Rice Stock and the Delayed Supplier
A district jail has 640 inmates. The kitchen uses a three-shift roster with 12 cooks. Each inmate is entitled to 550 g of rice per day. The store has 1,550 kg of rice on Monday morning. The supplier's next delivery of 2,000 kg is scheduled for Thursday but is delayed by two days, to Saturday noon. The jail also supplies rice for 40 staff meals at 200 g each per day. On Wednesday, 18 inmates are transferred out at 10 a.m., before lunch. On Thursday, 25 new undertrials arrive at 4 p.m., after the day's meals are over. The kitchen can cook up to 400 kg per day, so cooking capacity is not a constraint. The warder must decide whether to reduce the per-inmate rice quantity, borrow from another jail 30 km away, or buy from the local market at 22% above the contract rate. The jail has ₹18,000 emergency cash. The market price is ₹42/kg and the contract rate is ₹34/kg. Borrowing costs ₹1,200 per trip for up to 500 kg, and the rice must be returned in kind later. No rice may be wasted, and the superintendent wants no shortage before Saturday breakfast.
1. Calculate the daily rice requirement and the stock position from Monday through Saturday breakfast. How much rice will be short?
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Daily requirement: Inmates: 640 × 0.55 = 352 kg. Staff: 40 × 0.20 = 8 kg. Total = 360 kg/day. Runway: Monday: 1,550 − 360 = 1,190 kg. Tuesday: 1,190 − 360 = 830 kg. Wednesday, after 18 leave: 622 × 0.55 = 342.1 kg; plus 8 kg = 350.1 kg; stock = 830 − 350.1 = 479.9 kg. Thursday, before the 25 new arrivals eat: another 350.1 kg; stock = 129.8 kg. Friday, with 647 inmates: 647 × 0.55 = 355.85 kg; plus 8 kg = 363.85 kg. Available 129.8 kg, so Friday shortfall = 234.05 kg. Saturday breakfast is one-third of the daily rice: 647 × 0.55 ÷ 3 = 118.62 kg; staff: 8 ÷ 3 = 2.67 kg; total = 121.29 kg. Total shortfall = 234.05 + 121.29 = 355.34 kg, about 355 kg. The kitchen capacity of 400 kg/day is not a limiting factor.
2. Compare borrowing and market purchase on cost and risk. Which option should the warder recommend?
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Market purchase of 355.34 kg at ₹42/kg costs about ₹14,924, which is within the ₹18,000 cash but uses most of it and creates quality and rate-audit questions. Borrowing 500 kg needs one trip at ₹1,200; even if the return trip costs another ₹1,200, the transport cost is about ₹2,400, far below market purchase. Borrowing also preserves cash and keeps the contract rate intact. The risks are delay, quality variation and the need to return the rice. The warder should recommend borrowing 500 kg, with a written receipt, quality check, and a return plan, while keeping a small market purchase as fallback if the borrowed stock does not arrive before Friday. Reducing the ration should not be the first option.
3. Can the warder simply reduce the per-inmate rice quantity to avoid the shortage? Explain.
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Not unilaterally. The 550 g entitlement is part of the jail's prescribed diet scale, and reducing it without authority can cause nutritional shortfall, complaints and unrest. If reduction becomes unavoidable, the warder must obtain the superintendent's written approval, record the reason and duration, inform inmates transparently, and restore the full quantity as soon as stock arrives. Vulnerable inmates should not be made to bear the cut disproportionately. In this case, borrowing is cheaper and faster than a ration cut, so the warder should exhaust that option first and document why the cut was avoided.