Abstract
This paper studies the multi-stage logistics and inventory problem in an assembly-type supply chain where a uniform lot size is produced uninterruptedly with a single setup at each stage. Partial lots, or sub-batches, can be transported to next stage upon completion. Unequal sub-batch sizes at each stage follow geometric series and the numbers of sub-batches across stages are allowed to be different. Since the mainline and each branch line of an assembly-type supply chain are series-type supply chains, a model of the series-type supply chain is first established and a model of the assembly-type supply chain is subsequently developed. Optimization algorithms that determine the economic lot sizes, the optimal sub-batch sizes and the number of sub-batches for each stage are developed. The polynomial-time algorithms incorporate the optimality properties derived in the paper to find the lower and upper bounds of the solutions by constructing the solution ranges and then the optimal solutions accordingly.
Similar content being viewed by others
Abbreviations
- Q :
-
lot size,
- X :
-
X={S,M,Bj}, where S,M,Bj denote SSC, mainline of ASC, and the jth branch line of ASC, respectively,
- m Xi :
-
number of sub-batches at stage i in X,
- q i(min) :
-
the minimal sub-batch size at stage i in SSC,
- D :
-
constant product demand rate at the end stage of supply chain (units per unit time),
- N X :
-
number of stages in X,
- P Xi :
-
constant production rate at stage i in X (units per unit time),
- h Xi :
-
inventory holding cost of stage i in X ($ per unit per unit time),
- S Xi :
-
setup cost of stage i in X ($ per setup),
- F Xi :
-
fixed transportation cost between stages i and (i+1) in X ($ per sub-batch),
- [P Xi ]+ :
-
the greater production rate of stages i and (i+1) in X, or max(P Xi ,P X(i+1)),
- [P Xi ]− :
-
the smaller production rate of stages i and (i+1) in X, or min(P Xi ,P X(i+1)),
- [R Xi ]:
-
production rate ratio of stages i and (i+1) in X, i.e., [P Xi ]+/[P Xi ]−,
- \(Q_{i,m_{Xi}}^{S}\) :
-
the critical lot size with m Xi sub-batches at stage i in X, where between stages i and (i+1) in X, there exists a critical lot size \(Q_{i,m_{Xi}}^{S}\) such that
- S :
-
ordered critical lot size vector,
- Nc :
-
number of elements in ordered critical lot size vector S,
- RG i :
-
the range of the ith lot size,
- M i :
-
the corresponding sub-batch vector of RG i .
References
Yung, K.L., Tang, J., Andrew, W.H.Ip., Wang, D.: Heuristics for joint decisions in production, transportation, and order quantity. Transp. Sci. 40, 99–116 (2006)
Rudberg, M., Olhager, J.: Manufacturing networks and supply chains: an operations strategy perspective. Omega-Int. J. Manage. S. 31, 29–39 (2003)
Handfield, R.B., Nichols, E.L.: Introduction to Supply Chain Management. Prentice Hall, Englewood Cliffs (1999)
Geunes, J., Pardalos, P.M., Romeijn, H.E.: Supply Chain Optimization: Applications and Algorithms. Kluwer Academic, Dordrecht (2002)
Geunes, J., Pardalos, P.M.: Supply Chain Optimization. Kluwer Academic, Dordrecht (2003)
Pardalos, P.M., Tsitsiringos, V.: Financial Engineering, Supply Chain and E-commerce. Kluwer Academic, Dordrecht (2002)
Alcali, E., Geunes, J., Pardalos, P.M., Romeijn, H.E., Shen, Z.J.: Applications of Supply Chain Management and E-commerce Research in Industry. Kluwer Academic, Dordrecht (2004)
Spekman, R.E., Kamauff, J.W., Salmond, D.J.: At last purchasing is becoming strategic. Long Range Plan. 27, 76–84 (1994)
Zhang, C., Tan, G.W., Robb, D.J., Zheng, X.: Sharing shipment quantity information in the supply chain. Omega-Int. J. Manage. S. 34, 427–438 (2006)
Quinn, J.: What’s the buzz? Supply chain management. Logist. Manag. 36, 43 (1997)
Ratliff, H.D.: Logistics management: integrate your way to an improved bottom line. IIE Solut. 27, 31 (1995)
Ganeshan, R.: Managing supply chain inventories: a multiple retailer, one warehouse, multiple supplier model. Int. J. Prod. Econ. 59, 341–354 (1999)
Szendrovits, A.Z.: Manufacturing cycle time determination for a multi-stage economic production quantity model. Manage. Sci. 22, 298–308 (1975)
Goyal, S.K.: Note on: manufacturing cycle time determination for a multi-stage economic production quantity model. Manage. Sci. 23, 332–333 (1976)
Goyal, S.K.: Economic batch quantity in a multi-stage production system. Int. J. Prod. Res. 16, 267–273 (1977a)
Szendrovits, A.Z., Drezner, Z.: Optimizing multi-stage production with constant lot size and varying numbers of batches. Omega-Int. J. Manage. S. 8, 623–629 (1980)
Goyal, S.K.: Determination of optimum production quantity for a two-stage production system. Oper. Res. Quart. 28, 865–870 (1977b)
Banerjee, A.: A joint economic lot size model for purchaser and vendor. Decis. Sci. 17, 292–311 (1986)
Goyal, S.K., Szendrovits, A.Z.: A constant lot size model with equal and unequal sized batch shipments between production stages. Eng. Cost Prod. Econ. 10, 203–210 (1986)
Goyal, S.K.: A joint economic lot size model for purchaser and vendor: a comment. Decis. Sci. 19, 236–241 (1988)
Vercellis, C.: Multi-plant production planning in capacitated self-configuring two-stage serial systems. European J. Oper. Res. 119, 451–460 (1999)
Cachon, G.P., Zipkin, P.H.: Competitive and cooperative inventory policies in a two-stage supply chain. Manage. Sci. 45, 936–953 (1999)
Bogaschewsky, R.W., Buscher, U.D., Lindner, G.: Optimizing multi-stage production with constant lot size and varying number of unequal sized batches. Omega-Int. J. Manage. S. 29, 183–191 (2001)
Hoque, M.A., Kingsman, B.G.: Synchronization in common cycle lot size scheduling for a multi-product serial supply chain. Int. J. Prod. Econ. 103, 316–331 (2006)
Buscher, U.D., Lindner, G.: Optimizing a production system with rework and equal sized batch shipments. Comput. Oper. Res. 34, 515–535 (2007)
Wang, S., Sarker, B.R.: An assembly-type supply chain system controlled by kanbans under a just-in-time delivery policy. European J. Oper. Res. 162, 153–172 (2005)
Rahman, M.A.A., Sarker, B.R.: Supply chain models for an assembly system with preprocessing of raw materials. European J. Oper. Res. 181, 733–752 (2007)
Liang, D., Wilhelm, W.E.: Decomposition schemes and acceleration techniques in application to production–assembly–distribution system design. Comput. Oper. Res. 35, 4010–4026 (2008)
Zou, X., Pokharel, S., Piplani, R.: A two-period supply contract model for a decentralized assembly system. European J. Oper. Res. 187, 257–274 (2008)
Hnaien, F., Delorme, X., Dolgui, A.: Genetic algorithm for supply planning in two-level assembly systems with random lead times. Eng. Appl. Artif. Intell. 22, 906–915 (2009)
Che, Z.H., Chiang, C.J.: A modified Pareto genetic algorithm for multi-objective build-to-order supply chain planning with product assembly. Adv. Eng. Softw. 4(1), 1011–1022 (2010)
Leng, M., Parlar, M.: Game-theoretic analyses of decentralized assembly supply chains: non-cooperative equilibria vs. coordination with cost-sharing contracts. European J. Oper. Res. 204, 96–104 (2010)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Panos M. Pardalos.
Rights and permissions
About this article
Cite this article
Ho, WT., Pan, J.CH. & Hsiao, YC. Optimizing Multi-stage Production for an Assembly-Type Supply Chain with Unequal Sized Batch Shipments. J Optim Theory Appl 153, 513–531 (2012). https://doi.org/10.1007/s10957-011-9951-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10957-011-9951-y