \epsilon\ L}\ {Z}_{qtcnl}\le {W}_{cn}{ME}_{cn qt}\kern7em \forall c\ \epsilon\ C,n\ \epsilon N,t\ \epsilon\ T\kern1.5em $$

(7)

$$ \sum_{c\ \epsilon\ C}\sum_{n\ \epsilon\ N}\sum_{l\ \epsilon\ L}\ {Z}_{qtcnl}=\sum_{p\ \epsilon\ P}\sum_{l\ \epsilon\ L}\ {W}_{pqtl}\kern1.5em \forall q\ \epsilon\ Q,t\ \epsilon\ T $$

(8)

$$ \sum_{n\ \epsilon\ N}\sum_{q\in Q}\sum_{t\in T}{ME}_{cnqt}\le qtyc\ {A}_c\kern4.5em \forall c\ \epsilon\ C $$

(9)

$$ {ME}_{cn qt}=0\kern8em \forall c\ \epsilon\ C,n\ \epsilon\ N,q\ \epsilon\ Q,t\ \epsilon\ T:t<{TE}_{cn} $$

(10)

$$ \sum_{q\ \epsilon\ Q}\sum_{t\ \epsilon\ T}\ {Z}_{qtcnl}\le {QM}_l\kern0.5em {Y}_{lcn}\kern5em \forall l\ \epsilon\ L,c\ \epsilon\ C,n\ \epsilon\ N $$

(11)

$$ {Y}_{lcn},{S}_{lpq}\ \epsilon \kern0.50em {\textrm{Z}}^{+}\kern10.5em \forall l\ \epsilon\ L,c\ \epsilon\ C,n\ \epsilon\ N,p\ \epsilon\ P,q\ \epsilon\ Q $$

(12)

$$ {A}_c,{ME}_{cnqt},{X}_{pqt},{C}_p\ \epsilon \kern0.5em \left\{0,1\right\}\kern5em \forall c\ \epsilon\ C,n\ \epsilon\ N,p\ \epsilon\ P,q\ \epsilon\ Q,t\ \epsilon\ T $$

(13)

$$ {Z}_{qtcnl},{W}_{pqtl}\ge 0\kern9.5em \forall p\ \epsilon\ P,q\ \epsilon\ Q,t\ \epsilon \kern0.5em T,c\ \epsilon\ C,n\ \epsilon\ N,l\ \epsilon\ L $$

(14)

The objective function (1) seeks to minimize all the costs derived from the fruit purchase, transport, production process, and cold storage activities needed for the plant operation. Constraint (2) establishes that if any fruit variety is bought from a producer, all the producer’s fruit supply must be bought. Constraint (3) indicates that the quantity of fruit to buy of a specific type and specific storage time must meet the processing plant’s demand. Constraint (4) shows that the quantity of fruit to buy will be less than the supply that is available from the producers. Constraint (5) allows determining the number of total trips to be made per truck during the purchase season. Constraint (6) establishes that only one type of fruit can be stored in each cold chamber. Constraint (7) makes the amount of fruit to be stored in each of the cold chambers in the warehouses subject to the choice of chamber and its storage capacity. Constraint (8) permits joining the purchase and storage together given that the fresh produce purchased is equal to the fresh produce to be stored in the cold chambers. The other constraints for this model correspond to the constraints given in the purchasing and storing models. Constraint (9) shows the activation of a cold chamber within a warehouse in order to store fruit only if the warehouse is active. Constraint (10) ensures that fruit is not stored in a cold chamber if it has a length of storage time lower than the chamber’s refrigeration technology allowing it to stock. Constraint (11) limits the maximum number of trips per truck at full capacity according to truck type and the amount of fruit to buy from the producers. Constraints (12), (13), and (14) correspond to the integrality and non-negativity constraints on the decision variables, respectively.

Appendix 2

Table 10 presents different scenarios for fruit demand and price. In each scenario, the percentage variation for every fruit segregations (short, medium, or long term) is the same. The obtained results show that the number of selected producers and cold storage facilities does not have the same percentage variation than the fruit demand and price. Consequently, the total cost also varies in a different percentage.

Table 10 Purchase and storage plan for each scenario