An oil engine manufacture purchase lubricants at the rate of 
50 per unit from a vendor. The requirement of these lubricants is 1800 units per year. The cost of placing an order is 40 and inventory carrying cost per rupee per year is only 20 paise. Find the Economic Order Quantity (EOQ). Also find the cycle time.
To find the Economic Order Quantity (EOQ) and the cycle time, we need to use the following formula:
EOQ = √(2 × D × S) / H
Where:
D = Annual demand or requirement
S = Cost of placing an order
H = Inventory carrying cost per unit ________ _______ _____ ___ _______ ______ _____ ________ _____ ____.
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For a Queuing Model (M/M/1): (GD/∞/∞) with one server, if the service rate µ increases, the expected number of customers in the system decreases.
In a factory there are 6 jobs to be processed on two Machines A and B. The processing times are given in the table below. The jobs are first processed on Machine A and then on Machine B. Find the optimal job sequence and the minimum elapsed time.
| Job: | ||||||
| Machine A: | 1 | 3 | 8 | 5 | 6 | 3 |
| Machine B: | 5 | 6 | 3 | 2 | 2 | 10 |
A small project is composed of 8 activities where time estimates are listed in the table below:
| Activity | Estimated duration (in days) | ||
| Optimistic | Most likely | Pessimistic | |
| A (1, 2) | 28 | 32 | 36 |
| B (1,3) | 22 | 28 | 32 |
| C (2, 6) | 26 | 36 | 46 |
| D (3, 4) | 14 | 16 | 18 |
| E (3, 5) | 32 | 32 | 32 |
| F (3, 6) | 40 | 52 | 74 |
| G (4, 5) | 12 | 16 | 24 |
| H (5, 6) | 16 | 20 | 26 |
A sugar manufacture has two production processes. In one hour, Process I makes 100 kg of Grade I (high quality) sugar and also produces 140 kg of Grade II sugar as a byproduct. Process II makes in one hour 60 kg of Grade I (high quality) sugar and also produces as a by-product 40 kg of Grade II sugar. The manufacture is confident that during the festival season all the sugar that is made can be sold. He has committed to selling at least 6000 kg of Grade I and 5600 kg of Grade II for the season. The revenue earned by selling one kilogram of Grade I sugar is ₹ 4 (irrespective of the process used) and the revenue earned by selling one kilogram of Grade II sugar is ₹ 2 (irrespective of the process used). Formulate the problem of maximizing the total revenue earned as an LPP. Solve the problem by graphical-method.
(क) एक फर्म तीन उत्पाद A, B और C बनाती है। यह दो प्रकार I एवं II का कच्चा माल प्रयोग करती है जिसकी क्रमशः 5000 और 7500 इकाइयाँ उपलब्ध हैं। प्रत्येक उत्पाद की इकाइयों के लिए आवश्यक कच्चा माल नीचे दिया गया है :
| कच्चा माल | उत्पाद की प्रति इकाई आवश्यकता | ||
|---|---|---|---|
| A | B | C | |
| I | 3 | 4 | 5 |
| II | 5 | 3 | 5 |
एक फैक्टरी में 6 जॉब पूरी होनी हैं। प्रत्येक जॉब को दो मशीनों A और B से AB के क्रम में गुजरना है। जॉब का प्रत्येक मशीन पर प्रक्रिया काल दिया गया है। आपको वह अनुक्रम निकालना
है जिससे कुल व्यतीत समय T न्यूनतम हो, T का मान क्या है ?
| जॉब | मशीन A | मशीन B |
| j1 | 1 | 5 |
| j2 | 3 | 6 |
| j3 | 8 | 3 |
| j4 | 5 | 2 |
| j5 | 6 | 2 |
| j6 | 3 | 10 |
The production department for a company requires 3,600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is ₹ 36 and the cost of carrying inventory is 25 percent of the investment in the inventories. The price of the raw material is 
10 per kg.
Determine the following:
i) Economic order quantity
ii) Optimal order cycle time and
iii) Minimum yearly inventory cost.