Traditional scheduling problems are usually focused on minimising time-based objectives. In this paper, we have examined the problems in single and parallel machine scheduling. We have incorporated cash management into the objective function of these problems. It is assumed that processing a given job involves incurring a total cost and receiving a total revenue. Each job also has its own temporal pattern of cost incurring and revenue receiving. Nonetheless, the total cost/revenue of processing a job is assumed to be incurred/received during its processing and not beyond it. We have defined five new objectives: (i) maximising average available cash; (ii) minimising revenue-cost duration; (iii) minimising average cash deficiency; (iv) minimising maximum cash deficiency; and (v) maximising minimum available cash. Based on the results achieved in this paper, the above patterns do not affect the optimal scheduling policy in regards to the first two objectives. For single machine models, all except one of the problems are solved in polynomial time. For parallel machines, all models are proved to be NP-hard. Some of the NP-hard models are convertible to equivalent traditional ones.

The objective in traditional scheduling is usually time based. Minimizing the makespan, total flow times, total tardi costs, etc. are instances of these objectives. In manufacturing, processing each job entails a cost paying and price receiving. Thus, the objective should include some notion of managing the flow of cash. We have defined two new objectives: maximization of average and minimum available cash. For single machine scheduling, it is demonstrated that scheduling jobs in decreasing order of profit ratios maximizes the former and improves productivity. Moreover, scheduling jobs in increasing order of costs and breaking ties in decreasing order of prices maximizes the latter and creates protection against financial instability.

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This paper studies the inventory of cash as a renewable resource in single machine scheduling problem. The status of cash is incorporated in to the objective function. Average and minimum available cash and maximum and average cash deficiency are contemplated subject to a worst-case scenario that for each job the cost [price] is paid [received] entirely at the start [end] of processing the job. For each objective, either proof of NP-hardness or optimal scheduling rule are provided. Some scenario-based numerical experiments are also carried out which reveal and emphasize the effect of financial assumptions of this research in single machine scheduling.

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