2351-9789 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer review under responsibility of the organizing committee of the Industrial Engineering and Service Science 2015 (IESS 2015)doi: 10.1016/j.promfg.2015.11.067Procedia Manufacturing 4 ( 2015 ) 487 – 495Available online at www.sciencedirect.comScienceDirectIndustrial Engineering and Service Science 2015, IESS 2015Scheduling model in strawberry harvesting by considering productdecay during storageSazli Tutur Risyahadi*Diploma Program of Industrial Management, Bogor Agricultural University, Jl. Kumbang No 14, Bogor, IndonesiaAbstractDemand of strawberry from the supermarket required high-quality products with continuous supply. Asgita, an association ofstrawberry producers, is facing several problems regarding product’s supply that will influence their profits. One of the problemswas un-integrated supply chain between farmer and Asgita. A scheduling model for strawberry harvesting need to be developedto gain maximal profit. This model should provide an integrated system together with processing and storage. This model wasdeveloped using mix-integer linear programming updating by rolling horizon method. The result showed, harvesting with 90%maturity was more profitable, as long as the amount of supply and demand almost equal© 2015 The Authors. Published by Elsevier B.V.Peer-review under responsibility of the organizing committee of the Industrial Engineering and Service Science 2015 (IESS2015).Keywords: Harvest Scheduling; Mix Integer Linear Programming; Decay Function1. IntroductionNowadays, fruit selling through supermarkets in Indonesia is increasing. Asgita is the association of a strawberryfarmers who controls supply to the supermarket in Ciwidey Village. Most supermarkets require have set a productquality standard, as for strawberry it is with 90% maturity, good grading, sorting and packaging process. In the otherhand, a traditional market requires only 75% maturity. In strawberry farming, to reach 90% maturity, it needs fiveday cycle; and three-days cycle to reach 75% maturity. The excess of strawberry harvesting will be stored in a* Corresponding author.E-mail address: [email protected]© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer review under responsibility of the organizing committee of the Industrial Engineering and Service Science 2015 (IESS 2015)488 Sazli Tutur Risyahadi / Procedia Manufacturing 4 ( 2015 ) 487 – 495warehouse where the quality will decrease gradually as a function of time. The scheduling model will assist Asgitain deciding production and distribution schedule in order to gain maximal profit. In developing this model, we alsoconsider post-harvest behavior, post-harvest decay, labors, and delivery cost.This scheduling model has been developed in tea [1] and grape harvesting [2], however it hasn’t been integratedwith post harvest processing. In other cases, the scheduling model with post harvest processing integration has beendeveloped in raw sugar [3] and strawberry [4] but without including product decay during storage. Reference [5] hasdeveloped a model which considers product decay but it did not accommodate harvest day before planning periods.The scheduling model that developed in this study was integrating post harvest by considering product decay duringstorage and also accommodating harvest day before planning periods as well as supported by strawberry functiondecay during storage [6]2. Real SystemFig 1 describes Asgita harvest system that shows the relationship between five actors involved. There areproducer, association, supermarket, traditional market and home industry for strawberry jam. Producer givesinformation to the association about field capacity and the latest harvest day before planning periods whilesupermarkets give information about quantity demand each day. After that the association makes a harvest schedule,post harvest processes schedule, storage and delivers a schedule. From the sorting process, strawberries that meetsupermarket requirement will be sent directly to the supermarkets while others will be delivered to home industries. Farmer FieldsDetermining Sechedule ofharvestingHarvest ScheduleTraditional market Maturity levelPostharvestProcessing SortageHouse holdIndustryQ>DPrice FromTraditional marketField data75%90%rejectLolos sortasiYesNoDemand dataPrice fromHouseholdindustryFlow of productFlow of moneyFlow o finformationSupermarket payingPaying and profit sharing to farmer Association SupermarketHarvestingStorageFieldRegitrastiomDemand,Volume anddelivery timePaying from traditional marketPaying from houshold industry Sazli Tutur Risyahadi / Procedia Manufacturing 4 ( 2015 ) 487 – 495 489Figure 1. Flow of Product, Money and Information3. Mathematical ModelReal system in Asgita was modeled through mathematical relation, which consists of objective and constraintfunctions. Objective function describes maximization profit of Asgita, including revenue and total relevant cost.Asgita gain revenue from supermarket, home industry and traditional market while total cost consists of harvesting,post harvest, transportation, rejection and inventory cost3.1. Notation of Variables and ParameterScope of decision variable is within an operational level with day per day schedule. The decision variables cananswer the questions like: which field we are going to harvest, when we harvest, what type of maturity (90% or75%), when we deliver a product, how many inventory, how many strawberries (Kg) to supply supermarket directlyfrom packaging house, how many strawberry (Kg) to supply traditional market from packaging house, how manystrawberry (Kg) to supply supermarket from warehouse. Table 1 and Table 2 show the notation of decision variableand model parameter.Table 1. Notation and Desciption of decision variableNotation Variable Description xl,t75xl,t90vlSCt,p: Binner variable which has value 1 if the harvest even on field l on maturity 75% on day t, value 0 for others.: Binner variable which has value 1 if the harvest even on field l on maturity 90% on day t, value 0 for others.: Artificial variable Binner to restrict choosing 75% and 90%: Product volume which supplies to the supermarket directly from packaging house (Kg) on the sale day p and onharvest day t.: Product volume which supplies to the supermarket from warehouse storage (Kg) on the sale day p and on harvestday t.: Product volume which becomes a stock on warehouse (Kg) on the sale day p and on harvest day t.: Product volume which becomes a stock on warehouse (Kg) on the sale day p and on harvest day t.: Volume of 90% maturity to pass sorting process on harvest day t (kg)SWt,pSPWt,pINVt,pQHtZp: Shortage of supply volume to the supermarket on day sale p (kg) Table 2. Notation and Description of Paramater ModelParameter Notation Description hwl90Jl,tKpqlr75r90SL: Number of harvest labour on field l on 90% (man): The latest harvest day on field l before is scheduled on day t.: Maximum capacity of sorting process (kg): Viability volume of strawberry on field l (kg): Range day between harvest for 75% maturity (day): Range day between harvest for 90% maturity (day): Maximum shelf life of strawberryInvos: Beginning inventory for 90% maturity: Mean proportion for 90% maturity which passes sorting process (%) 490 Sazli Tutur Risyahadi / Procedia Manufacturing 4 ( 2015 ) 487 – 495NPp-t : Constantan decreasing quality from harvest day t for the day sale ptrl75 : Number of loading, which needed for strawberry 75% maturity on field l.trl90 : Number of loading, which needed for strawberry 90% maturity on field l.Cr : Cost of shortages for 90% maturity (Rp/Kg)Cl : Cost of chilling for 90% maturity (Rp/kg)Mc :Cost of packaging for 90% maturity (Rp/kg)Hc : Cost of Inventory for 90% maturity (Rp/kg)Hs : Cost of harvest labour (Rp/man/day)Pc : Cost of sorting and grading process for 90% maturity (Rp/Kg)pir : Strawberry price to home industry jam (Rp/Kg)pm : Strawberry price to the supermarket (Rp/Kg)pm t-p : Strawberry price to the supermarket on sale day t and harvest day p (Rp/Kg)ptr : Strawberry price to the traditional market (Rp/Kg)trfw : Cost of transportation form processing to warehouse facilities (Rp/kg)trfc : Cost of transportation form processing to the supermarket ( (Rp/kg)trwc : Cost of transportation form warehouse the supermarket ( (Rp/kg)tcl :Cost of transportation form field l to processing for every mode per times loading (Rp/loading)3.2. Mix Integer Linear Programming modelScheduling model with MILP consists of objective function to maximize the profit, constraint for the field,constraint on post harvest processing and constraint in storage facilities.Objective function Maximize Profitൌ ݔǡ௧ ହ ή ݍή ௧ୀଵെ்௧ୀଵ ݔǡ௧ ହ ή ݄ ݓή ݄ݏୀଵെ ݔǡ௧ ହ ή ݎݐହ ή ܿݐୀଵ்௧ୀଵ்௧ୀଵ ܵܥ௧ǡ ή ݉ୀଵ ܹܵ௧ǡ ή ି݉௧ୀଵ்௧ୀଵ்௧ୀଵ ݔǡ௧ ଽ ή ݍή ሺͳ െ ݏሻ ή െୀଵ்௧ୀଵݓ݂ݎݐ ܹܵܲ௧ǡ ήୀଵെ்௧ୀଵ݂ܿݎݐ ௧ǡ ήܥܵ ୀଵെ ܹܵ௧ǡ ή ܿݓݎݐୀଵെ்௧ୀଵ்௧ୀଵ ݔǡ௧ ଽ ή ݎݐଽ ή ܿݐୀଵെ்௧ୀଵ ݔǡ௧ ଽ ή ݄ݓଽ ή ݄ݏୀଵെ ݔǡ௧ ଽ ή ݍή ܿୀଵെ்௧ୀଵ்௧ୀଵ ݔǡ௧ ଽ ή ݍή ݏή ݉ܿୀଵെ்௧ୀଵ ݔǡ௧ ଽ ή ݍή ݏή ݈ܿୀଵ்௧ୀଵെ ܸܰܫ௧ǡ ή ݄ܿୀଵെ்௧ୀଵݎܿ ܼ ήୀଵെ ܹܵ௧ǡ ή ି݉௧ ή ܲିݎ௧ ǥ ǥ ǥ ǥ ǥ Ǥ Ǥ ሺͳሻୀଵ்௧ୀଵSazli Tutur Risyahadi / Procedia Manufacturing 4 ( 2015 ) 487 – 495 491Constraint function for Strawberry Field σ் ௧ୀଵ൫ݔǡ௧ ହ ݔǡ௧ ଽ൯ ൌ ͳǡ ݈ǣ݆ǡଵ ൌ ͳǥ ǥ ǥ ሺʹܽሻσ் ௧ୀଵ൫ݔǡ௧ ହ൯ ʹ ή ݒǡ ݈ǣ ݆ǡଵ ൌ ʹǥ ǥ ǥ ǥ ǥ Ǥ ሺʹܿሻא ݒሼͲǡͳሽ݈ǣ ݆ǡଵ ൌ ʹσ் ௧ୀଵ൫ݔǡ௧ ହ ݔǡ௧ ଽ൯ ʹǡ ݈ǣ ݆ǡଵ ൌ ͵ ǥ ǥ ሺʹ݁ሻσ் ௧ୀଵ൫ݔǡ௧ ଽ൯ ሺͳ െ ݒሻǡ ݈ǣ݆ǡଵ ൌ ͵ ǥ ǥ ሺʹ݃ሻσ் ௧ୀଵ൫ݔǡ௧ ଽ൯ ൌ ͳǡ ݈ǣ ݆ǡଵ ൌ Ͷ ǥ ǥ ǥ ǥ ǥ ǥ ǥ ǥ ሺʹ݅ሻσ் ௧ୀଵ൫ݔǡ௧ ଽ൯ ൌ ͳǡ ݈ǣ ݆ǡଵ ൌ ͷ ǥ ǥ ǥ ǥ ǥ Ǥ ǥ ሺʹ݇ሻ““`σ் ௧ୀଵ൫ݔǡ௧ ହ ݔǡ௧ ଽ൯ ʹǡ ݈ǣ ݆ǡଵ ൌ ʹǥ ǥ ǥ ǥ ሺʹܾሻσ் ௧ୀଵ൫ݔǡ௧ ଽ൯ ሺͳ െ ݒሻǡ ݈ǣ ݆ǡଵ ൌ ʹǥ ǥ ǥ ሺʹ݀ሻσ் ௧ୀଵ൫ݔǡ௧ ହ൯ ʹǤ ݒǡ ݈ǣ ݆ǡଵ ൌ ͵ ǥ ǥ ǥ ǥ ሺʹ݂ሻσ் ௧ୀଵ൫ݔǡ௧ ହ ݔǡ௧ ଽ൯ ʹǡ ݈ǣ ݆ǡଵ ൌ Ͷ ǥ ǥ ǥ ǥ ǥ ǥ ሺʹ݄ሻσ் ௧ୀଵ൫ݔǡ௧ ହ ݔǡ௧ ଽ൯ ʹǡ ݈ǣ ݆ǡଵ ൌ ͷ ǥ ǥ ǥ ǥ ǥ ሺʹ݆ሻ ݔǡ௧ହ ൌ Ͳǡ݈ǡ ݆ ݐǡ௧ ് ݎହǡ݆ǡ௧ ് ʹ ή ݎହǡ ݆ǡ௧ ് ݎହ ݎଽ….(3a)ݔǡ௧ଽ ൌ Ͳǡ݈ǡ ݆ ݐǡ௧ ് ݎଽ………………………………………………..(3b)Constraint function on Processing Facilitiesσݔ אǡ௧ ହ ή ݄ݓହ σݔ אǡ௧ ଽ ή ݄ݓଽ ൌ ݓ݄ܣǡ ݐǥ ሺͶሻ σ σ ் ௧ୀଵ ୀଵ ݔǡ௧ ଽ ή ݍή ݏൌ ܳܪ௧ ǥ ǥ ǥ ǥ Ǥ Ǥ ǥ ǥ ǥ ǥ ሺͷሻ ܵܥ௧ǡ ୀଵ்௧ୀଵ ܹܵܲ௧ǡ ൌܳܪ௧ୀଵ்௧ୀଵǡ݀ܽ݊ݐ ሺ െ ݐሻ ് ܵ ܮǥ Ǥ Ǥ ሺሻܹܵ௧ǡ ൌ Ͳǡ ൌ ݐǥ ǥ ሺሻ ܹܵܲ௧ǡ ൌ Ͳǡ ݐ ് ǥ ǥ ǥ ሺͺሻConstraint function on Storage Facilities ܵܥ௧ǡ ୀଵ்௧ୀଵ ܹܵ௧ǡ ܼ ൌୀଵܦୀଵ்௧ୀଵǡ݀ܽ݊ݐ ሺ െ ݐሻ ് ܵܮǤ Ǥ ሺͻሻ ܹܵܲଵǡ ൌଷୀଵ ܹܵଵǡଷୀଵǡ ܹܵܲଶǡ ൌସୀଶ ܹܵଶǡସୀଶ ܹܵܲଷǡ ൌହୀଷହ ܹܵଷǡ ǡୀଷ ܹܵܲସǡ ൌହୀସ ܹܵସǡହୀସǥ ሺͳͲሻݒ݊ܫͲ ܹܵܲ௧ǡ െୀଵ்௧ୀଵ ܹܵ௧ǡ ൌ ܸܰܫ௧ǡǡǡ ݐൌ ͳǡ ൌ ͳୀଵ்௧ୀଵୀଵǤ ሺͳͳܽሻ்௧ୀଵ ܹܵܲ௧ǡ െୀଵ்௧ୀଵ ܹܵ௧ǡ ܸܰܫ௧ǡିଵ ൌ ܸܰܫ௧ǡǡǡୀଵǤ ሺͳͳܾሻ்௧ୀଵୀଵ்௧ୀଵୀଵ்௧ୀଵܪ ܸܰ௧ǡ ൌܫ ௧ୀଵ ǥ ǥ ሺͳʹܽሻǡ ݔǡ௧ ଽאή ݇ ݍǡݐǥ ǥ Ǥ ሺͳʹܾሻ ܲ݉ି௧ ൌ ܲ݉ െ ൫ܲ݉ ή ܰܲି௧൯ ǥ ǥ ǥ ǥ ǥ ǥ ǥ ǥ ǥ ǥ Ǥ Ǥ ǥ ǥ ǥ ሺͳ͵ሻ ࢞ǡ ࢚ૠ אሼǡ ሽ,࢞ǡ א ૢ ࢚ሼǡ ሽ ǥ ǥ ǥ ǥ ǥ ǥ ǥ ǥ ǥ ሺሻ492 Sazli Tutur Risyahadi / Procedia Manufacturing 4 ( 2015 ) 487 – 495Profit is achieved by subtracted the cost from revenue; it describes by (1). Constraint function (2a) describes thefield that has been harvested one day before planning periods. Constraint function (2b), (2c) and (2d) describe thefield that has been harvested two days before planning period. Constraint function (2e), (2f) and (2g) describe thefield that has been harvested three days before planning period. Constraint function (2h) and (2i) describe the fieldthat has been harvested four days before planning periods. Constraint function (2j) and (2k) to describe the field thathas been harvested five days before planning periods.Constraint (3a) and (3b) show time period based on the type of maturity. Equation (4) shows the number ofharvest labour that needed not more than viability labour in every harvest day. Quantity of strawberry with 90%maturity is classified by sorting yield (5). Quantity of strawberry with 90% maturity which is delivered directly tosupermarket and to warehouse are depending on sorting process every day (6). Constraint (7) shows that strawberryform warehouse is strawberry that has been harvested few days before. Constraint (8) shows that the excess ofstrawberry must be saved in the warehouse (storage facilities).The balance of strawberry quantity between supermarket demand, strawberry warehouse, strawberry formprocessing and shortage are ensured by (9). Constraint (10) ensures that strawberry in the warehouse still in shelflife. The balance of strawberry quantity in the warehouse is ensured by (11a) and (11b). Maximum capacities ofstorage facilities and maximum capacity of processing facilities are described by (12a) and (12b). Constraint (13)shows that price given by supermarket depends on quality.4. Numerical Example4.1. Demand and Parameter ModelModel was validated by data which was collected from [4]. Supermarket gives demand quantity of 90% maturityevery day. Table 3 shows demand from the supermarket for seven days. Producer gives field data likes populationmedia, productivity, viability labor, transportation from field and latest harvest before planning periods. Table 4shows data every field form producer. Table 5 shows data parameters for price, processing and warehouse facilities.Table 3. Demand of Strawberry 90% maturity.Day1 2 3 4 5 6 7DEMAND 30 35 25 30 20 30 30Table 4. Parameter for every FieldFieldParameter 1 2 3 4 5 6 7 8 9Population media 2750 3250 3000 2500 2750 3250 2250 2500 3250Productivity (kg/harvest/media) 0,02 0,02 0,02 0,02 0,02 0,02 0,02 0,02 0,02Harvest volume 55 65 60 50 55 65 45 50 65hw75 3 4 3 3 3 4 3 3 4hw90 6 7 6 5 6 7 5 5 7tr75 2 2 2 2 2 2 1 2 2tr90 2 3 2 2 2 3 2 2 3tc 5000 7500 7500 7500 7500 10000 10000 5000 5000J 2 1 5 3 3 2 4 2 3Table 5. Parameter for price, processing and storage facilitiesParameter amountStrawberry price for traditional market (pt) (Rp/Kg) : 6000 Strawberry price for supermarket (pm) (Rp/Kg)Strawberry price homeindustry jam RT (pi) (Rp/Kg)Quality proportion of supermaket (s)Harvest labour cost (hs) (Rp/man/day): 22000: 1000: 0,6: 15000 Sazli Tutur Risyahadi / Procedia Manufacturing 4 ( 2015 ) 487 – 495 493Processing cost (pc) (Rp/Kg) : 400Packaging cost (mc) (Rp/Kg) : 4000Chiling Cost (cl) (Rp/Kg) : 500Inventory cost (hc) (Rp/Kg) : 12 Shortage cost (cr) (Rp/Kg)Cost of transportation form processing to warehouse facilities (Rp/kg)Cost of transportation form processing to the supermarket ( (Rp/kg)Cost of transportation form warehouse facilities to the supermarket ( (Rp/kg)Maximum storage (H) and Processing capacity (Kp) (Rp/Kg)Number of Avaibilty Number (Ahw) (Rp/Kg)Constanta quality for different one day between harvest and sale dayConstanta quality for different two day between harvest and sale dayRejection Proportion for different one day between harvest and sale dayRejection Proportion for different one day between harvest and sale day: 13800: 50: 700: 600: 250: 50: 0,17: 0,23: 0,2: 0,4 4.2. ResultOptimal schedule of harvest was shown by Table 6, which makes the maximum profit. The harvest modelMILP is solved by Lingo 11.0. Based on the result, the first harvest day the model chooses field 3 that has 90%maturity while field 5 and field 9 that have 75% maturity. The second harvest day, the model chooses field 7 thathas 90% maturity while field 1 and field 8 that have 75% maturity. The third harvest day, the model chooses field 4that has 90% maturity while field 2 that has 75% maturity. The fourth harvest day, the model chooses field 6 thathas 90% maturity while field 3 and field 9 that have 75% maturity. The fifth harvest day, there is no field for 90%maturity while field 1 and field 8 that have 75% maturity. The sixth harvest day, the model chooses field 5 that has90% maturity while field 2 and field 4 that have 75% maturity. The seventh harvest day, the model chooses field 7that has 90% maturity while field 3 and field 6 that have 75% maturity.Table 6. Harvest Schedule of 9 fields and 7 Days494 Sazli Tutur Risyahadi / Procedia Manufacturing 4 ( 2015 ) 487 – 495Table 7. Quantity Balancing between Delivery and Inventory for 90% MaturityTable 7 shows decision when and how many strawberry 90% will be delivered to supermarket (SC) andwarehouse storage (SPW) and also strawberry form warehouse to the supermarket (SW). For example, The first saleday, we have 36 kg from processing, which will deliver directly to the supermarket 30 kg and 6 kg to the warehousestorage. Total profit was gained from selling strawberry 75% and 90% maturity is Rp 6.329.578.If we compare, the profit of the model was lower than the model [4] which profits Rp 6.748.278. It is because themodel [4] doesn’t consider product decay during storage, which influences revenue. Harvesting with 90% maturitywas more profitable, as long as the amount of supply and demand closely equals each day. If there are two fields,which have quantity closely same with demand, model prefers to choose a fewer one. There was to avoid an excessquantity that will become inventory which strawberry will decay during storage. Decay function influences priceand rejection from the supermarket. Considering decay function is important to avoid losses, especially perishableproduct like strawberry.4.3. Sensitivity AnalysisSupermarket demand is always fluctuated and seems increase day by day. Sensitivity analysis is used tounderstand how the result of model change if demand fluctuation occurs. Based on Fig 2, when demand increases,the harvest of 90% maturity will also increase. However, the profit isnot always increasing. Profit will decrease iffield capacity is not enough to meet the demand. As a consequence, the shortage cost will increase which finally willaffect the total profit.Sazli Tutur Risyahadi / Procedia Manufacturing 4 ( 2015 ) 487 – 495 495Figure 2. Sensitivity Analysis when Increasing Demand5. ConclusionModel of harvest scheduling in strawberry farming by considering decay during storage has developed. Themodel is used to decide when, where and how many to harvest both 75% and 90% maturity that gives maximalprofit. The developed model represents the real system better as it has included quality decay and rejection bysupermarket; the longer strawberry in stock, the more its price decreases. Sensitivity analysis shows that f whendemand is fluctuated, it will change the schedule of harvestReferences[1] S.M. Budijati.’Model Penjadwalan Pemetikan dengan Progama Dinamis minimasi Biaya” Magister Thesis. Institute Technology Bandung,Bandung, 2000[2] J. C. Ferrer, A. M. Cawley, S. Maturana , S. Toloza and J. Vera, “An Optimization Approach For Scheduling Wine Grape Harvest Operation.Int J Production Economic vol 112, 2008, pp 985-999[3] M. Grunow, H. O. Gunther and R. Westiner, “Supply Optimization for the production of raw sugar,” Int. J Production Economics Vol 110,2007, pp 224-239.[4] Kusnandar, “Pengembangan Model Penjadwalan Panen Strawberri Terintegrasi Untuk Maksimasi Keuntungan,” Magister Thesis. InstituteTechnology Bandung, Bandung, 2010.[5] O. Ahumada and J.R. Villalobos, “Operational Model for Planning the Harvest and Distribution of Perishabel agricultural product,” Int.J.Production Economic Vol 133, 2011, pp 677-687,[6] M. Abrar, T. Sultan, A.Din and B. Nias, “Postharvest Physicochemcal Changes in Full Ripe Strawbeeries During Cold Storage,” Animal andPlant Sciences, Vol.21, No. 1, 2011, pp. 38-41QuantityHarvestIncreasing Demand0%, 10%, 20%,30% and 40%75%90%ProfitIncreasing Demand0%, 10%, 20%, 30% and 40%
