A multi-product, multi-period model to select supplier for deteriorating products while considering uncertainty as well as backorder

Subject Areas : Mathematical Optimization

Mohsen Lashgari ¹ (School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran)
Seyed Jafar Sadjadi ² (School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran)
Misugh Sahihi ³ (School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran)

Received: 2020-10-08 Accepted : 2020-10-08 Published : 2020-09-01

Keywords: Inventory control, Robust Optimization, deteriorating items, Pattern Search, Scenario-based,

Abstract :

Determining supplier and optimum order of the quantity is an issue of great importance in logistics management for many companies. In this regard, it is crucial to determine the best decisions for the order quantity as well as the most suitable supplier through considering existing limitations and uncertainties. To optimize a multi-product, multi-period model with select supplier for deteriorating products, while uncertainty of future economic conditions directly affects the problem conditions. In this regard, a mixed integer definite programing model is introduced, and afterwards, the proper robust structure is established through a two-phase scenario-based approach. The behavior of the main features of the inventory system elaborated upon in this article, that is, multi-product, uni-level, multi-period inventory system, has been modeled under the influence of uncertain economic environment. In the final phase pattern, search method is employed to determine proper answers, the results of which are analyzed, to shed light on various aspects of the solving procedure, as well as the problem itself. The applicability of the proposed model is shown by an illustrative example.

References:

Bakker M, Riezebos J, Teunter RH (2012) Review of inventory systems with deterioration since 2001. Eur J Oper Res 221(2):275–284
Bevilacqua M, Petroni A (2002) From traditional purchasing to supplier management: a fuzzy logic-based approach to supplier selection. Int J Logist 5(3):235–255
Diabat A, Taleizadeh AA, Lashgari M (2017) A lot sizing model with partial downstream delayed payment, partial upstream advance payment, and partial backordering for deteriorating items. J Manuf Syst 45(1):322–342
Ebrahim RM, Razmi J, Haleh H (2009) Scatter search algorithm for supplier selection and order lot sizing under multiple price discount environment. Adv Eng Softw 40(9):766–776
Hung K-C (2011) An inventory model with generalized type demand, deterioration and backorder rates. Eur J Oper Res
208(3):239–242 
Khanlarzade N, Yegane B et al (2014) Inventory control with deteriorating items: a state-of-the-art literature review. Int J Ind Eng Comput 5(2):179–198
Kumar M, Vrat P, Shankar R (2004) A fuzzy goal programming approach for vendor selection problem in a supply chain.
Comput Ind Eng 46(1):69–85
Lashgari M, Taleizadeh AA, Sana SS (2016) An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity. J Ind Manag Optim 12(3):1091–1119
Lee AHI, Kang H-Y, Lai C-M, Hong W-Y (2013) An integrated model for lot sizing with supplier selection and quantity
discounts. Appl Math Model 37(7):4733–4746
Li R, Lan H, Mawhinney JR (2010) A review on deteriorating inventory study. J Serv Sci Manag 3(01):117
Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43(2):264–281

Rabbani A (2011) Using fuzzy logic to multi-product lot sizing problem with constraint capacity in MRP system. J Ind Manag 5:15–27
Rezaei J, Davoodi M (2011) Multi-objective models for lot-sizing with supplier selection. Int J Prod Econ 130(1):77–86
Saaty TL (2004) Decision making—the analytic hierarchy and network processes (AHP/ANP). J Syst Sci Syst Eng 13(1):1–35
Sarkar T, Ghosh SK, Chaudhuri KS (2012) An optimal inventory replenishment policy for a deteriorating item with time-quadratic demand and time-dependent partial backlogging with shortages in all cycles. Appl Math Comput 218(18):9147–9155
Senyigit E, Soylemez I (2012) The analysis of heuristics for lot sizing with supplier selection problem. Proc Soc Behav Sci 62:672–676
Skouri K, Papachristos S (2002) A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging. Appl Math Model 26(5):603–617
Taleizadeh AA (2014) An EOQ model with partial backordering and advance payments for an evaporating item. Int J Prod Econ 155:185–193
Taleizadeh AA, Nematollahi M (2014) An inventory control problem for deteriorating items with back-ordering and financial considerations. Appl Math Model 38(1):93–109
Taleizadeh AA, Niaki STA, Aryanezhad M-B (2009a) A hybrid method of Pareto, TOPSIS and genetic algorithm to optimize
multi-product multi-constraint inventory control systems with random fuzzy replenishments. Math Comput Model
49(5):1044–1057
Taleizadeh AA, Niaki STA, Hoseini V (2009b) Optimizing the multiproduct, multi-constraint, bi-objective newsboy problem with discount by a hybrid method of goal programming and genetic algorithm. Eng Optim 41(5):437–457
Taleizadeh AA, Wee H-M, Sadjadi SJ (2010a) Multi-product production quantity model with repair failure and partial
backordering. Comput Ind Eng 59(1):45–54
Taleizadeh AA, Niaki STA et al (2010b) Optimising multi-product multi-chance-constraint inventory control system with stochastic period lengths and total discount under fuzzy purchasing price and holding costs. Int J Syst Sci 41(10):1187–1200
Taleizadeh AA, Niaki STA, Barzinpour F (2011) Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: a harmony search algorithm. Appl Math Comput
217(22):9234–9253
Taleizadeh AA, Jalali-Naini SG, Wee H-M, Kuo T-C (2013a) An imperfect multi-product production system with rework. Sci Iran 20(3):811–823
Taleizadeh AA, Wee H-M, Jolai F (2013b) Revisiting a fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Math Comput Model 57(5):1466–1479
Taleizadeh AA, Mohammadi B, Ca´rdenas-Barro´n LE, Samimi H (2013c) An EOQ model for perishable product with special sale and shortage. Int J Prod Econ 145(1):318–338
Taleizadeh AA, Noori-daryan M, Ca´rdenas-Barro´n LE (2015) Joint optimization of price, replenishment frequency, replenishment cycle and production rate in vendor managed inventory system
with deteriorating items. Int J Prod Econ 159:285–295
Valliathal M, Uthayakumar R (2009) An EOQ model for perishable items under stock and time-dependent selling rate with shortages. ARPN J Eng Appl Sci 4(8):8–14
Wagner HM (1975) Principles of operations research, 2nd edn. Prentice Hall, New Jersey
Xia W, Wu Z (2007) Supplier selection with multiple criteria in volume discount environments. Omega 35(5):494–504
Yu C-S, Li H-L (2000) A robust optimization model for stochastic logistic problems. Int J Prod Econ 64(1):385–397
Zhang J et al (2015) Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventorylevel-dependent demand. Int J Prod Econ 170:136–145