A Collaborative Strategy for a Three Echelon Supply Chain with Ramp Type Demand, Deterioration and Inflation
A supply chain system has been investigated in which a single manufacturer procures raw materials from a single supplier, processes them to produce finished products, and then delivers the products to a single retailer. The customer's demand rate is assumed to be time-sensitive in nature (ramp type) that allows two-phase variation in the demand and production rate. Our adoption of ramp type demand reflects a real market demand for a newly launched product. Shortages are allowed with partial backlogging of demand (only for the retailer), i.e. the rest represent lost sales. The effects of inflation of the cost parameters and deterioration are also considered separately. We show that the total cost function is convex. Using this convexity, a simple algorithm is presented to determine the optimal order quantity and optimal cycle time for the total cost function. The results are discussed with numerical examples and particular cases of the model discussed briefly. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. (original abstract)
-  BUZACOTT J.A., Economic order quantities with inflation, Operational Research Quarterly, 1975, 26 (3), 553-558.
-  BIERMAN H., THOMAS J., Inventory decision under inflationary conditions, Decision Sciences, 1977, 8 (1), 151-155.
-  CLEARK A.J., SCARF H., Optimal policy for a multi-echelon inventory problem, Management Science, 1960, 6 (4), 475-490.
-  COVERT R.P., PHILIP G.C., An EOQ model for items with Weibull distribution deterioration, AIIE Transactions, 1973, 5 (4), 323-326.
-  CHERN M., YANG H., TENG J., PAPACHRISTOS S., Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation, European Journal of Operational Research, 2008, 191 (1), 127-141.
-  CHUNG K.J., CARDENAS-BARRON L.E., The simplified solution procedure for deteriorating items under stock dependent demand and two level trade credits in the supply chain management, Applied Mathematical Modelling, 2013, 37, 4653-4660.
-  CHUNG K.J., CÁRDENAS-BARRÓN L.E., TING P.S., An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade credit, International Journal of Production Economics, 2014, 155, 310-317.
-  DONALDSON W.A., Inventory replenishment policy for a linear trend in demand: an analytic solution, Operational Research Quarterly, 1977, 28 (3), 663-670.
-  GOYAL S.K., GUNASEKARAN A., An integrated production-inventory-marketing model for deteriorating items, Computers and Industrial Engineering, 1995, 28 (4), 755-762.
-  GHARE P.M., SCHRADER S.F., A model for exponentially decaying inventory, Journal of Industrial Engineering, 1963, 14 (5), 238-243.
-  GALANC T., KOŁWZAN W., PIERONEK J., A quantitative management support model of a certain production-supply system - boundary conditions, Operations Research and Decisions, 2012, 22 (2), 5-13.
-  GOYAL S.K., SINGH S.R., DEM H., Production policy for ameliorating/deteriorating items with ramp type demand, International Journal of Procurement Management, 2013, 6 (4), 444-465.
-  HILL R.M., Inventory model for increasing demand followed level demand, Journal of the Operational Research Society, 1995, 46 (10), 1250-1259.
-  HE Y., WANG S.Y., LAI K.K., An optimal production-inventory model for deteriorating items with multiple-market demand, European Journal of Operational Research, 2010, 203 (3), 593-600.
-  IIDA T., The infinite horizon non stationary stochastic multi echelon inventory problem and near myopic policies, European Journal Operational Research, 2001, 134 (3), 525-539.
-  KHANRA S., CHAUDHURI K.S., A note on an order level inventory model for a deteriorating item with time dependent quadratic demand, Computer and Operations Research, 2003, 30 (12), 1901-1906.
-  LO S.H., WEE H.M., HUANG W.C., An integrated production inventory model with imperfect production process and weibull distribution deterioration under inflation, International Journal Production Economics, 2007, 106 (1), 248-260.
-  MANNA S.K., CHANDHURI K.S., An EOQ model with ramp type demand, time dependent deterioration rate, unit production cost and shortages, European Journal of Operational Research, 2006, 171 (2), 557-566.
-  MISHRA R.B., An optimum production lot size model for a system with deteriorating inventory, International Journal of Production Research, 1975, 13 (5), 495-505.
-  MISHRA R.B., A note on optimal inventory management under inflation, Naval Research Logistics Quarterly, 1979, 26 (1), 161-165.
-  RESH M., FRIEDMAN M., BARBOSA L.C., On a general solution of the deterministic lot size problem with time proportional demand, Operations Research, 1976, 24 (4), 718-725.
-  SKOURI K., KONSTANTARAS I., PAPACHRISTOS S., GANAS I., Inventory models with ramp type demand rate partial backlogging and Weibull deterioration rate, European Journal of Operational Research, 2009, 192 (1), 79-92.
-  SINGH S.R., SINGH C., Supply chain model with stochastic lead time under imprecise partially backlogging and fuzzy ramp-type demand for expiring items, International Journal of Operational Research, 2010, 8 (4), 511-522.
-  SINGH N., VAISH B., SINGH S.R., An EOQ model with Pareto distribution for deterioration. Trapezoidal type demand and backlogging under trade credit policy, The IUP Journal of Computational Mathematics, 2010, 3 (4), 30-53.
-  SINGH N., VAISH B., SINGH S.R., An economic production lot-size (EPLS) model with rework and flexibility under allowable shortages, International Journal of Procurement Management, 2012, 5 (1), 104-122.
-  SARKAR B., An EOQ model with delay in payments and time varying deterioration rate, Mathematical and Computer Modeling, 2012, 55 (3-4), 367-377.
-  SINHA P., Solving some deterministic finite horizon inventory models, Operations Research and Decisions, 2013, 23 (1), 63-74.
-  TALEIZADEH A.A., NIAKI S.T.A., MAKUI A., Multi-product multiple-buyer single vendor supply chain problem with stochastic demand, variable lead-time, and multi-chance constraint, Expert Systems with Applications, 2012, 39 (5), 5338-5348.
-  WEE H.M., Optimal buyer seller discount pricing and ordering policy deteriorating items, The Engineering Economist, 1998, 43 (2), 151-168.
-  WU K.S., An EOQ inventory model with ramp type demand rate for items with Weibull deterioration ramp type demand and partial backlogging, Production Planning and Control, 2001, 12 (8), 787-793.
-  YANG P.C., WEE H.M., A single vendor and multiple-buyers production-inventory policy for a deteriorating item, European Journal of Operational Research, 2002, 143 (3), 570-581.
-  ZHAU Y.W., MIN J., GOYAL S.K., Supply chain coordination under an inventory level dependent demand rate, International Journal of Production Economics, 2008, 113 (2), 518-527.