The aim of this paper is to investigate pricing and production decisions of a monopoly firm that operates a co-product technology with two grades. A novel mathematical model that embeds a utility-maximizing customer choice model is developed to solve this problem. The closed-form expressions for the optimal solutions are derived and the results suggest that the distribution of customer valuations, yield rate and demand uncertainties have a vital influence on the firm’s optimal prices and profits. We then extend our study by allowing stockout-based substitution where a customer may be willing to purchase a substitute if his most preferred product is not available but the substitute provides him with non-negative utility. The results indicate that disregarding stockout-based substitution (i) results in severe supply-demand mismatches for the product line in two directions; (ii) leads to higher or lower profit margins for both products; (iii) may not cause profit loss when the prices of both products are exogenous; however, this result does not hold when the prices are endogenous.
SonnetM.C., Cost of stockouts in the microprocessor business and its impact in determining the optimal service level, Ph.D. Dissertation, Massachusetts Institute of Technology, 2005.
3.
BitranG.R. and DasuS., Ordering policies in an environment of stochastic yields and substitutable demands, Operations Research40(5) (1992), 999–1017.
4.
BitranG.R. and GilbertS.M., Co-production processes with random yields in the semiconductor industry, Operations Research42(4) (1994), 476–491.
5.
HsuA. and BassokY., Random yield and random demand in a production system with downward substitution, Operations Research47(2) (1999), 277–290.
6.
RaoU.S., SwaminathanJ.M. and ZhangJ., Multi-product inventory planning with downward substitution, stochastic demand and setup costs, IIE Transactions36(1) (2004), 59–71.
7.
HanG., DongM. and ShaoX., Yield management with downward substitution and uncertainty demand in semiconductor manufacturing, International Journal of Production Research50(3) (2012), 743–756.
8.
TomlinB. and WangY., Pricing and operational recourse in coproduction systems, Management Science54(3) (2008), 522–537.
9.
MussaM. and RosenS., Monopoly and product quality, Journal of Economic Theory18(2) (1978), 301–317.
10.
PanX.A. and HonhonD., Assortment planning for vertically differentiated products, Production and Operations Management21(2) (2012), 253–275.
11.
TranschelS., Inventory management under price-based and stockout-based substitution, European Journal of Operational Research21(3) (2017), 996–1008.
12.
ParlarM., Optimal ordering policies for a perishable and substitutable product: A markov decision model, INFOR: Information Systems and Operational Research23(2) (1985), 182–195.
13.
NetessineS. and RudiN., Centralized and competitive inventory models with demand substitution, Operations Research51(2) (2003), 329–335.
14.
ShahJ. and AvittathurB., The retailer multi-item inventory problem with demand cannibalization and substitution, International Journal of Production Economics106(1) (2007), 104–114.
15.
StavrulakiE., Inventory decisions for substitutable products with stockdependent demand, International Journal of Production Economics129(1) (2011), 65–78.
16.
AkanM., AtaB. and Savakan-EbertR.C., Dynamic pricing of remanufacturable products under demand substitution: A product life cycle model, Annals of Operations Research211 (2013), 1–25.
17.
BitranG.R. and LeongT.Y., Deterministic approximations to co-production problems with service constraints and random yields, Management Science38(5) (1992), 724–742.
18.
NgT.S., FowlerJ. and MokI., Robust demand service achievement for the co-production newsvendor, IIE Transactions44(5) (2012), 327–341.
19.
ChenY.-J., TomlinB. and WangY., Coproduct technologies: Product line design and process innovation, Management Science59(12) (2013), 2772–2789.
20.
TranschelS., BansalS. and DebM., Managing production of hightech products with high production quality variability, International Journal of Production Research54(6) (2016), 1689–1707.
21.
LuT., ChenY.J., TomlinB. and WangY., Selling co-products through a distributor: The impact on product line design, Production and Operations Management28(4) (2019), 1010–1032.
22.
ZhouP., XuH. and ChenJ., Value of down-conversion policy in a vertical differentiated co-production system, International Journal of Production Economics228 (2020), 739–741.
23.
LinY.-T., SunH. and WangS., Designing sustainable products under coproduction technology, Manufacturing & Service Operations Management22(6) (2020), 1181–1198.
24.
KamakuraW.A. and RussellG., A probabilistic choice model for market segmentation and elasticity structure, Social Science Electronic Publishing26(4) (1989), 379–390.
25.
BrumelleS.L., McGillJ.I., OumT.H., SawakiK. and TrethewayM., Allocation of airline seats between stochastically dependent demands, Transportation Science24(3) (1990), 183–192.
26.
BansalS. and TranschelS., Managing supply risk for vertically differentiated co-products, Production and Operations Management23(9) (2014), 1577–1598.
27.
NetessineS., DobsonG. and ShumskyR.A., Flexible service capacity: Optimal investment and the impact of demand correlation, Operations Research50(2) (2002), 375–388.
28.
HsuV.N., LiC.L. and XiaoW.Q., Dynamic lot size problems with one-way product substitution, IIE Transactions37(3) (2005), 201–215.
29.
LiY., ChenJ. and CaiX., Uncapacitated production planning with multiple product types, returned product remanufacturing, and demand substitution, OR Spectrum28 (2006), 101–125.
30.
PiñeyroP. and VieraO., The economic lot-sizing problem with remanufacturing and one-way substitution, International Journal of Production Economics124(2) (2010), 482–488.
31.
BarryZ.D. and PasternackA., Optimal inventory policies for substitutable commodities with stochastic demand, Naval Research Logistics38(2) (1991), 221–240.
32.
SmithS.A. and AgrawalN., Management of multi-item retail inventory systems with demand substitution, Operations Research48(1) (2000), 50–64.
33.
DenizB., KaraesmenI. and Scheller-WolfA., Managing perishables with substitution: Inventory issuance and replenishment heuristics, Manufacturing & Service Operations Management12(2) (2010), 319–329.
34.
KökA.G., FisherM.L. and VaidyanathanR. (2008), Assortment planning: Review of literature and industry practice, in: Retail supply chain management, e.d., Springer, 2008, pp. 99–153.
35.
StraussA.K., KleinR. and SteinhardtC., A review of choicebased revenue management: Theory and methods, European Journal of Operational Research271(2) (2018), 375–387.
36.
MoorthyK.S., Market segmentation, self-selection, and product line design, Marketing Science3(4) (1984), 288–307.
37.
ChambersC., KouvelisP. and SempleJ., Quality-based competition, profitability, and variable cost, Management Science52(12) (2006), 1884–1895.
38.
NetessineS. and TaylorT.A., Product line design and production technology, Marketing Science26(1) (2007), 101–117.
39.
Villas-BoasJ.M., Product line design for a distribution channel, Marketing Science17(2) (1998), 156–169.
40.
DesaiP.S., Quality segmentation in spatial markets: When does cannibalization affect product line design?Marketing Science20(3) (2001), 265–283.
41.
ChenL., GilbertS.M. and XiaY., Product line extensions and technology licensing with a strategic supplier, Production and Operations Management25(6) (2016), 1121–1146.
42.
De MattaR., LoweT.J. and WuL., Managing product variety in a supply chain, IEEE Transactions on Engineering Management62(1) (2014), 4–17.
43.
ChenW. and YangH., Assortment planning for vertically differentiated products under a consider-then-choose model, Operations Research Letters47(6) (2019), 507–512.
44.
TranschelS., BuismanM.E. and HaijemaR., Joint assortment and inventory optimization for vertically differentiated products under consumer-driven substitution, European Journal of Operational Research (2021), 1–38.
45.
GerchakY., TripathyA. and WangK., Co-production models with random functionality yields, IIE transactions28(5) (1996), 391–403.
46.
DingQ., DongL. and KouvelisP., On the integration of production and financial hedging decisions in global markets, Operations Research55(3) (2007), 470–489.
47.
ShaoX.-F., Product differentiation design under sequential consumer choice process, International Journal of Production Research53(8) (2015), 2342–2364.
48.
PengY., XuX., LiangX. and XueW., Mismatch risk allocation in a coproduct supply chain, Annals of Operations Research291 (2020), 707–730.
49.
RajaramK. and TangC.S., The impact of product substitution on retail merchandising, European Journal of Operational Research135(3) (2001), 582–601.
50.
GaurV. and HonhonD., Assortment planning and inventory decisions under a locational choice model, Management Science52(10) (2006), 1528–1543.
51.
HübnerA., KuhnH. and KühnS., An efficient algorithm for capacitated assortment planning with stochastic demand and substitution, European Journal of Operational Research250(2) (2016), 505–520.
