Advanced supply chain planning with mixtures of backorders, lost sales, and lost contract.

*(English)*Zbl 1121.90013Summary: This paper investigates a supply chain system in which a supplier prepares for the selling season by building stock levels prior to the beginning of the season and shortages realized at the beginning of the season are represented as mixtures of backorders and lost sales. Backlogged items are replenished as soon as possible through an emergency procurement as opposed to waiting until the next scheduled delivery as in many continuous review scenarios, and the backorder rate is modeled as a piecewise linear function of the magnitude of the shortage. The often intangible cost associated with lost sales and customer goodwill is also quantified. In particular, the buyer and supplier are engaged in a contractual agreement and the loss of customer goodwill from the supplier’s perspective is represented as the expected cost associated with violating the conditions of the contract. The likelihood of contract cancellation is also represented as a function of the magnitude of shortage. The optimal solution is derived in closed form for the case of exponential demand distribution, and an example problem is illustrated with numerical data in order to demonstrate calculation of the optimal solution and corresponding sensitivity analysis for demand distributions in which the solution cannot be expressed in closed form.

##### Keywords:

inventory; stochastic demand; newsvendor problem; time-dependent partial backlogging; mixtures of backorders and lost sales; lost contract; sensitivity analysis
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\textit{E. J. Lodree jun.}, Eur. J. Oper. Res. 181, No. 1, 168--183 (2007; Zbl 1121.90013)

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##### References:

[1] | Abad, P., Optimal pricing and lot-sizing under conditions of perishability and partial backordering, Management science, 42, 8, 1093-1104, (1996) · Zbl 0879.90069 |

[2] | Abad, P., Optimal lot size for a perishable good under conditions of finite production and partial backordering and lost Sale, Computers and industrial engineering, 38, 4, 457-465, (2000) |

[3] | Abad, P.L., Optimal price and order size for a reseller under partial backordering, Computers and operations research, 28, 1, 53-65, (2001) · Zbl 0976.90001 |

[4] | Abad, P., Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost Sale, European journal of operational research, 144, 3, 677-685, (2003) · Zbl 1012.90002 |

[5] | Chang, H.-J.; Dye, C.-Y., EOQ model for deteriorating items with time varying demand and partial backlogging, Journal of the operational research society, 50, 11, 1176-1182, (1999) · Zbl 1054.90507 |

[6] | Chapra, S.C.; Canale, R.P., Numerical methods for engineers with software and programming applications, (2002), McGraw-Hill |

[7] | Chopra, S.; Meindl, P., Supply chain management: strategy, planning, and operation, (2004), Prentice Hall Upper Saddle River, NJ |

[8] | Chu, P.; Yang, K.-L.; Liang, S.-K.; Niu, T., Note on inventory model with a mixture of back orders and lost sales, European journal of operational research, 159, 2, 470-475, (2004) · Zbl 1065.90002 |

[9] | Dye, C.-Y., in press. Joint pricing and ordering policy for a deteriorating inventory with partial backlogging. Omega. |

[10] | Dye, C.-Y.; Ouyang, L.-Y., An EOQ model for perishable items under stock dependent selling rate and time-dependent partial backlogging, European journal of operational research, 163, 3, 776-783, (2005) · Zbl 1071.90505 |

[11] | Dye, C.-Y.; Chang, H.-J.; Teng, J.-T., A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging, European journal of operational research, 172, 2, 417-429, (2006) · Zbl 1168.90328 |

[12] | Hillier, F.S.; Lieberman, G.J., Introduction to operations research, (2001), McGraw-Hill Boston, MA, USA · Zbl 0155.28202 |

[13] | Khouja, M., Note on the newsboy problem with an emergency supply option, Journal of the operational research society, 47, 12, 1530-1534, (1996) · Zbl 0873.90022 |

[14] | Khouja, M., The single-period (news-vendor) problem: literature review and suggestions for future research, Omega: international journal of management science, 27, 537-553, (1999) |

[15] | Lau, H.-S.; Lau, A.H.-L., Reordering strategies for a newsboy-type product, European journal of operational research, 103, 3, 557-572, (1997) · Zbl 0921.90064 |

[16] | Lau, H.-S.; Lau, A.-L., Semi-analytical solution for a newsboy problem with mid-period replenishment, Journal of the operational research society, 48, 12, 1245-1253, (1997) · Zbl 0895.90075 |

[17] | Lau, A.-L.; Lau, H.-S., Decision models for single-period products with two ordering opportunities, International journal of production economics, 55, 1, 57-70, (1998) |

[18] | Lodree, E.; Jang, W.; Klein, C.M., Minimizing response time in a two stage supply chain system with variable lead time and stochastic demand, International journal of production research, 42, 11, 2263-2278, (2004) · Zbl 1059.90014 |

[19] | Montgomery, D.C.; Bazaraa, M.S.; Keswani, A.K., Inventory models with a mixture of backorders and lost sales, Naval research logistics quarterly, 20, 2, 255-263, (1973) · Zbl 0262.90020 |

[20] | Padmanabhan, G.; Vrat, P., Inventory model with a mixture of back orders and lost sales, International journal of systems science, 21, 8, 1721-1726, (1990) · Zbl 0715.90038 |

[21] | Papachristos, S.; Skouri, K., Optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type – backlogging, Operations research letters, 27, 4, 175-184, (2000) · Zbl 1096.90518 |

[22] | Papachristos, S.; Skouri, K., An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging, International journal of production economics, 83, 3, 247-256, (2003) · Zbl 1073.90511 |

[23] | Park, K.S., Another inventory model with a mixture of backorders and lost sales, Naval research logistics quarterly, 30, 3, 397-400, (1983) · Zbl 0528.90017 |

[24] | Rosenberg, D., New analysis of a lot-size model with partial backlogging, Naval research logistics quarterly, 26, 2, 349-353, (1979) · Zbl 0401.90038 |

[25] | San José, L.A.; Sicilia, J.; García-Laguna, J., An inventory system with partial backlogging modeled according to a linear function, Asia-Pacific journal of operational research, 22, 2, 189-209, (2005) · Zbl 1078.90009 |

[26] | San José, L.A.; Sicilia, J.; García-Laguna, J., Analysis of an inventory system with exponential partial backordering, International journal of production economics, 100, 76-86, (2006) |

[27] | Silver, E.A.; Pyke, D.F.; Rein, Inventory management and production planning and scheduling, (1998), Wiley |

[28] | Skouri, K.; Papachristos, S., A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging, Applied mathematical modelling, 26, 5, 603-617, (2002) · Zbl 1029.90010 |

[29] | Skouri, K.; Papachristos, S., Four inventory models for deteriorating items with time varying demand and partial backlogging: A cost comparison, Optimal control applications and methods, 24, 6, 315-330, (2003) · Zbl 1073.90511 |

[30] | Skouri, K.; Papachristos, S., Optimal stopping and restarting production times for an EOQ model with deteriorating items and time-dependent partial backlogging, International journal of production economics, 81-82, 525-531, (2003) |

[31] | Teng, J.-T.; Chang, H.-J.; Dye, C.-Y.; Hung, C.-H., An optimal replenishment policy for deteriorating items with time-varying demand and partial backlogging, Operations research letters, 30, 6, 387-393, (2002) · Zbl 1013.90006 |

[32] | Wang, S.-P., An inventory replenishment policy for deteriorating items with shortages and partial backlogging, Computers and operations research, 29, 14, 2043-2051, (2002) · Zbl 1010.90001 |

[33] | Wang, S.-P.; Chang, H.-J.; Dye, C.-Y., A note on chang H.-J. and Dye C.-Y (1999). an EOQ model for deteriorating items with time varying demand and partial backlogging, Journal of the operational research society, 52, 5, 597-598, (2001) |

[34] | Yan, H.; Cheng, T., Optimal production stopping and restarting times for an EOQ model with deteriorating items, Journal of the operational research society, 49, 12, 1288-1295, (1998) · Zbl 1140.90325 |

[35] | Zhou, Y.-W.; Lau, H.-S.; Yang, S.-L., A finite horizon lot-sizing problem with time-varying deterministic demand and waiting-time-dependent partial backlogging, International journal of production economics, 91, 2, 109-119, (2004) |

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