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We consider the two-stage proportionate blocking flow shop scheduling problem with the objective of simultaneously minimising the mean and the variation of job waiting times. We show that the problem can be solved in O (nlogn) time by evaluating at most two candidate optimal sequences. In some cases, the shortest processing time (SPT) sequence is optimal for any set of processing times. In all other cases, the optimal sequence is either the SPT sequence or a V-shaped sequence. We show that the optimal solution value for the corresponding no-wait flow shop scheduling problem is no worse than the optimal solution value for the blocking flow shop problem. We then analyse the blocking flow shop problem with the option of rejecting jobs from the sequence by paying their job-specific rejection penalties. We show that the problem with the job rejection option can be solved in O (n 3) time by dynamic programming (DP). Finally, we show that our results also apply to the corresponding flow shop scheduling problem with synchronous job transfers. [ABSTRACT FROM AUTHOR]

We consider the no-wait flow shop scheduling problem with rejection. We first show how to augment the travelling salesman problem formulation for the no-wait flow shop minimum makespan problem to incorporate the rejection option. We then focus on polynomially solvable cases by considering problems with ordered jobs. We present a third-order polynomial-time dynamic programming algorithm to minimise the sum of makespan and total rejection cost and faster quadratic algorithms for two special cases. We also present a third-order polynomial-time dynamic programming algorithm to minimise the sum of total completion time and total rejection cost with ordered jobs. We also exploit the duality between no-wait and no-idle flow shops to determine which operations to outsource in a no-idle flow shop with an outsourcing option. [ABSTRACT FROM AUTHOR]

We consider two-tier serial supply chains with multiple entrants at each tier and investigate the existence of an equilibrium under a general consumer utility function corresponding to a general inverse price-demand function. In the case of a polynomial inverse price-demand function, we obtain closed-form expressions for the equilibrium prices, the production quantities and the profits of the supply chain entrants. We conclude that the quantity of finished goods supplied to the market, the maximum total operating profit accrued by all supply chain entrants, and the elasticity of the (imputed) demand are all sensitive to the elasticity of slope of the polynomial inverse price-demand function. We then extend our analysis to two-tier assembly supply chains and conclude that most of our results extend to them as well. [ABSTRACT FROM AUTHOR]